Performance of solar air heater ducts with different types of ribs on the absorber plate

Energy 36 (2011) 6651e6660

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Performance of solar air heater ducts with different types of ribs on the absorber plate Giovanni Tanda* DIMSET, University of Genova, via Montallegro, 1, I-16145 Genova, Italy

a r t i c l e i n f o

a b s t r a c t

Article history: Received 2 March 2011 Received in revised form 22 July 2011 Accepted 28 August 2011 Available online 14 October 2011

Repeated ribs are considered an effective technique to enhance forced convection heat transfer in channels. In order to establish the performance of rib-roughened channels, both heat transfer and friction characteristics have to be accounted for. In the present paper, heat transfer coefficients and friction factors have been experimentally investigated for a rectangular channel having one wall roughened by repeated ribs and heated at uniform flux, while the remaining three walls were smooth and insulated. Angled continuous ribs, transverse continuous and broken ribs, and discrete V-shaped ribs were considered as rib configurations. Different performance evaluation criteria, based on energy balance or entropy generation analysis, were proposed to assess the relative merit of each rib configuration. All the rib-roughened channels performed better than the reference smooth channel in the medium-low range of the investigated Reynolds number values, which is that typically encountered in solar air heater applications. Ó 2011 Elsevier Ltd. All rights reserved.

Keywords: Roughened channel Solar air heater Effective efficiency Entropy generation

1. Introduction The use of artificial roughness or turbulence promoters, such as sand grains, ribs or wires, on a heated surface, is an effective technique to increase the heat transfer rate to a convective fluid [1,2]. In particular, rib-roughened channels with repeated rib turbulators along the main direction of flow have been recommended for the heat transfer augmentation in several engineering systems: gas-cooled nuclear reactors, electronic devices, compact heat exchangers, combustor walls, solar air heater ducts and internal passages gas turbine blades. In heat exchangers and gas turbines applications, the investigated channels have typically roughness elements (transverse, inclined, V-shaped ribs) on two opposite walls of the channel with a uniform heat flux boundary condition applied to all four sides [3]. In the case of solar air heater modeling, only one side of the channel (the one receiving the solar radiation) is roughened and heated at uniform heat flux [4]; the channel aspect ratio is usually higher than that studied for gas turbine internal cooling, while the range of Reynolds number and relative roughness height (ratio between rib height and channel hydraulic diameter) are lower than those of other applications in order to allow a sufficient air temperature rise

* Tel.: þ39 10 3532557; fax: þ39 10 3532566. E-mail address: [email protected]. 0360-5442/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2011.08.043

and to avoid high frictional losses and energy expenditure to pump the air through the collector. Literature on application of artificial roughness and/or extended surfaces in a solar air heater covers a wide range of roughness and fin geometries. Protrusions, fins and other kinds of extended surface geometries mainly produce augmented heat transfer surfaces as compared to a flat surface, and thus higher heat transfer rates. Examples of solar air heater ducts filled with fins are documented in [5,6]: a considerable enhancement of the efficiency of the finned collector has been found despite the increase in the pressure losses generated by the addition of the fins. The use of dimple-shape protrusions has been experimentally studied in [7]: correlations for Nusselt number and friction factor have been developed, and the augmentation of heat transfer and frictional losses, with respect to the smooth duct under similar flow conditions, is provided. Investigations of the performance of solar air collector with obstacles and double-flow passages have been performed in [8,9], where various shapes of extended surfaces were considered: triangular and rectangular fins deployed normal to the main flow in a staggered arrangement, and rows of circular cross-section channels (made of aluminum cans opened at top and bottom) installed, staggered or in-line, on the absorber plate and oriented along the main flow. Both the double-flow passage and the presence of the fins or cans contribute to increase the performance, relative to a conventional, one-passage, flat, solar air collector.

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Nomenclature cp C d,d0 D e f F0 FR h hx he H I k L L0 m0 Ng Nu N1 N2 N3 p Pm P DP

specific heat of air [J kg1K1] energy conversion factor used in Eq. (12) geometric parameters of discrete ribs [m] channel hydraulic diameter [m] rib height [m] friction factor collector efficiency factor collector heat-removal factor convection heat transfer coefficient in the channel [Wm2K1] local convection heat transfer coefficient in the channel [Wm2K1] convection heat transfer coefficient between the top glass cover and external air [Wm2K1] channel height [m] solar irradiation [W m2] thermal conductivity of air [W m1K1] channel (collector) length [m] distance between pressure taps [m] mass flow rate [kg s1] number of glass covers Nusselt number degree of heat transfer enhancement for the same pumping power, Eq. (8) effective efficiency ratio, Eq. (19) augmentation entropy generation number, Eq. (28) rib pitch [m] mechanical power consumed to pump the fluid [W] pressure [Pa] pressure drop [Pa]

The application of artificial roughness in the form of wires or ribs fixed on the absorber plate has been widely studied and recommended by several investigators [10e22]. Numerous roughness geometries for the study of heat transfer and friction characteristics have been dealt with in the literature: although there are several parameters affecting the thermal performance of rib-roughened channels, the relative roughness height (ratio between the rib height and hydraulic channel diameter) and the rib pitch-to-height ratio emerged as the most important geometric parameters [4]. As known, the use of artificial roughness elements like ribs is useful to break the laminar sublayer and create local wall turbulence due to flow separation and reattachment between the ribs, thus greatly enhancing the cooling effect. However, this phenomenon is typically accompanied by an increase in frictional losses which leads to more power required by the fan or blower. Therefore, the design of the roughness elements should be addressed by a criterion that takes into account both the convective heat transfer enhancement and the corresponding increase in friction losses. Several criteria for the practical performance evaluation of enhanced heat transfer surfaces (artificially roughened or finned) have been developed in the past, although no generally accepted performance criteria are available. First systematic studies, based on the first law analysis, were performed by Webb and Eckert [23] and Bergles et al. [24,25] and were mainly addressed to heat exchangers with single-phase fluids. These Authors proposed performance evaluation criteria which define the performance benefits of an enhanced surface (for which Stanton number and friction factor are available) relative to a reference (e.g. smooth) surface and under specified operating conditions. An alternative approach, based on the second law analysis, to evaluate the merit of

Pr qconv Qu Re s 

S gen Tf TLC Te Ti To Tw DTwf UL Ub0 W x

Prandtl number convective heat flux [W m2] useful gain of thermal power [W] Reynolds number specific entropy [J kg1K1] entropy generation rate [W K1] bulk air temperature [K] surface temperature measured by liquid crystals [K] environmental air temperature [K] inlet air temperature [K] outlet air temperature [K] absorber plate temperature [K] wall-to-fluid temperature difference [K] collector overall energy loss coefficient [Wm2K1] bottom and edges loss coefficient [Wm2K1] channel width [m] coordinate in the axial flow direction [m]

Greek symbols rib angle of inclination [deg], solar absorptance of the absorber plate surface thermal emittance of glass εg thermal emittance of the absorber plate surface εw h effective efficiency of the collector, Eq. (12) m dynamic viscosity of air [kg m1s1] r density of air [kg m3] s solar transmittance of the glass cover

a

Subscripts s smooth surface

augmentation techniques, has been proposed by Bejan [26]. It is well established that, in a heat exchanger unit, entropy is generated by the heat transferred due to the wall-to-fluid temperature difference and by the irreversible dissipation of kinetic energy due to fluid friction. Heat transfer enhancement devices increase the heat transfer rate and thus reduce the irreversibility due to heat transfer across the wall-to-fluid temperature difference but, at the same time, the friction factor associated with the flow and the related irreversibility are increased too. The entropy generation minimization compares the rates of entropy generation for an augmented passage or surface and for a reference one, with the ultimate purpose to minimize the ratio between the irreversibilities of the device after and before the implementation of the augmentation technique. Some examples of applications of the entropy generation minimization criterion are provided in [27e29], with specific reference to heat exchanger design. As attention is focused on solar air heaters with roughness elements or fins on the absorber plates, the performance analysis must include the friction penalty along with the useful energy collection rate. Cortes and Piacentini [30] defined an effective efficiency of solar air heater on the basis of net thermal energy gain obtained by subtracting the equivalent thermal energy, required to overcome the friction power, from the collector useful gain. The performance evaluation criterion based on the effective efficiency, ruled by the first law analysis, has been adopted, for instance, by Gupta et al. [13] and Mittal et al. [19], to compare the performance of solar air heaters with different types of roughness elements on the absorber plate; the effects of roughness parameters, insolation and flow rate were typically investigated. The second law analysis of solar air heaters, rarely encountered in the literature, has recently been

G. Tanda / Energy 36 (2011) 6651e6660

tackled by Layek et al. [20] and Esen [8]. Despite the transient nature of the solar air heater performance under real working conditions, these studies were developed in the steady-state due to the complexity of the analysis and the large number of variables involved. The aim of the present investigation is to compare the performance of several types of repeated ribs in a high aspect ratio, asymmetrically heated, rectangular channel. Since only one side (the heated one) of the channel was rib-roughened, as occurs in enhanced solar air heater collectors, the results of the study are mainly addressed to the solar air heater design. This study is organized into two parts. In the first part, heat transfer and friction characteristics were experimentally investigated for the channel roughened by inclined (at 45 deg), transverse (continuous and broken) and (discrete) V-shaped ribs; experimental setup and procedure as well as data reduction are described in Sections 2 and 3. In the second part, a number of performance evaluation criteria have been developed, with the purpose of applying them to experimental data obtained for each ribbed geometry. The analysis of each criterion and the method of computation are treated in Section 4. First, the heat transfer enhancement, relative to the smooth channel at fixed pumping power, has been proposed to assess the performance of each ribbed channel (Section 4.1). Second, the ratio between computed efficiencies of a solar collector with a ribbed or with a smooth absorbing plate, under given conditions of solar radiation and outdoor air temperature, has been introduced (Section 4.2). Third, the performance comparison among the ribbed geometries was based on a thermodynamic basis, i.e. the minimization of the thermodynamic irreversibility (Section 4.3). The experimental results (Nusselt number and friction factor) and the calculated dimensionless groups, properly introduced to evaluate the relative merits of each ribbed geometry, are presented in Section 5, while main conclusions are drawn in final Section 6.

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plate on the side opposite to the heater to measure local wall temperature. The unheated walls of the test section were thermally insulated to minimize conduction heat losses to the environment. Power was supplied by an adjustable DC source and measured by a voltmeter and an amperometer. Fine-gauge thermocouples were placed inside the rectangular channel directly exposed to the airflow and in several places inside the channel wall material. These sensors were used to measure the air temperature at the test section inlet, estimate conduction heat losses to the surroundings, and control the attainment of the steady-state conditions. Pressure taps, connected to a common alcohol manometer, were located at the inlet and outlet of the test section in the streamwise direction. A Venturi flowmeter, fitted in the exit section, was used for the measurement of mass flow rate. Thermosensitive, cholesteric liquid crystals were used to measure temperature distributions on the heated surface. The prepackaged LC sheet (0.15 mm thick) consisted of a thermochromic liquid crystal layer on a black background applied onto a mylar film and backed with a pressure-sensitive adhesive. LCs here employed had a red start temperature of 30  C with a bandwidth of 4  C. The color distribution of the liquid crystals was observed by a CCD video camera, through the wall, made of Plexiglas, opposite to the heated surface, and stored in a PC. The relationship between the color (hue) and the temperature of LCs was found by a separate calibration experiment described in [31]. The ribs were installed, at periodic streamwise stations, only on the heated side of the test section. They were square in section (side e equal to 3 mm), made of low thermal conductivity material (balsa wood) and their function was to generate turbulence in the airflow in order to increase the inter-rib heat transfer. Different types of roughness elements were considered in this study: (i) 45 deg inclined, continuous ribs, (ii) transverse continuous ribs, (iii) transverse broken ribs, (iv) discrete V-shaped ribs. Details of each geometry are shown in Fig. 2. The geometric characteristics of rib configurations are reported in Table 1. For all the rib geometries, the rib height to hydraulic diameter (e/D, relative roughness height) was fixed and equal to 0.09, while the rib pitchto-height ratio (p/e) was set at 13.33, with the exception of the inclined ribs, which were explored also for p/e ¼ 6.66, 10 and 20. Moreover, the discrete V-shaped ribs presented an angle (with respect to the longitudinal direction) of 45 or 60 deg.

2. The experiments A schematic diagram of the experimental apparatus is shown in Fig. 1. The open-circuit suction-type wind tunnel consisted of a hydrodynamic development section, the test section, and the exit section. The test section was a rectangular channel, as wide and high as the development section, having one side heated and the remaining sides unheated. The dimensions of the test section were: height H ¼ 0.02 m, width W ¼ 0.1 m, length L ¼ 0.28 m, channel aspect ratio W/H ¼ 5, hydraulic diameter D ¼ 2 W H/(WþH) ¼ 0.033 m. The heated plate was made of 0.5 mm thick stainless steel to which a plane heater had been attached to provide a controllable uniform heat flux. A thin liquid crystal (LC) sheet was applied to the

3. Data reduction The local heat transfer coefficient was deduced by local wall temperature measurements as follows

4 5 3

1

p

2 6

air

t 0.28 m

3m

9

8

1m

7 10 11

W=0.1 m

L=0.28 m 12 13

H=0.02 m

air

14

1- Thermostatic room 2- Air filter 3- Lamps 4- CCD Videocamera 5- PC 6- Test section 7- Venturi flowmeter 8- Valve 9- Blower 10- Plexiglas plate 11-Ribs 12-Pre-packaged LC sheet 13-Stainless steel plate 14-Heater 15-Thermal insulation tc-Thermocouples pt -Pressure taps

15

Fig. 1. Schematic layout of experimental setup and test section.

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G. Tanda / Energy 36 (2011) 6651e6660

Fig. 2. Geometry of rib configurations studied: A1-4: angled continuous ribs, T1: transverse continuous ribs, T2: transverse broken ribs, V1-2: discrete V-shaped ribs.

qconv  hx ¼
TLC  Tf

(1)

where qconv is the convective heat flux, assumed to be uniformly distributed over the heated plate, TLC is the surface temperature detected by the LCs, and Tf is the local air bulk temperature, at the x position along the streamwise direction, calculated assuming a linear air temperature rise along the test section. The convective heat flux qconv was evaluated as the ratio between the net heat transfer rate and the area of the heated plate exposed to the airflow (excluding the area of rib sides). The neat heat transfer rate was given by the measured input power to the heater minus the calculated heat loss rates by radiation and conduction and the calculated heat transfer rate dissipated from the ribs. Further details on the test apparatus and operating procedure are provided in previous papers [31,32]. Experimental data were recast in dimensionless form, introducing the Nusselt number Nu and the Reynolds number Re as follows

Nu ¼

hD k

(2)

Re ¼

m’D WHm

(3)

where h is the heat transfer coefficient averaged over the heat transfer area, D is the channel hydraulic diameter and m0 is the air mass flow rate in the channel. Table 1 Geometric characteristics of rib configurations. Configuration

e mm a deg d mm d0 mm p/e

A1 angled continuous ribs A2 angled continuous ribs A3 angled continuous ribs A4 angled continuous ribs T1 transverse continuous ribs T2 transverse broken ribs V1 discrete V-shaped ribs V2 discrete V-shaped ribs

3 3 3 3 3 3 3 3

45 45 45 45 90 90 60 45

e e e e e 40 40 40

e e e e e 20 20 20

6.66 10 13.33 20 13.33 13.33 13.33 13.33

e/D

e/H

0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09

0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15

To obtain a dimensionless representation of the pressure drop due to the ribs, the friction factor f, based on adiabatic conditions (i.e., test without heating), was introduced according to the Fanning definition

 f ¼



DP=L0 DrðWHÞ2 2m02

(4)

where DP is the pressure drop across the axial distance L0 between the two pressure taps, approximately equal to the test section length L. Thermal conductivity k, dynamic viscosity m and density r of air were evaluated at the film temperature. The uncertainty in the results (at the 95% confidence level) was evaluated by using a rootesquare combination of the effects of each individual measurement, according to the procedure outlined by Moffat [33]. Uncertainty in h (or Nu) values turned out to be 6%. This value takes into account the effects of measuring errors in voltage, current, air (by thermocouples) and wall (by LC thermography) temperature readings and of errors in the calculated radiative and conductive heat losses. The Reynolds number had a calculated uncertainty of 4%. Finally, the uncertainty in the friction factor f was estimated to be 8% at the lowest Reynolds numbers and 4% at the highest Reynolds numbers.

4. Performance evaluation criteria The use of artificial roughness in a rectangular channel enhances the heat transfer coefficient between the wall and the convective fluid; however, this is generally accompanied by a pressure drop increase and thus a pumping power penalty. The roughness geometry has to be selected on the basis of the maximum thermal gain with minimum friction losses. In particular, since the manufacturing of a rib-roughened channel can be expensive as compared with that of a smooth channel, the criterion to evaluate the performance of the enhanced geometry (the ribbed channel) should be developed by assuming a standard reference condition (i.e. the smooth channel) against which to quantify the impact of the channel roughening.

G. Tanda / Energy 36 (2011) 6651e6660

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4.1. Heat transfer enhancement for fixed geometry and constant pumping power A common performance criterion, mainly used for heat exchangers and internal passages of gas turbine blades, consists of evaluating the heat transfer enhancement achieved by the ribbed channel, relative to the smooth channel, according to the same power required to pump the convective fluid inside the two channels. In order to comply with this constraint, the mass flow rates passing through the enhanced (ribbed) and reference (smooth) channels cannot be the same; the relationships between the two mass flow rates (i.e. between the two Reynolds numbers) can be inferred from

fs Re3s ¼ f Re3

(5)

where Res is the value of the Reynolds number for the smooth channel and fs is the corresponding friction factor, given by literature correlations. Commonly adopted correlations for fs are [34]

fs ¼ 0:079Re0:25 s fs ¼ 0:046Re0:2 s

4 2  103 < Res < 2  10 6

2  104 < Res < 10

(6) (7)

The degree of heat transfer enhancement, under the same pumping power constraint, is given by

N1 ¼ Nu=Nus

(8)

where Nus is the Nusselt number given by the Dittus and Boelter equation, as introduced by McAdams [35] for the fully developed turbulent flow in a duct 0:4 Nus ¼ 0:023Re0:8 s Pr

(9)

For instance, if correlation (6) is taken for the smooth channel friction factor, the value of Res to be used in Eq. (9) to evaluate Nus is obtained from Eq. (5) as follows

Res ¼




12:658f Re3

0:3636

indicates the mechanical power consumed to pump the fluid inside the channel, the “effective efficiency” of the collector device is expressed as follows [30]

h¼

Qu  Pm =C IðWLÞ

(10)

4.2. Enhancement of the solar air collector efficiency for fixed geometry, mass flow rate, insolation and inlet air temperature When the rectangular duct, roughened only on one side, is seen as a device useful to increase the rate of solar energy transferred to a convective fluid (air), the criterion to assess the relative merit of a given ribbed channel (relative to a reference channel, i.e. the smooth channel) can be based on the evaluation of the augmentation of the solar air heater efficiency provided by the rib installation. A sketch of a conventional solar air heater is shown in Fig. 3. The absorber plate of the solar collector (length L, width W) transfers a part of the incoming solar radiation I to the air flowing inside the channel (height H), ribbed only on the absorber plate side. From the energy balance applied to the ribbed channel, the heat transfer rate given to the fluid is

(11)

where m0 is the mass flow rate, cp is the specific heat of air and To and Ti are the outlet and inlet air temperatures, respectively. If Pm

(12)

where I is the solar irradiation, (WL) the irradiated area of the absorber plate and C is the factor (well less than unity) to account for the conversion of high grade mechanical energy to thermal energy. In particular, C can be expressed as the product among the efficiency of the fan, the efficiency of the electric motor, the efficiency of electrical transmission from the power plant and the efficiency of thermal conversion of the power plant. The mechanical power can be easily developed as a function of the mass flow rate m0 , the air density r, the Fanning friction factor f and geometric characteristics of the channel 0

Conditions for which a ribbed geometry yields values of N1 larger than unity are advantageous because they provide an increased heat transfer rate, relative to the unribbed geometry, at the same energy expenditure to pump the convective fluid.

Qu ¼ m0 cp ðTo  Ti Þ

Fig. 3. Sketch of a conventional solar air heater.

Pm ¼ m DP=r ¼

  fL m03 =r2 ðW þ HÞ ðWHÞ3

(13)

The useful gain of thermal power Qu can be also calculated by using the following equations [36]

Qu ¼ ðWLÞ½I sa  UL ðTw  Te Þ

(14)

Qu ¼ ðWLÞFR ½I sa  UL ðTi  Te Þ

(15)

where Tw and Te are the mean absorber plate and environmental air temperatures, respectively, UL is the collector overall energy loss coefficient, s is the transmittance coefficient of the glass cover and a is the absorptance coefficient of the absorber plate. The heatremoval factor FR, introduced to make the formula for Qu independent of Tw, can be obtained analytically [36]

FR ¼

   m0 cp WLUL F 0 1  exp  WLUL m0 cp

(16)

where F 0 ¼ h/(hþUL) is the collector efficiency factor. The collector overall energy loss coefficient UL takes into account top, bottom and edge heat losses

UL ¼ Ut þ Ub0

(17) top loss coefficient and Ub0 ¼ UbþUe (Ae/Ab) is a loss includes the bottom (Ub) and edge (Ue) loss coeffi-

where Ut is the coefficient that cients, Ae and Ab being the surface areas of edges and absorber plate, respectively.

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G. Tanda / Energy 36 (2011) 6651e6660

While the energy losses through the bottom and edges of the collector can be mainly ascribed to the thermal conduction through the insulation (for Ae/Ab<<1, Ub0 z kins/tins, where kins is the thermal conductivity of the bottom insulation layer of thickness tins), the estimation of top loss coefficient is a more complex task. An empirical equation for Ut has been developed by Klein [37]

31

2

6 Ng 17 7 6 Ut ¼ 6  þ 7  0:33 4 f1 he 5 Tw  Te Tw þ

Ng þ f2




sðTw þ T e Tw2 þ Te2





2Ng þ f2  1 1  Ng þ εg εw þ 0:05Ng ð1  εw Þ

 Qu Wdx WL  ¼ m0 ds 
Tf þ DTwf



ð18Þ

where Ng is the number of glass covers, he is the convection coefficient between the top glass cover and the environmental air, s is the StefaneBoltzmann constant and εw and εg are the emittance of the absorber surface and glass, respectively. The parameters f1 and f2 in Eq. (18) can be expressed as f1 ¼ 365.9 (for horizontal collector) and f2 ¼ (1e0.04heþ0.0005h2e )(1 þ 0.091Ng). The computation of the efficiency according to Eq. (12) can be performed by the following procedure. The basic assumptions are: steady-state conditions, constant thermophysical properties of air, constant mass flow rate throughout the collector, inlet air temperature Ti set equal to the environmental air temperature Te. Once collector (W, L, H, s, a, εg, εw, Ng, Ub0 ), and environmental (Te, I, he) parameters have been selected, a given value of the Reynolds number is considered. For the selected Re, the mass flow rate is calculated (from Eq. (3)), Nusselt number Nu (and the heat transfer coefficient h) and friction factor f for the ribbed channel are deduced from experiments and the mechanical power Pm is evaluated from Eq. (13). To implement the calculations, an approximate initial temperature Tw for the absorber surface is assumed and the collector overall energy loss coefficient UL is calculated from Eqs. (17) and (18). Then, Eqs. (15) and (16) are used to calculate Qu and an updated value of Tw can be deduced from Eq. (14). The value of the new surface temperature and the initial guess are compared and, if the difference is higher than 105 (as a percentage of initial Tw in K), the procedure is repeated until the convergence is reached. Applying Eq. (12) and repeating the calculation for each Re allows the distribution of the effective efficiency h versus the Reynolds number to be obtained for each ribbed channel geometry. The same procedure has been applied to calculate the effective efficiency hs of the collector with the smooth duct, by using Eq. (6) for fs and Eq. (9) for Nus; this in order to obtain the ratio of the effective efficiency of a roughened solar air heater to that of a smooth one and thus to assess the improvement in the effective efficiency due to the roughening of the absorber plate side of the channel. This ratio, defined as

N2 ¼ h=hs

law analysis applied to the roughened duct. The aim of this analysis is to evaluate the entropy generation rate in the ribbed channel related to irreversibilities due to heat transfer across the wall-tofluid temperature difference and to the fluid friction, to compare it with that for the smooth, reference channel and to identify conditions for which introducing the ribs is thermodynamically advantageous [26].  With reference to Fig. 3, the rate of entropy generation d S gen for the channel slice of length dx is given by the second law of thermodynamics

(19)

is particularly suitable to establish the degree of enhancement obtained by roughening the solar air duct under the constraint of same mass flow rate (i.e., same Re number), collector geometry and insulation, and environmental conditions (environmental temperature and solar radiation). 4.3. Reduction of entropy generation for fixed geometry, insolation and air temperature rise in the solar air collector The relative merit of the augmentation technique of solar air heater can also be assessed on a thermodynamic basis, by a second

d S gen

(20)

where s is the specific entropy of the fluid, related to its thermodynamic state (temperature Tf, pressure P) and DTwf ¼ (Tw  Tf) is the wall-to-fluid temperature difference, assumed to be constant throughout the channel (uniform heat flux condition, i.e. Qu/(WL) constant with x). The specific entropy variation ðdsÞ is given, for a pure substance, by cpdTf/Tf  dP/(rTf), while Qu can be expressed as m0 cpL(dTf/dx); thus, introducing ðdsÞ and Qu, and dividing by ðdxÞ, Eq. (20) becomes

!   1 1 m0 dP   rTf dx Tf Tf þ DTwf
   dTf =dx DTwf m0 dP ¼ m0 cp  2 rTf dx T ð1 þ qÞ



d S gen =dx ¼ m0 cp



dTf dx



(21)

f

with q ¼ DTwf/Tf. Integrating Eq. (21) between x ¼ 0 and x ¼ L, assuming q<<1 and taking into account the effect of the fluid temperature variation along x, Tf ¼ Ti þ (To  Ti) x/L, as suggested by Zimparov [29], it follows 

ZL

Sgen ¼ 0

ðQu =LÞDTwf ½Ti þðTo Ti Þx=L

ZL dx 2 0

  m0 dP dx r½Ti þðTo Ti Þx=L dx (22)

and after some mathematical manipulation 

S gen ¼

Qu DTwf m0 L dP  ln rðTo  Ti Þ dx Ti To

  To Ti

(23)

Definitions of Nu (Eq. (2)) and f (Eq. (4)) are now introduced as follows

hD Nu ¼ ¼ k

f ¼

! Qu D DTwf WL k

(24)

ðdP=dxÞDrðWHÞ2 2m02

(25)

in order to yield 

S gen ¼

Qu2 D 2m03 Lf þ ln 2 NuWLkTi To r ðTo  Ti ÞDðWHÞ2



To Ti

 (26)

The calculation of the entropy generation rate can be performed by assuming steady-state conditions, constant thermophysical properties of air, constant mass flow rate throughout the collector, and inlet air temperature Ti set equal to the environmental air temperature Te. Collector parameters (W, L, H, s, a, εg, εw, Ng, Ub0 ), environmental data (Te, I, he) and the air temperature rise (To  Ti)

G. Tanda / Energy 36 (2011) 6651e6660

are specified, as done by Layek et al. [20] in a similar study. As for the efficiency calculation, an iterative procedure is involved in the calculation of the entropy generation rate. A guess for the initial temperature Tw for the absorber surface is made in order to calculate the collector overall energy loss coefficient UL from Eqs. (17) and (18) and then the heat transfer rate Qu from Eq. (14). The mass flow rate can be recovered by Eq. (11), as Qu and (To  Ti) are known and Re is calculated from Eq. (3). The values of Nu and f are deduced by experiments, so h is obtained and a new value for Qu can be evaluated from the application of Eqs. (15) and (16). This Qu value is inserted in Eq. (14) in order to extract the updated value of Tw. The updated and the initial values of the surface temperature Tw are compared and, if the difference is higher than 105 (as a percentage of initial Tw in K), the procedure is repeated until the convergence is reached. When a smooth solar air duct is considered, Eq. (26) can be rewritten assuming, for the smooth and the roughened passages, the same inlet and outlet fluid temperatures 

S gen;s

2 D Qu;s 2m0 3s Lfs ¼ þ ln Nus WLkTi To r2 ðTo  Ti ÞDðWHÞ2

  To Ti





180 160 140

Nu

120 100 80

A1 A2 A3 A4 T1 T2 V1 V2 Eq.(9)

60 40 20

10000

20000

(27)

30000

40000

Re

Fig. 4. Nusselt number for the rib configurations and for the smooth channel (Eq. (9)).

and calculation steps are repeated as for the roughened passage, by assuming as input data the same collector and environmental parameters as well as the same air temperature rise. Since (To  Ti) is forced to be the same for the smooth and roughened channel, application of Eq. (11) implies that the ratio between the heat transfer rates for the roughened and smooth channel (Qu/Qu,s) is equal to the ratio between the respective mass flow rates ðm0 =m0s Þ, the latter being equal to the ratio between the Re values (Re/Res), as emerges from Eq. (3). Therefore, the assumed constraint of fixed air temperature rise implies that Re/Res differs from unity, unlike what occurs in the efficiency analysis described in the previous paragraph. Calculation of the rates of entropy generation, for the roughened and smooth passages, by Eqs. (26) and (27) is then repeated to cover a significant range of the air temperature rise. In order to quantify the thermodynamic impact of the augmentation technique, the augmentation entropy generation number N3 is defined as

N3 ¼ S gen =S gen;s

6657

(28)

Values of N3 less than unity are thermodynamically advantageous since they correspond to a reduction in the irreversibility of the system due to the rib insertion, under the constraint of same collector geometry and insulation, environmental conditions (environmental temperature and solar radiation) and air temperature rise. 5. Results and discussion Fig. 4 shows the distributions of the Nusselt number with Reynolds number for the 45 deg inclined ribs (A1eA4), for the transverse (continuous and broken) ribs (T1,T2), and for the discrete Vshaped ribs (V1,V2), together with the Nusselt number for the smooth channel given by Eq. (9). It is apparent that, at the same Reynolds number (i.e. same mass flow rate), heat transfer is greatly enhanced when the ribs are introduced. In particular, the transverse (broken and continuous) ribs, namely T2 and T1, provides the largest heat transfer coefficients. Unfortunately, as emerges from inspection of Fig. 5, where the friction factor of each configuration is reported, the most promising ribbed geometries from the heat transfer point of view are those featured by the highest friction; therefore the

performance comparison has to take into account both heat transfer and pressure drop penalties. Experimental heat transfer and friction data were obtained in a relatively large field of variation of Reynolds number, namely Re ¼ 9000e36,000 for Nu and Re ¼ ffi 8000e40000 for f. The pffiffiffiffiffiffiffi roughness Reynolds number (eþ ¼ f =2 Re e/D) was always well above 20, indicated by Karwa et al. [14] as the initiation value of the fully rough flow. In order to calculate the performance according to the criteria outlined in the previous section, measured Nu and f values for the rib configurations were extrapolated, in some circumstances, down to Re ¼ 4000. Even at the lowest Re(¼4000), the extrapolated eþ values always fell in the fully rough flow (eþ > 20). The value of N1 (as defined by Eq. (8)) reported in Fig. 6 (where the abscissa Res was chosen as a convenient reference for all the ribbed channels) can determine whether or not a given surface is potentially advantageous under the requirement that the pumping power must be the same. The plotted range of Res is between 5000 and 40,000, while the corresponding Re values for every roughened channel can be inferred from Eq. (10), which rules the relationship

0.04 0.03

0.02

f

A1 A2 A3 A4 T1 T2 V1 V2 Eq.(6)

0.01

0.005

10000

20000

30000

Re

40000

Fig. 5. Friction factor for the rib configuration and for the smooth channel (Eq. (6)).

6658

G. Tanda / Energy 36 (2011) 6651e6660

2.2

0.80 A1 A2 A3 A4 T1 T2 V1 V2

2.0

N1 1.8

0.75

0.70

1.6

η 0.65

1.4 A1 A2 A3 A4 T1 T2 V1 V2 smooth

0.60

1.2

10000

20000

30000

Re s

40000

Fig. 6. Ratio of Nusselt number with and without ribs (N1) versus the Reynolds number of the smooth channel (Res), under the under the same pumping power constraint.

between f, Re and Res for the constraint of the same pumping power. According to the results shown in the figure, all the ribbed configurations exhibit a value of N1 larger than one and thus a heat transfer enhancement, relative to the smooth channel for the fixed pumping power constraint, is achieved for the entire range of the Reynolds number. However, the degree of the heat transfer enhancement is generally reduced as Res is increased. The transverse broken ribs (configuration T2) have still the best relative heat transfer performance, even for the constant pumping power criterion. Conversely, the transverse continuous ribs (T1) are less efficient under the considered constraint, since V-shaped ribs (V1,V2) and the angled ribs A3 (at the highest Res) and A4 (at the lowest Res) have a similar or even better performance. The performance evaluation criterion based on the N1 ratio is worth for a wide range of applications, from compact heat exchangers to internal passages for the cooling of turbine blades. When the roughened channel is employed to improve the heat transfer capability of a solar air heater collector, performance evaluation criteria based either on the relative effective efficiency (N2) or on the reduction of exergy destruction (N3) are probably more indicated. The calculation of the effective efficiency h of the solar air heater with ribs on the absorber plate has been carried out by setting the input values summarized in Table 2; in particular, two values of the solar radiation intensity I were considered: 500 and 1000 W/m2. The effective efficiency of the solar air collector is plotted against the Reynolds number in Figs. 7 and 8: each distribution has Table 2 Collector parameters and environmental data. Parameter

Value

H L W

0.02 m 1.5 m 0.1 m 0.85 1 0.95 0.95 1 W/m2K 9.5 W/m2K (*) 0.2 (**) 300 K 300 K 500e1000 W/m2

sa Ng εg εw Ub0 he C Te Ti I

(*) Corresponding to a wind speed of 1 m/s [37]. (**) Not required for second law analysis (Section 4.3).

0.55

0.50

5000

10000

15000

Re

20000

Fig. 7. Effective efficiency h versus the Reynolds number for the rib configurations. Insolation I ¼ 1000 W/m2.

a relative maximum which corresponds to a relatively low Re value for the roughened channels and to a relatively high Re value for the smooth channel. At the highest solar radiation intensity (Fig. 7) the maximum efficiency obtained by the roughened channels is significantly higher than that of the smooth channel for Re lower than 15,000e16,000. Similar styles of the curves of the efficiency versus Re were found by Mittal et al. [19]; in their study, the solar air heater efficiency was computed for different types of geometry of roughness elements (transverse, inclined, V-shaped ribs) on the absorber plate. Despite the larger rib height to hydraulic diameter (e/D ¼ 0.09) here considered with respect to those reported in [19] (the other geometric and environmental parameters being similar), similar levels of effective efficiency are reached (h larger than 0.70 in the Re ¼ 9000e13,000 range). As I is reduced from 1000 to 500 W/m2 (Fig. 8), the maximum effective efficiency slightly decreases for every rib configuration 0.80

0.75

0.70

η 0.65

0.60

A1 A2 A3 A4 T1 T2 V1 V2 smooth

0.55

0.50

5000

10000

15000

20000

Re Fig. 8. Effective efficiency h versus the Reynolds number for the rib configurations. Insolation I ¼ 500 W/m2.

G. Tanda / Energy 36 (2011) 6651e6660

a 1.4

b 1.4 A1 A2 A3 A4 T1 T2 V1 V2

1.3

1.2

N2

1.2

N2 1.1

1.0

1.0

0.9

0.9

5000

10000

15000

Re

A1 A2 A3 A4 T1 T2 V1 V2

1.3

1.1

0.8

6659

20000

0.8

5000

10000

15000

Re

20000

Fig. 9. Ratio of effective efficiency with and without ribs (N2) versus the Reynolds number. (a) I ¼ 1000 W/m2, (b) I ¼ 500 W/m2.

and the “optimum” Re value (at which maximum h occurs) moves from 10,000e11,000 to 8000e9000. It is pointed out that, as the insolation decreases, the rate of heat transfer to the air is reduced due to the reduction in the absorber plate temperature and this reduction becomes more marked as Re increases. Conversely, the variation of the power expenditure with Re is not affected by the solar radiation intensity; as a consequence, the point of maximum effective efficiency shifts to a lower Re number for every rib configuration, as well as for the smooth channel. The analysis based on the efficiency criterion shows that, for both the values of the solar radiation intensity, the transverse broken ribs (configuration T2) still give the best performance at the lowest Re values (up to the “optimum” Re); as Re is increased, the angled ribs at the largest rib pitch-to-height ratio (A4) provide the largest effective efficiency. However, the spread of efficiency values for the roughened solar air heaters at a given Re number is small (the efficiency values for the roughened solar air heaters are very close to each other), especially in the proximity of the “optimum” Re number. The ratio of the effective efficiency of the roughened solar air heater to that of the smooth one (Fig. 9), termed N2, shows that the augmentation induced by roughening the absorber plate (when N2 > 1) is remarkable at the lowest Re value and vanishes as Re exceeds a limiting value that is sensitive to the solar radiation intensity, as found by Gupta et al. [13]. This result contrasts with that inferred from the performance analysis based on the heat transfer enhancement in the channel under the fixed pumping power constraint (N1, Fig. 6), for which the augmentation provided by the roughened channel was achieved for the entire range of the Reynolds number. Therefore, when the roughened channel is used to model a solar air heater duct, the effective efficiency of the solar collector is enhanced by the insertion of ribs on the plate absorber only within a restricted range of the Reynolds number. The performance criterion based on the second law analysis compares the entropy production rates of the roughened and smooth solar air heaters, under the constraint of fixed geometry, environmental conditions and air temperature rise in the channel. The best performance is obtained when ratio N3 between the respective entropy production rates is well below unity: this condition guarantees that roughening the absorber plate is convenient from the thermodynamic point of view. The input data

employed for the entropy production calculation are the same as for the efficiency calculation (Table 2). Again two values of the solar radiation intensity I were considered: 500 and 1000 W/m2. Figs. 10 and 11 show the augmentation entropy production number N3 as a function of the temperature rise parameter, defined as (To  Ti)/I, for I ¼ 1000 and 500 W/m2, respectively. For both the solar radiation values, N3 is lower than unity in a relatively wide range of (To  Ti)/I and each individual curve has a relative minimum corresponding to the best performance from the thermodynamic point of view. At I ¼ 1000 W/m2 (Fig. 10), the best performance, relative to the smooth channel, is achieved by the transverse broken ribs (configuration T2) for (To  Ti)/I ¼ 0.013e0.014 (i.e. 13e14 K of air temperature rise over the 1.5 m collector length); the corresponding Re number is about 7000. As the solar radiation is reduced to 500 W/m2 (Fig. 11), the best performance, relative to the smooth channel, is obtained again by the rib configuration T2, but at higher values of the temperature rise parameter (from 0.015 to 0.02), to which correspond Re values lower than 6000 and outlet to inlet air temperature differences from 7.5 to 10 K, over the 1.5 m collector length. The present results show some analogies with those obtained by Layek et al. [20] for chamfered rib-groove roughness.

1.0 A1 A2 A3 A4 T1 T2 V1 V2

0.9

N3

0.8 0.7 0.6 0.5

0.006

0.008

0.010

0.012

0.014

0.016

0.018

0.020

(To -Ti ) / I Fig. 10. Augmentation entropy production number N3 versus the temperature rise parameter (To  Ti)/I. Insolation I ¼ 1000 W/m2.

6660

G. Tanda / Energy 36 (2011) 6651e6660

1.2 1.1

N3

A1 A2 A3 A4 T1 T2 V1 V2

1.0 0.9 0.8 0.7 0.6 0.5

0.006

0.008

0.010

0.012

0.014

0.016

0.018

0.020

(To -Ti ) / I Fig. 11. Augmentation entropy production number N3 versus the temperature rise parameter (To  Ti)/I. Insolation I ¼ 500 W/m2.

Despite the different roughness geometry, the augmentation entropy generation number calculated in [20], for similar operating conditions, has a similar shape when plotted versus the temperature rise parameter. However, the relative minimum (N3 z 0.5) was achieved for (To  Ti)/I z 0.007, i.e. for a relative increase of air temperature smaller than that given, in the present study, by the transverse broken ribs (T2) under the optimal performance conditions. Moreover, among the parameters investigated in [20], the entropy generation was found to be particularly sensitive to the relative roughness height e/D, with performance improving as e/D changes from 0.022 to 0.04. This result may justify the choice, in the present investigation, of a value of e/D relatively high (0.09) even though rarely considered in artificially roughened ducts of solar air heaters [4]. 6. Conclusions In this paper heat transfer and friction characteristics for roughened channels with different rib configurations have been experimentally investigated and presented. The performance of each rib geometry was evaluated according to different criteria, based on energy balance or entropy generation analysis. These criteria, making use of heat transfer coefficients and friction factors as main input data, can be applied, in principle, to a large database covering a range of roughness geometries wider than that here considered. Emphasis was given to establish whether and in which conditions the use of repeated ribs is a good technique to improve the performance of a solar air heater. From both the analyses based on first law (relative effective efficiency) or second law (augmentation entropy generation number) of thermodynamics, it was found that all the rib configurations here considered performed better than a reference smooth channel in the medium-low range of the Reynolds number, which is that typically encountered in solar air heater applications. In particular, roughening the heat transfer surface by transverse broken ribs appeared to be the most promising enhancement technique of the investigated rib geometries. References [1] Webb RL, Eckert ERG, Goldstein RJ. Heat transfer and friction in tubes with repeated-rib roughness. Int J Heat Mass Transfer 1971;14:601e17. [2] Han JC, Glicksman LR, Rohsenow WM. An investigation of heat transfer and friction for rib-roughened surfaces. Int J Heat Mass Transfer 1978;21:1143e56. [3] Han JC, Dutta S, Ekkad SV. Gas turbine heat transfer and cooling technology. New York: Taylor & Francis; 2000.

[4] Bhushan B, Singh R. A review on methodology of artificial roughness used in duct of solar air heaters. Energy 2010;35:202e12. [5] Hachemi A. Thermal performance enhancement of solar air heaters, by a fan-blown absorber plate with rectangular fins. Int J Energy Res 1995;19: 567e77. [6] Moummi N, Ali SY, Moummi A, Desmons JY. Energy analysis of a solar air collector with rows of fins. Renewable Energy 2004;29:2053e64. [7] Saini RP, Verma J. Heat transfer and friction factor correlations for a duct having dimple-shape artificial roughness for solar air heaters. Energy 2008; 33:1277e87. [8] Esen H. Experimental energy and exergy analysis of a double-flow solar air heater having different obstacles on absorber plates. Build Environ 2008;43: 1046e54. [9] Ozgen F, Esen M, Esen H. Experimental investigation of thermal performance of a double-flow solar air heater having aluminium cans. Renewable Energy 2009;34:2391e8. [10] Prasad BN, Saini JS. 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