- Email: [email protected]
Heat transfer coefficients measurement in industrial freezing equipment by using heat flux sensors
Journal of Food Engineering 66 (2005) 377–386 www.elsevier.com/locate/jfoodeng
Heat transfer coefficients measurement in industrial freezing equipment by using heat flux sensors Alvaro Amarante *, Jean-Louis Lanoiselle Universite de Technologie de Compiegne, Laboratoire Genie de Procedes Industriels––UMR CNRS 6067, 60205 Compiegne, France Received 8 December 2003; accepted 5 April 2004
Abstract Heat transfer coefficients, either for convection or conduction mechanisms were determined by using heat flux sensors coupled to temperature measurement devices. Three distinct pieces of equipment were assessed with respect to their heat transfer capabilities. The dynamic variability of heat transfer coefficients was determined along the processing length of a conduction–convection SuperContact tunnel and a fluidized bed freezer. The main sources of heat transfer inefficiency were uneven air speed profiles for convection and high thermal contact resistance for conduction mechanisms. Fluctuation of coolant temperature was determined to be the limiting factor in a plate freezer. Simulations either with Tylose gel (SuperContact tunnel) or with mashed carrot (plate freezer) were carried out to predict improvement in heat transfer coefficients. 2004 Elsevier Ltd. All rights reserved. Keywords: Heat flux; Heat transfer coefficient; Heat flux sensor; Freezing
1. Introduction The simulation of the performance of a freezing system is required for its design, adaptation and operation. For this, the accurate knowledge of the heat transfer coefficients is essential in order to obtain a reliable prediction. Heat transfer coefficients and refrigeration loads, however, are often complex to be estimated in industrial processing conditions. Uncertainty in the order of 10–30% is commonly reported in the literature € (Becker & Fricke, 2003; Cleland & Ozilgen, 1998). It is still common practice to collect product temperature–time data and apply regression analysis using different models to derive the heat transfer coefficients. Analytical modeling is difficult due to the discontinuity inherent to phase change and to unsteady conditions (Heldman & Taylor, 1997). Numerical modeling, although accurate, is strongly dependent on the thermophysical properties of the product undergoing freezing, and results in an average value for the heat transfer coefficient during the entire processing cycle (Cleland, 1990). The dynamic variation of coefficients in function *
Corresponding author. Tel.: +33-3-44-23-44-49; fax: +33-3-44-2319-80. E-mail address: [email protected] (A. Amarante). 0260-8774/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2004.04.004
of time and in different locations in the equipment can be modeled by using CFD techniques (Verboven, Nicola€ı, Scheerlinck, & De Baerdemaeker, 1997), but again the complexity of realistic problem formulation and the intensive calculation required still keep this method of little use for practitioners. Experimentally calculated heat transfer coefficients for food products were systematically collected in the form of dimensionless correlations by different authors (Arce & Sweat, 1980; Fricke & Becker, 2002; Stewart, Becker, Greer, & Stickler, 1990), frequently in the form of Nu ¼ f ðRe; PrÞ. These correlations are useful for a first approach, but their use in real engineering problems finds limitations due to the specific configuration used in the experiments or partially available information. Moreover, information about heat transfer coefficients in industrial scale equipment is scarce in the literature. Recent research work (Harris, Lovatt, & Willix, 1999; Harris, Willix, & Lovatt, 2003) has presented a customized sensor for local heat transfer coefficient determination. A good accuracy was achieved, but the system needs further development for other applications, particularly for reduced geometries and unsteady processing conditions. The aim of this work is to present the use of heat flux sensors coupled to a plastic support in order to map heat
378
A. Amarante, J.-L. Lanoiselle / Journal of Food Engineering 66 (2005) 377–386
Nomenclature Bi e F h H m n Nu Pr q R Re S SSQ t T T U V x x
Biot Number; dimensionless thickness (m) temperature correction factor; dimensionless surface heat transfer coefficient (W m2 C1 ) volumetric enthalpy (J m3 ) number of thermocouple locations nth node in a grid Nusselt number; dimensionless Prandtl number; dimensionless heat flux (W m2 ) thermal resistance (m2 C W1 ) Reynolds number; dimensionless sensitivity (V m2 W1 ) sum of squared residuals time (s) temperature (C) dimensionless temperature global heat transfer coefficient (W m2 C1 ) electromotive force (mV) space coordinate (m) space coordinate; dimensionless (x ¼ x=e)
transfer in industrial scale freezing equipment. The simplicity of the method has a great potential to provide practitioners with a simple tool to estimate the heat transfer coefficients and rates in real processing situations, in an on-line basis, and without any knowledge of the thermophysical properties of the product or extensive calculation. The mechanisms of heat conduction and convection were analyzed in three different pieces of equipment: a fluidized bed tunnel, a contact plate freezer and a conduction–convection SuperContact tunnel. The heat flux sensor consists of a serial array of very small thermocouples embedded in a substrate material. The thin flat sensor formed has the thermocouple junctions distributed symmetrically along both plane surfaces and works as a differential thermocouple. It is designed to be attached to the surface of the material that exchanges heat with the environment. The instantaneous heat flux (W m2 ) traversing the surface of the sensor is calculated by dividing the measured electromotive force (lV) by the sensitivity (lV m2 W1 ) of the instrument. Flux sensors, although used regularly in other fields like pipe insulation testing or building thermal comfort assessment (Langley, Barnes, Matijasevic, & Gandhi, 1999), still find little use in food engineering. The main reasons are the difficulty of reliable calibration procedures, proper selection of sensor’s size and sensitivity, and of finding suitable attachment methods to the food surface. These topics were presented in a previous work (Amarante, Lanoiselle, & Ramirez, 2003a).
Greek symbols a thermal diffusivity (m2 s1 ) k thermal conductivity (W m2 C1 ) Subscripts and superscripts a ambient air air-exposed surface cool coolant hs heat sink compound i initial j jth thermal resistance k kth time interval l lth thermocouple position n node at the air-exposed surface 0 node at the isolated surface p predicted pl plastic q heat flux sole related to the sole steel related to the sole material T temperature
2. Materials and methods 2.1. Instruments and data acquisition By selecting flux sensors, a small ratio of thickness to radius of the sensor is a general guideline in order to reduce the protrusion caused by the instrument’s implantation on the surface of the substrate to be measured (Barnes, 1999). This is important to reduce the disruption of fluid flow lines on the surface of the system, which could disturb the convection mechanism. On the other hand small surface areas help in reducing the physical barrier imposed to the system by the sensor, and consequently minimizes the effects of different thermal conductivities (conduction disturbance) and emissivities (radiation disturbance) between the sensor and the substrate. Thus, heat flux sensors RdF 27036-3 (RdF Corp., USA) were chosen for their small surface area (6.0 mm width · 16.0 mm length) and thickness (0.30 mm), and high nominal sensitivity (0.36 lV m2 W1 ). The flux sensors were connected to a SRMini data acquisition System (13-bit conversion, TCSA, France), which allowed a resolution of 2 lV for the signal delivered by the instrument. Complementarity to the flux sensors, 10 wire thermocouples (T type, diameter 1.0 and 0.5 mm), two low thermal mass foil thermocouples (Ref. 20117, type T, foil thickness 5 · 103 mm, surface area 63.0 mm2 , RdF Corp., USA) and a propeller anemometer (Miniair 64, range 0.3–20.0
A. Amarante, J.-L. Lanoiselle / Journal of Food Engineering 66 (2005) 377–386
m s1 , accuracy ±0.1 m s1 , Schiltknecht, Switzerland) were connected by 20-m long cables to the same acquisition system. The resolution of the temperature measurement system was 0.1 C and the calibration in the range 100 to )35 C resulted in a mean standard error of measurement of 0.7% in the scale extreme temperatures and an accuracy of ±0.2 C at 0 C. The signal of the instruments was recorded every 5 s in a PC running the supervision software Specview (TCSA, France). 2.2. Plastic supports Two different supports machined direct from a PVC block were employed. This material was chosen because its thermophysical properties are well known, it is isotropic and of easy machinability. In experiments where the size was not a limiting factor (sensors calibration and SuperContact tunnel), a macrosupport was used. The macrosupport (Fig. 1a) consists of a cylinder of solid PVC that was machined to measure 150 mm in diameter and 30 mm in thickness. The side and bottom surfaces of the PVC support were isolated by 80 mm thick polystyrene foam. Along the axis were inserted five thermocouples (diameter 1.0 mm) spaced of 5 mm. On its air-exposed surface was installed a low thermal mass foil thermocouple. One fluxmeter was attached to each plane surface of the PVC cylinder by a double-face adhesive tape (k ¼ 0:6 W m 1 C1 , 0.1 mm thickness, Vatell Corp., USA). In the fluidized bed freezer, the geometry of the PVC support limits its application. In this case a mini support was used, which consists of a PVC disk measuring 50 mm in diameter and 3.0 mm thickness (Fig. 1b). The chosen dimensions had the objective to simulate transversally cut round zucchinis (diameter 40–50 mm, thickness 5 mm). The microsupport had approximately the same mass to surface area ratio as a regular cut zucchini in order to favor fluidization. A high diameter to thickness ratio was used to minimize lateral heat transfer. A heat flux sensor and a low
379
thermal mass foil thermocouple were installed on the surface of the PVC disk by means of the double face adhesive tape. 2.3. Heat flux sensors calibration Once the fluxmeters are used attached to different substrates, the adhesive tape introduces a thermal contact resistance between the sensor and the support material. The apparent sensitivity of the sensor is thus altered and a new calibration procedure is required. A modified method of Joannis, Banevitch, Lanoiselle, and Piar (2000) was used to calibrate the sensors directly on the PVC substrate. The macrosupport was allowed to cool from ambient temperature to )40 C in a freezing chamber (MDF-U 20863, Sanyo, Japan) with internal dimensions 370(w) · 490(d) · 1200(h) mm, equipped with an axial fan (W2E 250, Airtechnic, France) to promote air circulation in the range 0–7 m s1 . The instrumented PVC support was placed at 400 mm distance from the fan helixes and transversally to the air flow. The air speed was measured by the propeller anemometer 100 mm upstream from the surface of the PVC surface. The fluxmeter was calibrated at stabilized air speed of 0, 1, 3, 5 and 7 m s1 and each experiment was repeated three times. Heat conduction in the PVC was axial, therefore the x-direction was considered perpendicular to the plane surfaces, the nodes 0 and n corresponding respectively to the isolated and air-exposed surfaces. The temperature gradients inside and at the air-exposed surface of the cylinder, as well as the signal in lV from the calibrating fluxmeter (air-exposed surface) and from a previously calibrated fluxmeter (isolated surface) were recorded. The calibration procedure consisted in a numerical simulation of the cooling inside the PVC, followed by two sequential regression analyses. The one-dimensional simulated temperatures inside the PVC were predicted by the Fourier’s equation of heat diffusion:
Fig. 1. Instrumented macro- (a) and mini PVC support (b).
380
A. Amarante, J.-L. Lanoiselle / Journal of Food Engineering 66 (2005) 377–386
oT o oT ¼ a ot ox ot
ð1Þ
The boundary conditions used were the heat flux measured at the insulated bottom, chosen instead of the classical zero heat flux in order to improve the accuracy of the calculations. At the air-exposed surface a convective condition involving the surface heat transfer coefficient h (W m2 C1 ) was employed. Both conditions are expressed respectively by Eqs. (2) and (3): oT k ¼ q0 ð2Þ ox x¼0 oT ð3Þ k ¼ qn ¼ hðTa Tn Þ ox x¼n The measured temperature distribution at t ¼ 0 was used as the initial condition and the measured ambient temperature at every instant k was introduced in the calculations. The system was numerically solved by using a finite difference fully explicit schema implemented in Microsoft Excel 5.0. The calculation routines were developed in Visual Basic language and the time steps were chosen taking into account scheme stability criteria described by Chandra and Singh (1994). The first regression analysis was performed by using the Newton–Raphson method, where the heat transfer coefficient was set as the variable used to minimize the mean quadratic error between experimental and simulated temperatures at every thermocouple location, as expressed by Eq. (4). Once the heat transfer coefficient was obtained, the predicted temperatures and heat fluxes at every instant k were calculated automatically. The predicted air-exposed surface temperature served to calibrate/check the quality of measurement provided by the surface thermocouple. A second regression analysis was then performed using the same method as the first, in which the apparent sensitivity (S) was calculated by minimization of the mean quadratic error given by Eq. (5) for every instant k: 1 XX p 2 SSQT ¼ ðTl;k Tl;k Þ ð4Þ m all l all k 2 X p Vk F SSQq ¼ qn k ð5Þ S all k
(type E for the 27036-3) is not linear with respect to the temperature. Thus, the correction factor is straightforward calculated from the Seebeck coefficient (lV K1 ), available in standard reference tables for thermocouples. 2.4. Measurement of heat transfer coefficients in freezing equipment The calibrated heat flux sensors were employed for the on-line measurement of the heat transfer coefficients, either attached to PVC supports or in the interface product-equipment walls. The measurements conducted in air-exposed surfaces resulted in the effective surface heat transfer coefficient (h), which groups the effects of convection and radiation (Cleland, 1990). Measurements carried out in the interface product or PVC support-equipment walls furnished a global heat transfer coefficient (U ). Three distinct industrial scale freezers were chosen for assessment and the experiments were conducted during regular product processing. 2.4.1. Plate freezer The plate freezer (Samifi Babcock, Germany) consists of vertical plates measuring 500 · 500 mm and distanced 90 mm from each other. Each plate is a part of the evaporator, inside which boiling ammonia is used as the coolant. The plates are distributed in a parallel arrangement forming compartments, where liquid or paste like foods are fed by pumping. Fig. 2 shows schematically a plate configuration. The equipment works in batch cycles, the product being charged hot and discharged when the center reaches a desired temperature. Mashed carrot (89.3% moisture content wet basis) was introduced in the equipment at 77 C and allowed to freeze until )15 C in the center of the slab. Four thermocouples (diameter 1.0 mm) were inserted in the product, one in the center and the three others respectively at 10, 20 and 30 mm from the center. A fluxmeter and a surface thermocouple were adhered to the internal wall of a plate, in the interface with the
In Eq. (5) F is the correction factor for temperature obtained from the polynomial regression equation (Eq. (6)) adjusted from data available in the calibration sheet furnished by the manufacturer of the sensor (r2 ¼ 0:99). F ¼ 6E 11T 4 2E 08T 3 þ 4E 06T 2 0:0012T þ 1:0289
ð6Þ
The temperature correction is needed because the tension delivered by the fluxmeter thermocouple junctions
Fig. 2. Schematic diagram of the plate freezer.
A. Amarante, J.-L. Lanoiselle / Journal of Food Engineering 66 (2005) 377–386
product. The NH3 line temperature at the exit of the plates was recorded manually approximately every 10– 15 min with precise time identification. We adopted this procedure to overcome the limitations found to connect the automatic data acquisition system to the NH3 line in the industrial site. A numerical method based on enthalpy formulation and adapted from Mannapperuma and Singh (1988) was used in order to predict the global heat transfer coefficient (Uw ) and freezing time in the thermal center of the mashed carrot. The governing equation for a onedimensional system in rectangular coordinates is given by: oH o oT ¼ k ð7Þ ot ox ox A computer code was developed in Visual Basic with interface to Microsoft Excel to solve this equation by a finite difference numerical method using an explicit scheme. This choice was an attempt to develop a simple and robust system, accessible to practitioners and possible to be used in almost every PC. In order to avoid numerical instabilities the time steps used were at least three times smaller than the values calculated by the stability criteria equations developed by the authors of the method. For the same reason the temperature dependency of the thermal conductivity was taken in function of enthalpy. The boundary conditions used were the classical zero heat flux in the center of the product slab (x ¼ 0) and a pseudo-convective condition at the plate wall (x ¼ n), which is expressed by: oT k ¼ qw ¼ Uw ðTcool Tn Þ ð8Þ ox x¼n The enthalpy–temperature curve for mashed carrot was obtained from Toumi, Amarante, Lanoiselle, and Clausse (2004) and its thermal conductivity in function of enthalpy was determined by the conductivity of each individual constituent of the product, taking into account the ice fraction calculated for every temperature below the freezing point (ASHRAE, 2002). The regression analysis conducted to calculate Uw was similar to that used for the flux sensors calibration using Eq. (4). The global plate heat transfer coefficient was obtained alternatively for every instant t, where the NH3 line temperature was recorded, by using Eq. (8). In this procedure, qw ðtÞ is the heat flux determined by the fluxmeter, Tcool ðtÞ and Tn ðtÞ are respectively the manually recorded NH3 temperature at the exit of the plates and the interface product–wall temperature. 2.4.2. Conduction–convection SuperContact tunnel In the prototype SuperContact tunnel (CIMS, France) heat is exchanged with the product by conduction from the bottom conveying plastic belt, which slides
381
Fig. 3. Transversal section of the SuperContact tunnel showing the macro-PVC support in central width location.
on a flat heat exchanger (sole), and by convection from the air-exposed surface (fans and evaporator). The transversal section of the tunnel is presented schematically in Fig. 3. This principle of operation enables to match the quick freezing produced by contact with the simplicity and hygienic processing obtained in a conveying tunnel. The total processing length is 3.5 m by 0.75 m width. Five axial fans (2.2 m3 s1 and 0.90 kW each) installed upstream the evaporator promote air circulation. Tyfoxit cooled at )41 C in a separate system (13 kW) is pumped to the sole and to the evaporator to bring the equipment to the operation temperature of )38/)39 C. The belt speed was set up to 2.0 mm s1 in forward and 3.3 mm s1 in backward motion for all experiments. The heat transfer coefficients were measured in the tunnel by using the macrosupport described in the preceding section. The PVC support was conveyed in alternate runs through the full processing length of the tunnel in the center of the belt width. Each experiment was repeated at least three times. For the determination of the air-side heat transfer coefficient (hair ) the PVC support was conveyed in horizontal position with its exposed surface facing the evaporator. The anemometer and an extra thermocouple (diameter 1.0 mm) were installed 100 mm upstream the surface of the PVC in order to measure the air speed and the ambient temperature profiles along the tunnel. The measurement of the sole global heat transfer coefficient (Usole ) required the exposed surface of the support to be adhered to the plastic belt by means of a thin layer of heat sink compound (k ¼ 4:0 W m1 C1 , CM 6018, Jelt, France). The recorded instantaneous heat fluxes and PVC surface temperatures were used to calculate directly the instantaneous values of hair or Usole at every location inside the equipment by Newton’s law of cooling. These coefficients were also determined by numerical calculation. The procedure used for the calculation of the air heat transfer coefficient was similar as for the fluxmeters calibration, and involved the simultaneous solution of Eq. (1) through Eq. (4). The calculation of the sole heat transfer coefficient required a new boundary condition for the surface in contact with the plastic belt. Thus, Eq. (3) was replaced by:
382
q0 ¼ k
A. Amarante, J.-L. Lanoiselle / Journal of Food Engineering 66 (2005) 377–386
oT ¼ Usole ðTcool T0 Þ ox x¼0
ð9Þ
The sole heat transfer coefficient (Usole ) introduced above can be represented by (adapted from Lanoiselle, Guyomard, Piar, Lanoiselle, & Munoz, 1998): X 1 Usole ¼ Rj 1 1 esteel eair epl ehs ¼ þ þ þ ð10Þ þ hsole ksteel kair kpl khs In order to validate the heat transfer coefficients obtained by the procedures described above, Tylose gel samples (77% moisture, Ref. MH 1000 P2, Clariant, Germany) molded in the form of a shallow cylinder (diameter 150 mm, thickness 20 mm) were submitted to asymmetrical freezing in the tunnel by traversing its full processing length in a complete forward followed by a backward motion cycle. The samples were insulated laterally with 80 mm thick polystyrene foam to avoid edge heat transfer and three thermocouples were carefully placed in the interior along the axis of the gel at regular intervals of 5 mm. Simulations of the Tylose asymmetrical freezing were conducted by using the enthalpy formulation expressed in Eq. (7). The boundary conditions used to describe the air-exposed surface and the sole conditions were represented respectively by Eqs. (3) and (9). The thermal properties of the Tylose gel were obtained from (Pham, 1987) and the calculation procedure was similar to that used for the mashed carrot as described in the previous section. 2.4.3. Fluidized bed freezer An IQF fluidized bed freezer (SBL, Samifi Babcock, Germany) with approximate capacity of 10 ton h1 (cut vegetables basis) was assessed for heat transfer capabilities when processing cut zucchini. Two sequential perforated belts installed inside a common hood form the tunnel, which is displayed schematically in Fig. 4. In the first belt the product is fluidized by ascending air (10 m s1 ) to promote a quick surface freezing and avoid lumps formation. The second belt promotes the
completion of freezing at air speed of 6 m s1 . The instrumented mini support was conveyed through the tunnel in a central belt position with the sensors facing the belt side. The instantaneous heat flux and temperature on the surface of the mini support were recorded while it traveled through the entire processing length of the equipment. The ambient temperature over the two belts was recorded manually every 10–15 min and the observation times were precisely reported. Three complete runs were conducted and the air heat transfer coefficient (hair ) was determined at every instant k by the law of cooling.
3. Results and discussion 3.1. Heat flux sensors calibration The noise resulting from the heat flux measurement was evaluated. The internal electronic noise of the acquisition system and the noise when measuring heat flux under conduction heat transfer were small, respectively within 2 and 8 lV. Under convection heat transfer the noise was considerably more intense, respectively 16 and 50 lV for 0 and 7 m s1 air speed. This noise is resulting form the high frequency circular motion of the fan’s blades and has a repetitive harmonic variation pattern. In these cases the lV signal data were treated by using a centered moving average algorithm. The curve fitting by regression analysis of the experimental and predicted time–temperature profiles in the PVC support, shown in Fig. 5 for a trial at 1 m s1 , allowed the estimation of the surface heat transfer coefficient. This curve was also used to check the calibration of the thermocouple attached to the surface of the PVC. The mean surface temperature standard error of estimate for all experiments was within 4.2%, indicating that the RdF 20117 provides acceptable surface temperature measurements. The heat flux was subsequently calculated at every instant k and adjusted by a new regression using Eq. (5) to the signal delivered by the
Fig. 4. Schematic longitudinal section of the fluidized bed tunnel showing the fluidization and the finishing freezing sections.
A. Amarante, J.-L. Lanoiselle / Journal of Food Engineering 66 (2005) 377–386
Fig. 5. Temperature history during calibration of the sensor 27036-3/1 at 1 m s1 air speed.
fluxmeter, resulting in the sensitivity SPVC displayed in Fig. 6. This figure compares also the temperaturecorrected and non-corrected heat fluxes by the F factor defined in Eq. (6). The calibration temperature is the film temperature, which is the arithmetic mean between the surface and the ambient temperatures. It was observed that temperature correction is required, being the standard error of measurement higher when lower temperatures are involved. A summary of calculated sensitivities for the sensor identified by 27036/1 between 0 and 7 m s1 speed is presented in Fig. 7. In this interval of air speed the Biot number ranged between 1.44 and 9.77 for the macrosupport. Under the examined conditions no significant sensitivity changes or trend was identified. The mean standard deviation for the treatments was found to be 4.8%. The mean sensitivity calculated for all treatments was reduced by approximately 6.5% as compared with the nominal sensitivity provided by the manufacturer. This is due to the thermal resistance introduced by the adhesive tape used to attach the sensor to the PVC surface. This thermal resistance was estimated to be 2 · 103 C m2 W1 , taking into account the expected heat flux using the nominal sensitivity and the measured heat flux (Van der Graaf, 1990).
Fig. 6. Temperature correction for the heat flux at the surface of the macrosupport during calibration of the sensor 27036-3/1 at 1 m s1 air speed.
383
Fig. 7. Summary of calibration data for the flux sensor 27036-3/1 attached to the macrosupport.
3.2. Heat transfer coefficients 3.2.1. Plate freezer It was observed during the entire freezing cycle that the cooling medium temperature increased slowly from )41 to )37 C. The recorded instantaneous heat flux and interface product–wall temperature, and the manually recorded NH3 line temperature were introduced directly in Eq. (8) and resulted in a mean plate heat transfer coefficient Uw ðtÞ equal to 560.0 W m2 C1 . Uw ðtÞ showed a standard deviation within 3% along the entire processing cycle. This indicates that the wet interface product–walls and the static processing conditions resulted in a quite steady plate heat transfer coefficient. The uniformity of the Uw with time allowed the calculation of the coolant temperature for every instant k by using the same equation (8) and the continuously recorded heat flux and interface temperature. Following to this, the coolant temperature at every time step was introduced in the numerical procedure, which compared the predicted temperature history with the experimentally measured one. The Uw obtained by regression analysis was 561.0 W m2 C1 , which confirms the result obtained by the use of the heat flux sensor. Fig. 8 shows the experimental and predicted heat fluxes, surface and local coolant temperatures.
Fig. 8. Heat flux, coolant and surface temperature for mashed carrot freezing in the plate freezer (Uw ¼ 560 W m2 C1 ).
384
A. Amarante, J.-L. Lanoiselle / Journal of Food Engineering 66 (2005) 377–386
The coolant temperature and the heat transfer coefficient are the two external driving forces that affect the freezing time. This lead us to simulate separately the effects of increasing the heat transfer coefficient or keeping constant the NH3 temperature. As Uw was increased to 750, 1000 and 2000 W m2 C1 the freezing time (time to reach )15 C in the center) was respectively reduced by 3.9%, 6.5% and 10.3%. If we consider only the effort in design and the need for new materials the resulting performance seems not to be promising. Alternatively, a new simulation was conducted, where the system remained unchanged and solely the coolant temperature was kept constant at )40 C from the beginning of the process. Under these conditions the freezing time was reduced by 8.4%. The results clearly show that the weight factor of coolant temperature magnitude is greater than that of the heat transfer coefficients for the particular conditions of this experiment (elevated heat transfer coefficients). 3.2.2. SuperContact tunnel Nicola€ı and De Baerdemaeker (1996) demonstrated that for processes with a low surface heat transfer coefficient, using air at moderate speeds, small deviations in the heat transfer coefficient may result in large deviations of the center temperature of the food. For freezing processes this sensitivity is expected to be even more pronounced, as the result of the increased thermal conductivity of the food due to ice formation. An accurate knowledge of the variability of the heat transfer coefficient is then important to predict the evolution of the food temperature. The manipulation of the heat flux by the fluxmeter and the surface and medium temperatures results by application of Eqs. (3) and (9) in the direct calculation of the instantaneous hair or Usole at every location inside the tunnel. Conversely, when the heat transfer coefficients are calculated numerically by comparing predicted and experimental temperature histories, the variability of the coefficients may not be detected or may not be considered in its entire extension as the result of the thermal inertia inside the support. For this reason, this method allows only the determination of a mean value of the heat transfer coefficients for the entire processing cycle. A set of results is displayed in Fig. 9, where the instantaneous values are plotted in comparison with the mean value predicted by numerical calculation for a complete travel of the support inside the SuperContact tunnel. A quasi-harmonic variability of the measured hair is noticed, which can be explained by the characteristic curve of the fans used in the equipment. The speed profile of axial fans (three of which are located in the graph) is known by low speed in the axis and increased speed near the tip of the helices. The hair profile near the inlet of the tunnel was rather uniform. This is, however, due to test conditions, which demanded the elimination of the curtain at the entrance
Fig. 9. Heat transfer coefficients found in two distinct runs along the processing length of the SuperContact tunnel with the macrosupport facing respectively the evaporator (hair ) and the sole (Usole ). In detail, location of three axial fans allowed the identification of low efficiency heat transfer zones (adapted from Amarante, Lanoiselle, & Ramirez, 2003b).
to allow the introduction of the instrumentation in the tunnel. For this reason, a local horizontal air flow exiting the tunnel was formed, which leveled the effect of the air speed in the hair at that location. The measured Usole profile also exhibited a non-uniform pattern, this time as a consequence of adhered ice on the sole, which creates air gaps between the sole and the transporting belt. In a previous work, Lanoiselle et al. (1998) concluded that the thermal resistance imposed by the air gaps limits the heat transfer by the sole. This explains the low values for the Usole found, when compared with conventional values for conduction mechanism. The two strong depressions found respectively in the sole coefficient at 1.13 and 2.60 m correspond to locations were sole modules were welded together, causing disruption in coolant flow and also local temperature rise. For the example shown in Fig. 9 the effect of the variability in the sole coefficient is expected to be more marked in the thermal center than that of the ambient air. The fluctuations observed in the sole are more pronounced and the ice front progresses more rapidly at this side, which amplifies the sensitivity due to the thermal conductivity effect. Low efficiency heat transfer zones were thus detected and led us to carry out experimentation coupled to numerical simulation. Asymmetrical freezing experiments with Tylose slabs were then conducted in order to validate the measured coefficients and also to simulate eventual freezing time reductions by improving heat transfer. The main simulation results are summarized in Fig. 10. The plotted experimental ambient temperature curve corresponds to case (a), but it can be considered quite similar to that of case (b) and was introduced in the simulation for case (c). In case (a) the regular tunnel air and sole conditions were used to freeze the Tylose slabs. The temperature history prediction took into account the former estimated hair equal to 28.1 W m2 C1 and resulted in a Usole equal to 39.6 W m2 C1 (see
A. Amarante, J.-L. Lanoiselle / Journal of Food Engineering 66 (2005) 377–386
Fig. 10. Freezing of Tylose slabs (diameter 150 mm, thickness 20 mm, insulated laterally) in the SuperContact tunnel: (a) regular operation conditions, (b) improvement of Usole by creating a wet thermal contact and (c) expected optimized tunnel operation (adapted from Amarante et al., 2003b).
Fig. 9). A good agreement between experimental and predicted data was obtained, but a complete forward/ backward motion cycle was not enough to decrease the temperature of any location inside the Tylose slab to the desired final temperature of )20 C. In order to improve the sole heat transfer, a mixture ethylene glycol/ water (1:1) was sprayed on the sole along the two initial meters of the processing length (case b). This attempt had the objective to dissolve the ice crystals between the sole and the plastic belt and thus to create a wet thermal contact. The numerical simulation used the regular 28.1 W m2 C1 air-side coefficient and the simulation resulted in a sole coefficient of 191.3 W m2 C1 for the first 2 m and 60.0 W m2 C1 for the remaining sole length. The dragging caused by the belt motion caused the ethylene to progress further on the sole and by this to increase the Usole along the entire processing length. The time to reach )20 C at the slowest cooling node (x ¼ 0:75) was substantially reduced to 36 min and the sole coefficients found were compatible with conventional values found in conduction processes. After the 2-m transition zone a sudden temperature rise is perceptible near the sole nodes, as the result of the pronounced change in the sole coefficient. A further simulation was then conducted in case (c), where the best set of coefficients found in all experiments was fixed as constant for the entire processing cycle (hair ¼ 40.0 W m2 C1 and Usole ¼ 191:3 W m2 C1 ). The freezing time was reduced to 25.5 min at the thermal center (x ¼ 0:88), representing 29% reduction as compared with case (b), and enabling the use of one single forward motion to accomplish the freezing operation. 3.2.3. Fluidized bed freezer The mechanical conception of the fluidized bed freezer is complex and exhibit product revolving devices and superposed belts. The access to the interior of the equipment is limited to very short periods of time to inspect the instrumentation and must be avoided be-
385
Fig. 11. Heat transfer coefficient profile along the fluidization and finishing freezing sections of the fluidized bed freezer as measured with the mini PVC support.
cause this introduces false air flow conditions. Therefore, these limitations led us to monitor heat exchange only with the mini support. In all three experiments conducted in the fluidized bed freezer the heat flux followed approximately the same pattern on the surface of the PVC mini support. The heat flux variability in the fluidization section was significantly more pronounced than in the finishing section. This implies that the air speed distribution along this section is rather non-uniform, and as a consequence a high variability in hair profile inside the tunnel is also expected. As the ambient air remained fairly constant at )39 C in both sections of the tunnel, a straightforward calculation using the Newton’s law of cooling enabled the estimation of hair along the processing length of the equipment. The hair profile inside the tunnel for run Nr. 1 is shown in Fig. 11. It ranges within 36 and 92 W m2 C1 in the fluidization section and between 35 and 50 W m2 C1 in the finishing freezing section. The thermal center of the product is expected to be sensitive to this variability and hence the freezing time may be largely increased as compared with the optimal condition.
4. Conclusions Heat flux sensors were calibrated and used with satisfactory results to experimentally measure heat transfer coefficients profiles inside different industrial equipment. The coefficients obtained were validated by numerical simulation. The detected variability of the coefficients in the SuperContact and in the fluidized bed tunnels can result in increased freezing times. The assessment of heat transfer conditions in all three industrial freezers brought light to possible improvement and substantial reduction in freezing times. Heat flux sensors attached to plastic supports showed to be a simple tool that can be useful to practitioners in the assessment of the capabilities of a determined freezing system.
386
A. Amarante, J.-L. Lanoiselle / Journal of Food Engineering 66 (2005) 377–386
References Amarante, A., Lanoiselle, J.-L., & Ramirez, A. (2003a). Direct measurement of heat transfer rates and coefficients in freezing processes by the use of heat flux sensors. Chemical Engineering Research and Design, 81, 1105–1112. Amarante, A., Lanoiselle, J.-L., & Ramirez, A. (2003b). Use of fluxmeter-attached plastic supports for on-line measurement of heat transfer coefficients in freezing process. In Proceedings of the 21st international congress of refrigeration. Washington, DC: International Institute of Refrigeration. Arce, J., & Sweat, V. E. (1980). Survey of published heat transfer coefficients encountered in food refrigeration processes. ASHRAE Transactions, 86, 235–260. ASHRAE (2002). ASHRAE Refrigeration Handbook (pp. 8.1–8.30). Atlanta, GA: ASHRAE. Barnes, A. (1999). Heat flux sensors––part 1: theory. Sensors, 16, 39– 43. Becker, B. R., & Fricke, B. A. (2003). Determination of heat transfer coefficients for the freezing of foods. In Proceedings of the 21st international congress of refrigeration. Washington, DC: International Institute of Refrigeration. Chandra, P. K., & Singh, R. P. (1994). Applied numerical methods for food and agricultural engineers. Boca Raton: CRC Press, 500 p. Cleland, A. C. (1990). Food refrigeration processes: analysis design and simulation. London: Elsevier Science Publishers, 271 p. € Cleland, A. C., & Ozilgen, S. (1998). Thermal design calculations for food freezing equipment: past, present and future. International Journal of Refrigeration, 21, 359–371. Fricke, B. A., & Becker, B. R. (2002). Calculation of heat transfer coefficients for foods. International Communications in Heat and Mass Transfer, 29, 731–740. Harris, M. B., Lovatt, S. J., & Willix, J. (1999). Development of a sensor for measuring local heat transfer coefficients on carcass shaped objects. In Proceedings of the 20th international congress of refrigeration. Sydney: International Institute of Refrigeration. Harris, M. B., Willix, J., & Lovatt, S. J. (2003). Development of a method for measuring local heat transfer coefficients on carcass shaped objects. In Proceedings of the 21st international congress of
refrigeration. Washington, DC: International Institute of Refrigeration. Heldman, D. R., & Taylor, T. A. (1997). Modeling of food freezing. In M. C. Erickson & Y.-C. Hung (Eds.), Quality in frozen food (pp. 51–63). New York: Chapman and Hall. Joannis, C., Banevitch, L., Lanoiselle, J.-L., & Piar, J. (2000). Determination des coefficients d’echange thermique dans un tunnel de surgelation mixte, Actes du Congres Francois de Thermique SFT 2000, Lyon, (pp. 53–58). Langley, L. W., Barnes, A., Matijasevic, G., & Gandhi, P. (1999). High-sensitivity, surface attached heat flux sensors. Microelectronics Journal, 30, 1163–1168. Lanoiselle, J.-L., Guyomard, P., Piar, G., Lanoiselle, P., & Munoz, Y. (1998). Surgelation de produits alimentaires convoyes par film plastique mince sur sole refroidie. Revue Generale du Froid, 982, 38–45. Mannapperuma, J. D., & Singh, R. P. (1988). Prediction of freezing and thawing times of foods using a numerical method based on enthalpy formulation. Journal of Food Science, 53, 626–630. Nicola€ı, B. M., & De Baerdemaeker, J. (1996). Sensitivity analysis with respect to the surface heat transfer coefficients as applied to thermal process calculations. Journal of Food Engineering, 28, 21–33. Pham, Q. T. (1987). Calculation of bound water in frozen food. Journal of Food Science, 28, 210–212. Stewart, W. E., Becker, B. R., Greer, M. E., & Stickler, L. A. (1990). An experimental method of approximating effective heat transfer coefficients for food products. ASHRAE Transactions, 96, 142–147. Toumi, S., Amarante, A., Lanoiselle, J.-L., & Clausse, D. (2004). Freezing of foodstuffs: experimental determination of calorimetric properties and freezing simulation using an enthalpy–temperature formulation. In 9th international conference of engineering and food. Montpellier: International Association for Engineering and Food. Van der Graaf, F. (1990). Heat flux sensors. In T. Ricolfi & J. Scholz (Eds.), Thermal Sensors 4 (pp. 297–322). Germany: VCH Verlagsgesellschaft. Verboven, P., Nicola€ı, B. M., Scheerlinck, N., & De Baerdemaeker, J. (1997). The local surface heat transfer coefficient in thermal food process calculations: a CFD approach. Journal of Food Engineering, 33, 15–35.
Heat transfer coefficients measurement in industrial freezing equipment by using heat flux sensors Alvaro Amarante *, Jean-Louis Lanoiselle Universite de Technologie de Compiegne, Laboratoire Genie de Procedes Industriels––UMR CNRS 6067, 60205 Compiegne, France Received 8 December 2003; accepted 5 April 2004
Abstract Heat transfer coefficients, either for convection or conduction mechanisms were determined by using heat flux sensors coupled to temperature measurement devices. Three distinct pieces of equipment were assessed with respect to their heat transfer capabilities. The dynamic variability of heat transfer coefficients was determined along the processing length of a conduction–convection SuperContact tunnel and a fluidized bed freezer. The main sources of heat transfer inefficiency were uneven air speed profiles for convection and high thermal contact resistance for conduction mechanisms. Fluctuation of coolant temperature was determined to be the limiting factor in a plate freezer. Simulations either with Tylose gel (SuperContact tunnel) or with mashed carrot (plate freezer) were carried out to predict improvement in heat transfer coefficients. 2004 Elsevier Ltd. All rights reserved. Keywords: Heat flux; Heat transfer coefficient; Heat flux sensor; Freezing
1. Introduction The simulation of the performance of a freezing system is required for its design, adaptation and operation. For this, the accurate knowledge of the heat transfer coefficients is essential in order to obtain a reliable prediction. Heat transfer coefficients and refrigeration loads, however, are often complex to be estimated in industrial processing conditions. Uncertainty in the order of 10–30% is commonly reported in the literature € (Becker & Fricke, 2003; Cleland & Ozilgen, 1998). It is still common practice to collect product temperature–time data and apply regression analysis using different models to derive the heat transfer coefficients. Analytical modeling is difficult due to the discontinuity inherent to phase change and to unsteady conditions (Heldman & Taylor, 1997). Numerical modeling, although accurate, is strongly dependent on the thermophysical properties of the product undergoing freezing, and results in an average value for the heat transfer coefficient during the entire processing cycle (Cleland, 1990). The dynamic variation of coefficients in function *
Corresponding author. Tel.: +33-3-44-23-44-49; fax: +33-3-44-2319-80. E-mail address: [email protected] (A. Amarante). 0260-8774/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2004.04.004
of time and in different locations in the equipment can be modeled by using CFD techniques (Verboven, Nicola€ı, Scheerlinck, & De Baerdemaeker, 1997), but again the complexity of realistic problem formulation and the intensive calculation required still keep this method of little use for practitioners. Experimentally calculated heat transfer coefficients for food products were systematically collected in the form of dimensionless correlations by different authors (Arce & Sweat, 1980; Fricke & Becker, 2002; Stewart, Becker, Greer, & Stickler, 1990), frequently in the form of Nu ¼ f ðRe; PrÞ. These correlations are useful for a first approach, but their use in real engineering problems finds limitations due to the specific configuration used in the experiments or partially available information. Moreover, information about heat transfer coefficients in industrial scale equipment is scarce in the literature. Recent research work (Harris, Lovatt, & Willix, 1999; Harris, Willix, & Lovatt, 2003) has presented a customized sensor for local heat transfer coefficient determination. A good accuracy was achieved, but the system needs further development for other applications, particularly for reduced geometries and unsteady processing conditions. The aim of this work is to present the use of heat flux sensors coupled to a plastic support in order to map heat
378
A. Amarante, J.-L. Lanoiselle / Journal of Food Engineering 66 (2005) 377–386
Nomenclature Bi e F h H m n Nu Pr q R Re S SSQ t T T U V x x
Biot Number; dimensionless thickness (m) temperature correction factor; dimensionless surface heat transfer coefficient (W m2 C1 ) volumetric enthalpy (J m3 ) number of thermocouple locations nth node in a grid Nusselt number; dimensionless Prandtl number; dimensionless heat flux (W m2 ) thermal resistance (m2 C W1 ) Reynolds number; dimensionless sensitivity (V m2 W1 ) sum of squared residuals time (s) temperature (C) dimensionless temperature global heat transfer coefficient (W m2 C1 ) electromotive force (mV) space coordinate (m) space coordinate; dimensionless (x ¼ x=e)
transfer in industrial scale freezing equipment. The simplicity of the method has a great potential to provide practitioners with a simple tool to estimate the heat transfer coefficients and rates in real processing situations, in an on-line basis, and without any knowledge of the thermophysical properties of the product or extensive calculation. The mechanisms of heat conduction and convection were analyzed in three different pieces of equipment: a fluidized bed tunnel, a contact plate freezer and a conduction–convection SuperContact tunnel. The heat flux sensor consists of a serial array of very small thermocouples embedded in a substrate material. The thin flat sensor formed has the thermocouple junctions distributed symmetrically along both plane surfaces and works as a differential thermocouple. It is designed to be attached to the surface of the material that exchanges heat with the environment. The instantaneous heat flux (W m2 ) traversing the surface of the sensor is calculated by dividing the measured electromotive force (lV) by the sensitivity (lV m2 W1 ) of the instrument. Flux sensors, although used regularly in other fields like pipe insulation testing or building thermal comfort assessment (Langley, Barnes, Matijasevic, & Gandhi, 1999), still find little use in food engineering. The main reasons are the difficulty of reliable calibration procedures, proper selection of sensor’s size and sensitivity, and of finding suitable attachment methods to the food surface. These topics were presented in a previous work (Amarante, Lanoiselle, & Ramirez, 2003a).
Greek symbols a thermal diffusivity (m2 s1 ) k thermal conductivity (W m2 C1 ) Subscripts and superscripts a ambient air air-exposed surface cool coolant hs heat sink compound i initial j jth thermal resistance k kth time interval l lth thermocouple position n node at the air-exposed surface 0 node at the isolated surface p predicted pl plastic q heat flux sole related to the sole steel related to the sole material T temperature
2. Materials and methods 2.1. Instruments and data acquisition By selecting flux sensors, a small ratio of thickness to radius of the sensor is a general guideline in order to reduce the protrusion caused by the instrument’s implantation on the surface of the substrate to be measured (Barnes, 1999). This is important to reduce the disruption of fluid flow lines on the surface of the system, which could disturb the convection mechanism. On the other hand small surface areas help in reducing the physical barrier imposed to the system by the sensor, and consequently minimizes the effects of different thermal conductivities (conduction disturbance) and emissivities (radiation disturbance) between the sensor and the substrate. Thus, heat flux sensors RdF 27036-3 (RdF Corp., USA) were chosen for their small surface area (6.0 mm width · 16.0 mm length) and thickness (0.30 mm), and high nominal sensitivity (0.36 lV m2 W1 ). The flux sensors were connected to a SRMini data acquisition System (13-bit conversion, TCSA, France), which allowed a resolution of 2 lV for the signal delivered by the instrument. Complementarity to the flux sensors, 10 wire thermocouples (T type, diameter 1.0 and 0.5 mm), two low thermal mass foil thermocouples (Ref. 20117, type T, foil thickness 5 · 103 mm, surface area 63.0 mm2 , RdF Corp., USA) and a propeller anemometer (Miniair 64, range 0.3–20.0
A. Amarante, J.-L. Lanoiselle / Journal of Food Engineering 66 (2005) 377–386
m s1 , accuracy ±0.1 m s1 , Schiltknecht, Switzerland) were connected by 20-m long cables to the same acquisition system. The resolution of the temperature measurement system was 0.1 C and the calibration in the range 100 to )35 C resulted in a mean standard error of measurement of 0.7% in the scale extreme temperatures and an accuracy of ±0.2 C at 0 C. The signal of the instruments was recorded every 5 s in a PC running the supervision software Specview (TCSA, France). 2.2. Plastic supports Two different supports machined direct from a PVC block were employed. This material was chosen because its thermophysical properties are well known, it is isotropic and of easy machinability. In experiments where the size was not a limiting factor (sensors calibration and SuperContact tunnel), a macrosupport was used. The macrosupport (Fig. 1a) consists of a cylinder of solid PVC that was machined to measure 150 mm in diameter and 30 mm in thickness. The side and bottom surfaces of the PVC support were isolated by 80 mm thick polystyrene foam. Along the axis were inserted five thermocouples (diameter 1.0 mm) spaced of 5 mm. On its air-exposed surface was installed a low thermal mass foil thermocouple. One fluxmeter was attached to each plane surface of the PVC cylinder by a double-face adhesive tape (k ¼ 0:6 W m 1 C1 , 0.1 mm thickness, Vatell Corp., USA). In the fluidized bed freezer, the geometry of the PVC support limits its application. In this case a mini support was used, which consists of a PVC disk measuring 50 mm in diameter and 3.0 mm thickness (Fig. 1b). The chosen dimensions had the objective to simulate transversally cut round zucchinis (diameter 40–50 mm, thickness 5 mm). The microsupport had approximately the same mass to surface area ratio as a regular cut zucchini in order to favor fluidization. A high diameter to thickness ratio was used to minimize lateral heat transfer. A heat flux sensor and a low
379
thermal mass foil thermocouple were installed on the surface of the PVC disk by means of the double face adhesive tape. 2.3. Heat flux sensors calibration Once the fluxmeters are used attached to different substrates, the adhesive tape introduces a thermal contact resistance between the sensor and the support material. The apparent sensitivity of the sensor is thus altered and a new calibration procedure is required. A modified method of Joannis, Banevitch, Lanoiselle, and Piar (2000) was used to calibrate the sensors directly on the PVC substrate. The macrosupport was allowed to cool from ambient temperature to )40 C in a freezing chamber (MDF-U 20863, Sanyo, Japan) with internal dimensions 370(w) · 490(d) · 1200(h) mm, equipped with an axial fan (W2E 250, Airtechnic, France) to promote air circulation in the range 0–7 m s1 . The instrumented PVC support was placed at 400 mm distance from the fan helixes and transversally to the air flow. The air speed was measured by the propeller anemometer 100 mm upstream from the surface of the PVC surface. The fluxmeter was calibrated at stabilized air speed of 0, 1, 3, 5 and 7 m s1 and each experiment was repeated three times. Heat conduction in the PVC was axial, therefore the x-direction was considered perpendicular to the plane surfaces, the nodes 0 and n corresponding respectively to the isolated and air-exposed surfaces. The temperature gradients inside and at the air-exposed surface of the cylinder, as well as the signal in lV from the calibrating fluxmeter (air-exposed surface) and from a previously calibrated fluxmeter (isolated surface) were recorded. The calibration procedure consisted in a numerical simulation of the cooling inside the PVC, followed by two sequential regression analyses. The one-dimensional simulated temperatures inside the PVC were predicted by the Fourier’s equation of heat diffusion:
Fig. 1. Instrumented macro- (a) and mini PVC support (b).
380
A. Amarante, J.-L. Lanoiselle / Journal of Food Engineering 66 (2005) 377–386
oT o oT ¼ a ot ox ot
ð1Þ
The boundary conditions used were the heat flux measured at the insulated bottom, chosen instead of the classical zero heat flux in order to improve the accuracy of the calculations. At the air-exposed surface a convective condition involving the surface heat transfer coefficient h (W m2 C1 ) was employed. Both conditions are expressed respectively by Eqs. (2) and (3): oT k ¼ q0 ð2Þ ox x¼0 oT ð3Þ k ¼ qn ¼ hðTa Tn Þ ox x¼n The measured temperature distribution at t ¼ 0 was used as the initial condition and the measured ambient temperature at every instant k was introduced in the calculations. The system was numerically solved by using a finite difference fully explicit schema implemented in Microsoft Excel 5.0. The calculation routines were developed in Visual Basic language and the time steps were chosen taking into account scheme stability criteria described by Chandra and Singh (1994). The first regression analysis was performed by using the Newton–Raphson method, where the heat transfer coefficient was set as the variable used to minimize the mean quadratic error between experimental and simulated temperatures at every thermocouple location, as expressed by Eq. (4). Once the heat transfer coefficient was obtained, the predicted temperatures and heat fluxes at every instant k were calculated automatically. The predicted air-exposed surface temperature served to calibrate/check the quality of measurement provided by the surface thermocouple. A second regression analysis was then performed using the same method as the first, in which the apparent sensitivity (S) was calculated by minimization of the mean quadratic error given by Eq. (5) for every instant k: 1 XX p 2 SSQT ¼ ðTl;k Tl;k Þ ð4Þ m all l all k 2 X p Vk F SSQq ¼ qn k ð5Þ S all k
(type E for the 27036-3) is not linear with respect to the temperature. Thus, the correction factor is straightforward calculated from the Seebeck coefficient (lV K1 ), available in standard reference tables for thermocouples. 2.4. Measurement of heat transfer coefficients in freezing equipment The calibrated heat flux sensors were employed for the on-line measurement of the heat transfer coefficients, either attached to PVC supports or in the interface product-equipment walls. The measurements conducted in air-exposed surfaces resulted in the effective surface heat transfer coefficient (h), which groups the effects of convection and radiation (Cleland, 1990). Measurements carried out in the interface product or PVC support-equipment walls furnished a global heat transfer coefficient (U ). Three distinct industrial scale freezers were chosen for assessment and the experiments were conducted during regular product processing. 2.4.1. Plate freezer The plate freezer (Samifi Babcock, Germany) consists of vertical plates measuring 500 · 500 mm and distanced 90 mm from each other. Each plate is a part of the evaporator, inside which boiling ammonia is used as the coolant. The plates are distributed in a parallel arrangement forming compartments, where liquid or paste like foods are fed by pumping. Fig. 2 shows schematically a plate configuration. The equipment works in batch cycles, the product being charged hot and discharged when the center reaches a desired temperature. Mashed carrot (89.3% moisture content wet basis) was introduced in the equipment at 77 C and allowed to freeze until )15 C in the center of the slab. Four thermocouples (diameter 1.0 mm) were inserted in the product, one in the center and the three others respectively at 10, 20 and 30 mm from the center. A fluxmeter and a surface thermocouple were adhered to the internal wall of a plate, in the interface with the
In Eq. (5) F is the correction factor for temperature obtained from the polynomial regression equation (Eq. (6)) adjusted from data available in the calibration sheet furnished by the manufacturer of the sensor (r2 ¼ 0:99). F ¼ 6E 11T 4 2E 08T 3 þ 4E 06T 2 0:0012T þ 1:0289
ð6Þ
The temperature correction is needed because the tension delivered by the fluxmeter thermocouple junctions
Fig. 2. Schematic diagram of the plate freezer.
A. Amarante, J.-L. Lanoiselle / Journal of Food Engineering 66 (2005) 377–386
product. The NH3 line temperature at the exit of the plates was recorded manually approximately every 10– 15 min with precise time identification. We adopted this procedure to overcome the limitations found to connect the automatic data acquisition system to the NH3 line in the industrial site. A numerical method based on enthalpy formulation and adapted from Mannapperuma and Singh (1988) was used in order to predict the global heat transfer coefficient (Uw ) and freezing time in the thermal center of the mashed carrot. The governing equation for a onedimensional system in rectangular coordinates is given by: oH o oT ¼ k ð7Þ ot ox ox A computer code was developed in Visual Basic with interface to Microsoft Excel to solve this equation by a finite difference numerical method using an explicit scheme. This choice was an attempt to develop a simple and robust system, accessible to practitioners and possible to be used in almost every PC. In order to avoid numerical instabilities the time steps used were at least three times smaller than the values calculated by the stability criteria equations developed by the authors of the method. For the same reason the temperature dependency of the thermal conductivity was taken in function of enthalpy. The boundary conditions used were the classical zero heat flux in the center of the product slab (x ¼ 0) and a pseudo-convective condition at the plate wall (x ¼ n), which is expressed by: oT k ¼ qw ¼ Uw ðTcool Tn Þ ð8Þ ox x¼n The enthalpy–temperature curve for mashed carrot was obtained from Toumi, Amarante, Lanoiselle, and Clausse (2004) and its thermal conductivity in function of enthalpy was determined by the conductivity of each individual constituent of the product, taking into account the ice fraction calculated for every temperature below the freezing point (ASHRAE, 2002). The regression analysis conducted to calculate Uw was similar to that used for the flux sensors calibration using Eq. (4). The global plate heat transfer coefficient was obtained alternatively for every instant t, where the NH3 line temperature was recorded, by using Eq. (8). In this procedure, qw ðtÞ is the heat flux determined by the fluxmeter, Tcool ðtÞ and Tn ðtÞ are respectively the manually recorded NH3 temperature at the exit of the plates and the interface product–wall temperature. 2.4.2. Conduction–convection SuperContact tunnel In the prototype SuperContact tunnel (CIMS, France) heat is exchanged with the product by conduction from the bottom conveying plastic belt, which slides
381
Fig. 3. Transversal section of the SuperContact tunnel showing the macro-PVC support in central width location.
on a flat heat exchanger (sole), and by convection from the air-exposed surface (fans and evaporator). The transversal section of the tunnel is presented schematically in Fig. 3. This principle of operation enables to match the quick freezing produced by contact with the simplicity and hygienic processing obtained in a conveying tunnel. The total processing length is 3.5 m by 0.75 m width. Five axial fans (2.2 m3 s1 and 0.90 kW each) installed upstream the evaporator promote air circulation. Tyfoxit cooled at )41 C in a separate system (13 kW) is pumped to the sole and to the evaporator to bring the equipment to the operation temperature of )38/)39 C. The belt speed was set up to 2.0 mm s1 in forward and 3.3 mm s1 in backward motion for all experiments. The heat transfer coefficients were measured in the tunnel by using the macrosupport described in the preceding section. The PVC support was conveyed in alternate runs through the full processing length of the tunnel in the center of the belt width. Each experiment was repeated at least three times. For the determination of the air-side heat transfer coefficient (hair ) the PVC support was conveyed in horizontal position with its exposed surface facing the evaporator. The anemometer and an extra thermocouple (diameter 1.0 mm) were installed 100 mm upstream the surface of the PVC in order to measure the air speed and the ambient temperature profiles along the tunnel. The measurement of the sole global heat transfer coefficient (Usole ) required the exposed surface of the support to be adhered to the plastic belt by means of a thin layer of heat sink compound (k ¼ 4:0 W m1 C1 , CM 6018, Jelt, France). The recorded instantaneous heat fluxes and PVC surface temperatures were used to calculate directly the instantaneous values of hair or Usole at every location inside the equipment by Newton’s law of cooling. These coefficients were also determined by numerical calculation. The procedure used for the calculation of the air heat transfer coefficient was similar as for the fluxmeters calibration, and involved the simultaneous solution of Eq. (1) through Eq. (4). The calculation of the sole heat transfer coefficient required a new boundary condition for the surface in contact with the plastic belt. Thus, Eq. (3) was replaced by:
382
q0 ¼ k
A. Amarante, J.-L. Lanoiselle / Journal of Food Engineering 66 (2005) 377–386
oT ¼ Usole ðTcool T0 Þ ox x¼0
ð9Þ
The sole heat transfer coefficient (Usole ) introduced above can be represented by (adapted from Lanoiselle, Guyomard, Piar, Lanoiselle, & Munoz, 1998): X 1 Usole ¼ Rj 1 1 esteel eair epl ehs ¼ þ þ þ ð10Þ þ hsole ksteel kair kpl khs In order to validate the heat transfer coefficients obtained by the procedures described above, Tylose gel samples (77% moisture, Ref. MH 1000 P2, Clariant, Germany) molded in the form of a shallow cylinder (diameter 150 mm, thickness 20 mm) were submitted to asymmetrical freezing in the tunnel by traversing its full processing length in a complete forward followed by a backward motion cycle. The samples were insulated laterally with 80 mm thick polystyrene foam to avoid edge heat transfer and three thermocouples were carefully placed in the interior along the axis of the gel at regular intervals of 5 mm. Simulations of the Tylose asymmetrical freezing were conducted by using the enthalpy formulation expressed in Eq. (7). The boundary conditions used to describe the air-exposed surface and the sole conditions were represented respectively by Eqs. (3) and (9). The thermal properties of the Tylose gel were obtained from (Pham, 1987) and the calculation procedure was similar to that used for the mashed carrot as described in the previous section. 2.4.3. Fluidized bed freezer An IQF fluidized bed freezer (SBL, Samifi Babcock, Germany) with approximate capacity of 10 ton h1 (cut vegetables basis) was assessed for heat transfer capabilities when processing cut zucchini. Two sequential perforated belts installed inside a common hood form the tunnel, which is displayed schematically in Fig. 4. In the first belt the product is fluidized by ascending air (10 m s1 ) to promote a quick surface freezing and avoid lumps formation. The second belt promotes the
completion of freezing at air speed of 6 m s1 . The instrumented mini support was conveyed through the tunnel in a central belt position with the sensors facing the belt side. The instantaneous heat flux and temperature on the surface of the mini support were recorded while it traveled through the entire processing length of the equipment. The ambient temperature over the two belts was recorded manually every 10–15 min and the observation times were precisely reported. Three complete runs were conducted and the air heat transfer coefficient (hair ) was determined at every instant k by the law of cooling.
3. Results and discussion 3.1. Heat flux sensors calibration The noise resulting from the heat flux measurement was evaluated. The internal electronic noise of the acquisition system and the noise when measuring heat flux under conduction heat transfer were small, respectively within 2 and 8 lV. Under convection heat transfer the noise was considerably more intense, respectively 16 and 50 lV for 0 and 7 m s1 air speed. This noise is resulting form the high frequency circular motion of the fan’s blades and has a repetitive harmonic variation pattern. In these cases the lV signal data were treated by using a centered moving average algorithm. The curve fitting by regression analysis of the experimental and predicted time–temperature profiles in the PVC support, shown in Fig. 5 for a trial at 1 m s1 , allowed the estimation of the surface heat transfer coefficient. This curve was also used to check the calibration of the thermocouple attached to the surface of the PVC. The mean surface temperature standard error of estimate for all experiments was within 4.2%, indicating that the RdF 20117 provides acceptable surface temperature measurements. The heat flux was subsequently calculated at every instant k and adjusted by a new regression using Eq. (5) to the signal delivered by the
Fig. 4. Schematic longitudinal section of the fluidized bed tunnel showing the fluidization and the finishing freezing sections.
A. Amarante, J.-L. Lanoiselle / Journal of Food Engineering 66 (2005) 377–386
Fig. 5. Temperature history during calibration of the sensor 27036-3/1 at 1 m s1 air speed.
fluxmeter, resulting in the sensitivity SPVC displayed in Fig. 6. This figure compares also the temperaturecorrected and non-corrected heat fluxes by the F factor defined in Eq. (6). The calibration temperature is the film temperature, which is the arithmetic mean between the surface and the ambient temperatures. It was observed that temperature correction is required, being the standard error of measurement higher when lower temperatures are involved. A summary of calculated sensitivities for the sensor identified by 27036/1 between 0 and 7 m s1 speed is presented in Fig. 7. In this interval of air speed the Biot number ranged between 1.44 and 9.77 for the macrosupport. Under the examined conditions no significant sensitivity changes or trend was identified. The mean standard deviation for the treatments was found to be 4.8%. The mean sensitivity calculated for all treatments was reduced by approximately 6.5% as compared with the nominal sensitivity provided by the manufacturer. This is due to the thermal resistance introduced by the adhesive tape used to attach the sensor to the PVC surface. This thermal resistance was estimated to be 2 · 103 C m2 W1 , taking into account the expected heat flux using the nominal sensitivity and the measured heat flux (Van der Graaf, 1990).
Fig. 6. Temperature correction for the heat flux at the surface of the macrosupport during calibration of the sensor 27036-3/1 at 1 m s1 air speed.
383
Fig. 7. Summary of calibration data for the flux sensor 27036-3/1 attached to the macrosupport.
3.2. Heat transfer coefficients 3.2.1. Plate freezer It was observed during the entire freezing cycle that the cooling medium temperature increased slowly from )41 to )37 C. The recorded instantaneous heat flux and interface product–wall temperature, and the manually recorded NH3 line temperature were introduced directly in Eq. (8) and resulted in a mean plate heat transfer coefficient Uw ðtÞ equal to 560.0 W m2 C1 . Uw ðtÞ showed a standard deviation within 3% along the entire processing cycle. This indicates that the wet interface product–walls and the static processing conditions resulted in a quite steady plate heat transfer coefficient. The uniformity of the Uw with time allowed the calculation of the coolant temperature for every instant k by using the same equation (8) and the continuously recorded heat flux and interface temperature. Following to this, the coolant temperature at every time step was introduced in the numerical procedure, which compared the predicted temperature history with the experimentally measured one. The Uw obtained by regression analysis was 561.0 W m2 C1 , which confirms the result obtained by the use of the heat flux sensor. Fig. 8 shows the experimental and predicted heat fluxes, surface and local coolant temperatures.
Fig. 8. Heat flux, coolant and surface temperature for mashed carrot freezing in the plate freezer (Uw ¼ 560 W m2 C1 ).
384
A. Amarante, J.-L. Lanoiselle / Journal of Food Engineering 66 (2005) 377–386
The coolant temperature and the heat transfer coefficient are the two external driving forces that affect the freezing time. This lead us to simulate separately the effects of increasing the heat transfer coefficient or keeping constant the NH3 temperature. As Uw was increased to 750, 1000 and 2000 W m2 C1 the freezing time (time to reach )15 C in the center) was respectively reduced by 3.9%, 6.5% and 10.3%. If we consider only the effort in design and the need for new materials the resulting performance seems not to be promising. Alternatively, a new simulation was conducted, where the system remained unchanged and solely the coolant temperature was kept constant at )40 C from the beginning of the process. Under these conditions the freezing time was reduced by 8.4%. The results clearly show that the weight factor of coolant temperature magnitude is greater than that of the heat transfer coefficients for the particular conditions of this experiment (elevated heat transfer coefficients). 3.2.2. SuperContact tunnel Nicola€ı and De Baerdemaeker (1996) demonstrated that for processes with a low surface heat transfer coefficient, using air at moderate speeds, small deviations in the heat transfer coefficient may result in large deviations of the center temperature of the food. For freezing processes this sensitivity is expected to be even more pronounced, as the result of the increased thermal conductivity of the food due to ice formation. An accurate knowledge of the variability of the heat transfer coefficient is then important to predict the evolution of the food temperature. The manipulation of the heat flux by the fluxmeter and the surface and medium temperatures results by application of Eqs. (3) and (9) in the direct calculation of the instantaneous hair or Usole at every location inside the tunnel. Conversely, when the heat transfer coefficients are calculated numerically by comparing predicted and experimental temperature histories, the variability of the coefficients may not be detected or may not be considered in its entire extension as the result of the thermal inertia inside the support. For this reason, this method allows only the determination of a mean value of the heat transfer coefficients for the entire processing cycle. A set of results is displayed in Fig. 9, where the instantaneous values are plotted in comparison with the mean value predicted by numerical calculation for a complete travel of the support inside the SuperContact tunnel. A quasi-harmonic variability of the measured hair is noticed, which can be explained by the characteristic curve of the fans used in the equipment. The speed profile of axial fans (three of which are located in the graph) is known by low speed in the axis and increased speed near the tip of the helices. The hair profile near the inlet of the tunnel was rather uniform. This is, however, due to test conditions, which demanded the elimination of the curtain at the entrance
Fig. 9. Heat transfer coefficients found in two distinct runs along the processing length of the SuperContact tunnel with the macrosupport facing respectively the evaporator (hair ) and the sole (Usole ). In detail, location of three axial fans allowed the identification of low efficiency heat transfer zones (adapted from Amarante, Lanoiselle, & Ramirez, 2003b).
to allow the introduction of the instrumentation in the tunnel. For this reason, a local horizontal air flow exiting the tunnel was formed, which leveled the effect of the air speed in the hair at that location. The measured Usole profile also exhibited a non-uniform pattern, this time as a consequence of adhered ice on the sole, which creates air gaps between the sole and the transporting belt. In a previous work, Lanoiselle et al. (1998) concluded that the thermal resistance imposed by the air gaps limits the heat transfer by the sole. This explains the low values for the Usole found, when compared with conventional values for conduction mechanism. The two strong depressions found respectively in the sole coefficient at 1.13 and 2.60 m correspond to locations were sole modules were welded together, causing disruption in coolant flow and also local temperature rise. For the example shown in Fig. 9 the effect of the variability in the sole coefficient is expected to be more marked in the thermal center than that of the ambient air. The fluctuations observed in the sole are more pronounced and the ice front progresses more rapidly at this side, which amplifies the sensitivity due to the thermal conductivity effect. Low efficiency heat transfer zones were thus detected and led us to carry out experimentation coupled to numerical simulation. Asymmetrical freezing experiments with Tylose slabs were then conducted in order to validate the measured coefficients and also to simulate eventual freezing time reductions by improving heat transfer. The main simulation results are summarized in Fig. 10. The plotted experimental ambient temperature curve corresponds to case (a), but it can be considered quite similar to that of case (b) and was introduced in the simulation for case (c). In case (a) the regular tunnel air and sole conditions were used to freeze the Tylose slabs. The temperature history prediction took into account the former estimated hair equal to 28.1 W m2 C1 and resulted in a Usole equal to 39.6 W m2 C1 (see
A. Amarante, J.-L. Lanoiselle / Journal of Food Engineering 66 (2005) 377–386
Fig. 10. Freezing of Tylose slabs (diameter 150 mm, thickness 20 mm, insulated laterally) in the SuperContact tunnel: (a) regular operation conditions, (b) improvement of Usole by creating a wet thermal contact and (c) expected optimized tunnel operation (adapted from Amarante et al., 2003b).
Fig. 9). A good agreement between experimental and predicted data was obtained, but a complete forward/ backward motion cycle was not enough to decrease the temperature of any location inside the Tylose slab to the desired final temperature of )20 C. In order to improve the sole heat transfer, a mixture ethylene glycol/ water (1:1) was sprayed on the sole along the two initial meters of the processing length (case b). This attempt had the objective to dissolve the ice crystals between the sole and the plastic belt and thus to create a wet thermal contact. The numerical simulation used the regular 28.1 W m2 C1 air-side coefficient and the simulation resulted in a sole coefficient of 191.3 W m2 C1 for the first 2 m and 60.0 W m2 C1 for the remaining sole length. The dragging caused by the belt motion caused the ethylene to progress further on the sole and by this to increase the Usole along the entire processing length. The time to reach )20 C at the slowest cooling node (x ¼ 0:75) was substantially reduced to 36 min and the sole coefficients found were compatible with conventional values found in conduction processes. After the 2-m transition zone a sudden temperature rise is perceptible near the sole nodes, as the result of the pronounced change in the sole coefficient. A further simulation was then conducted in case (c), where the best set of coefficients found in all experiments was fixed as constant for the entire processing cycle (hair ¼ 40.0 W m2 C1 and Usole ¼ 191:3 W m2 C1 ). The freezing time was reduced to 25.5 min at the thermal center (x ¼ 0:88), representing 29% reduction as compared with case (b), and enabling the use of one single forward motion to accomplish the freezing operation. 3.2.3. Fluidized bed freezer The mechanical conception of the fluidized bed freezer is complex and exhibit product revolving devices and superposed belts. The access to the interior of the equipment is limited to very short periods of time to inspect the instrumentation and must be avoided be-
385
Fig. 11. Heat transfer coefficient profile along the fluidization and finishing freezing sections of the fluidized bed freezer as measured with the mini PVC support.
cause this introduces false air flow conditions. Therefore, these limitations led us to monitor heat exchange only with the mini support. In all three experiments conducted in the fluidized bed freezer the heat flux followed approximately the same pattern on the surface of the PVC mini support. The heat flux variability in the fluidization section was significantly more pronounced than in the finishing section. This implies that the air speed distribution along this section is rather non-uniform, and as a consequence a high variability in hair profile inside the tunnel is also expected. As the ambient air remained fairly constant at )39 C in both sections of the tunnel, a straightforward calculation using the Newton’s law of cooling enabled the estimation of hair along the processing length of the equipment. The hair profile inside the tunnel for run Nr. 1 is shown in Fig. 11. It ranges within 36 and 92 W m2 C1 in the fluidization section and between 35 and 50 W m2 C1 in the finishing freezing section. The thermal center of the product is expected to be sensitive to this variability and hence the freezing time may be largely increased as compared with the optimal condition.
4. Conclusions Heat flux sensors were calibrated and used with satisfactory results to experimentally measure heat transfer coefficients profiles inside different industrial equipment. The coefficients obtained were validated by numerical simulation. The detected variability of the coefficients in the SuperContact and in the fluidized bed tunnels can result in increased freezing times. The assessment of heat transfer conditions in all three industrial freezers brought light to possible improvement and substantial reduction in freezing times. Heat flux sensors attached to plastic supports showed to be a simple tool that can be useful to practitioners in the assessment of the capabilities of a determined freezing system.
386
A. Amarante, J.-L. Lanoiselle / Journal of Food Engineering 66 (2005) 377–386
References Amarante, A., Lanoiselle, J.-L., & Ramirez, A. (2003a). Direct measurement of heat transfer rates and coefficients in freezing processes by the use of heat flux sensors. Chemical Engineering Research and Design, 81, 1105–1112. Amarante, A., Lanoiselle, J.-L., & Ramirez, A. (2003b). Use of fluxmeter-attached plastic supports for on-line measurement of heat transfer coefficients in freezing process. In Proceedings of the 21st international congress of refrigeration. Washington, DC: International Institute of Refrigeration. Arce, J., & Sweat, V. E. (1980). Survey of published heat transfer coefficients encountered in food refrigeration processes. ASHRAE Transactions, 86, 235–260. ASHRAE (2002). ASHRAE Refrigeration Handbook (pp. 8.1–8.30). Atlanta, GA: ASHRAE. Barnes, A. (1999). Heat flux sensors––part 1: theory. Sensors, 16, 39– 43. Becker, B. R., & Fricke, B. A. (2003). Determination of heat transfer coefficients for the freezing of foods. In Proceedings of the 21st international congress of refrigeration. Washington, DC: International Institute of Refrigeration. Chandra, P. K., & Singh, R. P. (1994). Applied numerical methods for food and agricultural engineers. Boca Raton: CRC Press, 500 p. Cleland, A. C. (1990). Food refrigeration processes: analysis design and simulation. London: Elsevier Science Publishers, 271 p. € Cleland, A. C., & Ozilgen, S. (1998). Thermal design calculations for food freezing equipment: past, present and future. International Journal of Refrigeration, 21, 359–371. Fricke, B. A., & Becker, B. R. (2002). Calculation of heat transfer coefficients for foods. International Communications in Heat and Mass Transfer, 29, 731–740. Harris, M. B., Lovatt, S. J., & Willix, J. (1999). Development of a sensor for measuring local heat transfer coefficients on carcass shaped objects. In Proceedings of the 20th international congress of refrigeration. Sydney: International Institute of Refrigeration. Harris, M. B., Willix, J., & Lovatt, S. J. (2003). Development of a method for measuring local heat transfer coefficients on carcass shaped objects. In Proceedings of the 21st international congress of
refrigeration. Washington, DC: International Institute of Refrigeration. Heldman, D. R., & Taylor, T. A. (1997). Modeling of food freezing. In M. C. Erickson & Y.-C. Hung (Eds.), Quality in frozen food (pp. 51–63). New York: Chapman and Hall. Joannis, C., Banevitch, L., Lanoiselle, J.-L., & Piar, J. (2000). Determination des coefficients d’echange thermique dans un tunnel de surgelation mixte, Actes du Congres Francois de Thermique SFT 2000, Lyon, (pp. 53–58). Langley, L. W., Barnes, A., Matijasevic, G., & Gandhi, P. (1999). High-sensitivity, surface attached heat flux sensors. Microelectronics Journal, 30, 1163–1168. Lanoiselle, J.-L., Guyomard, P., Piar, G., Lanoiselle, P., & Munoz, Y. (1998). Surgelation de produits alimentaires convoyes par film plastique mince sur sole refroidie. Revue Generale du Froid, 982, 38–45. Mannapperuma, J. D., & Singh, R. P. (1988). Prediction of freezing and thawing times of foods using a numerical method based on enthalpy formulation. Journal of Food Science, 53, 626–630. Nicola€ı, B. M., & De Baerdemaeker, J. (1996). Sensitivity analysis with respect to the surface heat transfer coefficients as applied to thermal process calculations. Journal of Food Engineering, 28, 21–33. Pham, Q. T. (1987). Calculation of bound water in frozen food. Journal of Food Science, 28, 210–212. Stewart, W. E., Becker, B. R., Greer, M. E., & Stickler, L. A. (1990). An experimental method of approximating effective heat transfer coefficients for food products. ASHRAE Transactions, 96, 142–147. Toumi, S., Amarante, A., Lanoiselle, J.-L., & Clausse, D. (2004). Freezing of foodstuffs: experimental determination of calorimetric properties and freezing simulation using an enthalpy–temperature formulation. In 9th international conference of engineering and food. Montpellier: International Association for Engineering and Food. Van der Graaf, F. (1990). Heat flux sensors. In T. Ricolfi & J. Scholz (Eds.), Thermal Sensors 4 (pp. 297–322). Germany: VCH Verlagsgesellschaft. Verboven, P., Nicola€ı, B. M., Scheerlinck, N., & De Baerdemaeker, J. (1997). The local surface heat transfer coefficient in thermal food process calculations: a CFD approach. Journal of Food Engineering, 33, 15–35.