Heat transfer characteristics on lignite thin-layer during hot air forced convective drying

Fuel 154 (2015) 132–139

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Heat transfer characteristics on lignite thin-layer during hot air forced convective drying B.A. Fu, M.Q. Chen ⇑, Y.W. Huang Institute of Thermal Engineering, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China Beijing Key Laboratory of Flow and Heat Transfer of Phase Changing in Micro and Small Scale, Beijing 100044, China

h i g h l i g h t s  Heat transfer on lignite thin-layer during hot air convective drying was studied.  Effects of hot air temperature and speed on temperature of thin layer were gained.  Average surface heat transfer behaviors in two falling rate stages were determined.  Dimensionless heat transfer correlation in the 1st falling rate stage was obtained.

a r t i c l e

i n f o

Article history: Received 5 December 2014 Received in revised form 16 March 2015 Accepted 29 March 2015 Available online 4 April 2015 Keywords: Lignite Thin-layer drying Heat transfer coefficient Falling rate period

a b s t r a c t Heat transfer characteristics of the lignite thin-layer during the hot air forced convective drying were investigated experimentally as a function of hot air temperatures (100, 110, 120, 130, 140, 150, and 160 °C) and speeds (0.6, 1.4, and 2.0 m s1). The average temperature and surface temperature of the thin-layer increased rapidly in the first falling rate period, whereas those rose slightly in the second falling rate period. The stabilized temperature of the thin layer at hot air temperature range of 100–160 °C, increased by about 4.2% to 14.8% when the wind speed rose from 0.6 m s1 up to 2.0 m s1. The average surface heat transfer coefficients in the first falling rate period were about 2–3 times of those in the second falling rate period. With an increase of the hot air temperature from 100 to 160 °C, the average surface heat transfer coefficients increased by about 71.9% to 80.9% in the first falling rate period and about 56.8% to 146.0% in the second falling rate period. The dimensionless surface heat transfer correlation of the lignite thin-layer was obtained for the first falling rate period. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Lignite accounts for nearly half of the global coal reserves and over 130.3 billion tons in China, which are about 13% of the total world coal reserves [1]. Lignite is emerging as an economic fuel of power plants, provided the SO2 emission could be controlled [2]. However, high moisture content (25–40%) and low calorific value have restricted its wide use [3]. The direct combustion of lignite in boiler can lead to low thermal efficiency [4], high greenhouse emission, high operation and maintenance costs [5]. The optimization of the drying process in future lignite power plants may lead to an efficiency increase of 4–6% [6]. Besides, reduced moisture content of lignite can decrease transportation costs, ⇑ Corresponding author at: Institute of Thermal Engineering, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China. Tel.: +86 10 51683423. E-mail address: [email protected] (M.Q. Chen). http://dx.doi.org/10.1016/j.fuel.2015.03.075 0016-2361/Ó 2015 Elsevier Ltd. All rights reserved.

lower ash disposal requirements and decrease power plant emissions [7]. The hot air convective drying of lignite is a convenient method for the power plants utilization. Tahmasebi et al. [8] examined the effect of temperature, particle size and gas flow rate on drying characteristics of lignite. Evans [9] clarified the water in the lignite into bulk water (free water), capillary water, and sorbed water, and suggested that the bulk water was removed during the initial period, while the capillary water and sorbed water were removed during the falling rate period. Thin-layer drying is a convenient approach in investigating diffusion and convection transient problems which may be used whenever diffusion inside the material is much faster than the diffusion across the boundary of the solid [10]. Yet the validity of the deep-bed drying model is directly dependent on how accurately the thin layer drying kinetics behaved [11–13]. Celma et al. [14] examined the thin-layer drying behavior of sludge at air temperature range of 20–80 °C and air velocity of 1 m s1. The drying

B.A. Fu et al. / Fuel 154 (2015) 132–139

133

Nomenclature A C h k l m MR Nu Re T t u k

surface area (m2) specific heat capacity (J kg1 K1) heat transfer coefficients (W m2 K1) thermal conductivity (W m1 K1) characteristic length (m) mass (kg) moisture ratio Nusselt number Reynolds number temperature (°C) time (s) wind speed (m s1) latent heat (kJ kg1)

kinetics of olive stone thin-layer (thickness of 10 mm) at air temperatures of 100–250 °C and air velocity of 1 m s1 were studied by Gómez-de la Cruz et al. [15]. There were many publications primarily focused on the heat transfer characteristics of the agricultural products under low drying temperature. The temperature distribution was studied experimentally during the potato and apple slices thin-layer drying by Rahman et al. [16] at the hot air temperature of 55 °C and air velocity of 1 m s1. The product temperature increased sharply at the initial stage, however, slowly as the drying processed and stabilized at the end of drying. Similar results were also studied by Barati and Esfahani [17] during the carrot thin-layer drying at the hot air temperature of 70 °C and air velocity of 2 m s1. The surface and center temperature profiles were separated at the initial stage, whilst they tended to overlap as soon as the drying processed. Velic et al. [18] investigated the influence of the air velocity (0.64–2.75 m s1) on the heat transfer coefficients of apple slice thin-layer drying at hot air temperature of 60 °C, which varied from 21.4 W m2 K1 to 44.3 W m2 K1. Tremblay et al. [19] determined that the surface heat transfer coefficients of the red pine slices increased from 5.8 W m2 K1 to 20.9 W m2 K1 with the air velocity from 1.0 m s1 up to 5.0 m s1 and hot air temperature of 56 °C. Corrales et al. [20] investigated the influence of the hot air temperature (50–70 °C) on the heat transfer characteristics of mango slice at air velocity of 0.2 m s1 and revealed that the heat transfer coefficients varied from 2.0 to 5.0 W m2 K1. Ratti and Crapiste [21] evaluated that heat transfer coefficients of potato, apple and carrot slices during hot air drying rose from 25.8 to 53.0 W m2 K1, 41.7 to 63.7 W m2 K1, and 41.0 to 58.2 W m2 K1, respectively, with air temperature from 40 °C up to 65 °C and velocity from 1 m s1 up to 5 m s1. Kondjoyan and Daudin [22] proposed a new heat transfer correlation considering the moisture migration in plaster during hot air convective drying. Keey [23] found that the heat transfer coefficients of moist bodies during hot air convective drying were greater than those of the dried bodies under the certain wind speed and temperature. Lebedev [24] proposed an universal dimensionless heat transfer correlation in which moisture ratio of wet porous media was introduced. The heat and mass transfer characteristics of fruit leather were investigated by using the above correlation [25]. Ol’shanskii [26] determined the heat transfer coefficients in the drying process of moist materials (porous ceramics, sole leather, asbestos sheets, clay and woolen felt) using the above dimensionless heat transfer correlations. Some work has been conducted on convective drying kinetics of lignite, but as of now, no information is available to date on the

Greek symbols m kinematic viscosity (m2 s1) Superscripts and subscripts a average b bottom d dried sample e evaporated f film g gas l lignite res resolution s surface sys system w water

potential impact of the drying behavior for lignite thin layer at medium temperatures, especially the heat transfer characteristics of lignite thin layer is not found in the literatures. In the present work, heat transfer behaviors of the lignite thin-layer during hot air forced convective drying were investigated experimentally. The effects of hot air temperatures and speeds on the average temperature, surface temperature and surface heat transfer coefficients of the lignite thin layer were estimated. The dimensionless heat transfer correlations of the thin layer in the first falling rate period were also obtained. 2. Material and methods 2.1. Materials The pulverized Chinese lignite was collected from Sanhe power plant at the city of Sanhe in Hebei Province, China. The sample was sieved by using 425–500 lm sieves, and was stored in an air-tight container to prevent the water evaporation. To reduce the transport effect on the kinetics of sample, the thin-layer drying experiments were investigated. The proximate and ultimate analyses of the lignite were listed in Table 1. Proximate analyses of the lignite were performed in a thermogravimetric analyzer (TGA/SDTA851, Mettler Toledo) with a precision of 0.001 mg, the detailed measuring methods were reported in Refs. [27,28]. The heating value in Table 1 was estimated by using the method reported in Ref. [29]. The ultimate analyses of the lignite were conducted in an Element Analyzer (EA3000, Leeman). 2.2. Experimental apparatus and procedure The experiments were carried out in a laboratory convective dryer shown in Fig. 1. The system consisted of a tunnel, a frequency fan, a heater, a drying chamber, a dehumidification unit and a set of data acquisition. The air induced from the frequency conversion fan was heated by the 3000 W heater. Then the hot air was dehumidified through the dehumidification unit containing calcium oxide drying agent and circulated about 15 min. About 40 g of the prepared lignite sample was uniformly spread as a thin layer on a square steel tray (80 mm  80 mm  10 mm), which was over a digital balance was placed in the drying chamber. The samples had initial moisture content of 0.03–0.04 kg kg1 (d.b.), and the thickness of the thin layer was about 10 mm. The thin layer was dried by the convective heat exchange of the dehumidified hot air, which was back to the dehumidification unit for dehumidification. Drying experiment was finished when the mass change rate was less

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Table 1 Proximate and ultimate analyses of lignite. Sample

Lignite a

Proximate analyses (wt.%)

HHV (MJ kg1)

Ultimate analyses (wt.%)

Mara

Var

FCar

Aar

Car

Har

Nar

Oar

Sar

6.84

39.12

22.43

31.61

41.40

3.14

0.68

54.46

0.32

13.78

ar is the abbreviation of ‘as received basis’.

Fig. 1. Convective dryer setup. 1. Frequency conversion fan, 2. Steam generator, 3. Heater, 4. Tray, 5. Balance, 6. Radiation heater, 7. CCD, 8. Silica glass, 9. Tray, 10. Digital balance, 11. Speed regulation, 12. Data acquisition, 13. Dehumidification unit, 14. Air chamber, 15. Steel baffle, 16. Pressure sensor, 17. Temperature sensor.

than 0.002% in 10 min. The rectangular tunnel which was made of stainless steel was 100 cm in length, 14 cm in width, and 9 cm in height. The tunnel was insulated by covering a layer of rock wool to minimize the energy loss. The wind speed was adjusted by regulating the output power of the fan (XINXING; 150FLJ, China). The wind speed over the thin layer was measured by digital anemometer (TECMAN; TM826, China). The drying temperature was regulated by a temperature controller (YUYAO; XMTD-808P, China). Three temperature sensors (PT100) were used to measure the air temperature, the surface temperature and bottom temperature of the thin layer. A data acquisition card (ADVANTECH; ADAM4017, China) was applied for collecting the temperature. During the drying process, mass of thin layer was recorded at an interval of 90 s by the digital balance (OHAUS; CP413, China) with an accuracy of 0.0001 g. The experimental conditions were selected as drying temperatures of 100, 110, 120, 130, 140, 150, and 160 °C, hot air speeds of 0.6, 1.4, and 2.0 m s1. All experiments were repeated at least three times to guarantee reproducibility. The results demonstrated that a good reproducibility was maintained for each run because the relative deviations of mass and temperature of the sample were generally within ±1.5% and ±2.0%, respectively.

tray in this work are dependent on the experimental conditions and the instruments, which are affected by systematic errors and resolution. The overall uncertainty of the direct measured parameter (X) is expressed as [30–32],

dX ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðdX sys Þ2 þ ðdX res Þ2

ð1Þ

where dX sys is the systematic uncertainty, which can be obtained from information provided by the manufacturer, and dX res is the standard resolution uncertainty, which can be evaluated by pffiffiffi Dx=2 3 (Dx: instrument resolution). Standard resolution uncertainty is preferable to guarantee a consistent comparison with uncertainty due to random errors. The quality of a measurement cannot be solely determined by its absolute uncertainty. The quality of a measurement is better expressed by the relative uncertainty, dX=X. The smaller the relative uncertainty is, the higher the quality of the measurement. Relative uncertainty of an indirect measured parameter (Y) can be given by,

2.3. Uncertainties analysis

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u  2 X dX i dY u ¼t Y Xi i

The uncertainties of all direct measured parameters such as temperature, hot air speed, and mass of sample and length of the

Relative uncertainties of all parameters in this work were evaluated as follows,

ð2Þ

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B.A. Fu et al. / Fuel 154 (2015) 132–139

Temperature: Hot air speed: Mass of sample: Length of the tray: Surface area of the thin layer: Surface heat transfer coefficient: Nusselt number:

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 0:352 0:1=2pffiffi32 dT ¼ 0:30% þ 100 T ¼  100 pffiffi 0:1=2 3 du  u ¼  0:6 ¼ 4:80% pffiffi 0:001=2 3  dm ¼ 0:0008% m ¼  38 pffiffi 3  dll ¼  0:1=2 ¼ 0:04% 80 qffiffiffiffiffiffiffiffiffiffiffiffi  2  2 dll ¼ 0:056% qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2 dT 2 dA2ffi  dm þ T þ A ¼ 0:30% m qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dh2 dl2ffi þ l ¼ 0:31%  h

Nu ¼ aRe0:5

MR ¼

During the thin layer drying of the lignite, energy balance equation can be described as [33],

ðmd C l þ mw C w Þ

dT a ¼ hAðT g  T s Þ  me k dt

ð3Þ

where md is the mass of dried lignite sample (kg), mw the mass of water in the lignite sample (kg), me the mass of evaporated water (kg), t the time (s), h the heat transfer coefficient (W m2 K1), A the surface area of the thin layer (m2), Ts the surface temperature of the sample (°C), Tg the hot air temperature (°C), Ta the average temperature of the sample (°C), which is determined approximately as,

Ts þ Tb Ta ¼ 2

ð4Þ

where Tb is the bottom temperature of the lignite sample (°C). Cl is the specific heat capacity of the dried lignite (J kg1 K1), which was determined by the DSC (404F3, NETZSCH, Germany) thermal analysis experiments. The relation between the dried lignite specific heat capacity and the average temperature is determined as,

C l ¼ 3:29  7:64  102 T a þ 9:27  104 T 2a  3:15  106 T 3a  5:41  109 T 4a

hl k

ð11Þ

ul

ð12Þ

v

where l is characteristic length (m); u the wind speed (m s1); m the kinematic viscosity of the hot air (m2 s1); k the thermal conductivity of the hot air (W m1 K1), and then can be determined as follows [37],

k ¼ 2:38  102 þ 7:12T f

ð13Þ

m ¼ 1:34  105 þ 8:78  108 T f þ 9:17  1011 T 2f

ð14Þ

where Tf is the film temperature (°C), which is equal to arithmetic average temperature between the thin layer surface and hot air. Then, Eq. (9) can be written in logarithmic form,

( ln Nu

," Re0:5

 2 #) T g þ 273 ¼ n ln MR þ ln a T s þ 273

ð15Þ

Values of the parameters, n and a can be determined by plotting   2

T þ273 ln Nu Re0:5 Tgs þ273 versus ln MR. 4. Results and discussion 4.1. Drying curves and temperature curves

C w ¼ 4:17 þ 1:50  103 T a  4:58  105 T 2a þ 5:32  107 T 3a  1:67  109 T 4a

ð6Þ 1

k is the latent heat of water (kJ kg ), based on thermal data of water, the correlation between the water latent heat and surface temperature is expressed as follows [35],

k ¼ 2:49  103  2:10T s  2:80  103 T 2s

ð7Þ

From Eq. (3), the surface heat transfer coefficients of the thin layer can be determined as follows,

ðmd C l þ mw C w Þ dTdta þ me k AðT g  T s Þ

ð10Þ

ð5Þ

The formula is similar to the polynomial expression of the specific heat capacity for bituminous coal proposed by Kozlowski [34]. Cw is the specific heat capacity of water (J kg1 K1), based on thermal data of water. The correlation between the water specific heat capacity and average temperature is expressed as follows [35],

h¼

Mt M0

where Mt, M0 are the moisture content at any time (%, db) and the initial moisture content (%, db). Nu and Re are the Nusselt number and Reynolds number, respectively, which are given by,

Re ¼

3.1. Evaluation of heat transfer coefficient

ð9Þ

where a and n are two constants correlated to drying conditions, MR the moisture ratio of sample, which is given as [36],

Nu ¼ 3. Analytical method

 2 T g þ 273 ðMRÞn T s þ 273

ð8Þ

Lebedev proposed a dimensionless heat transfer correlation of the wet porous media during convective drying [24],

Moisture ratios and average temperatures of the lignite thinlayer versus time curves were shown in Fig. 2(a)–(c). Drying rates and surface temperatures versus time curves were shown in Fig. 3(a)–(c). The experimental conditions were selected as wind speeds of 0.6, 1.4, and 2.0 m s1 and drying temperatures of 100, 110, 120, 130, 140, 150, and 160 °C. As can be observed in Fig. 2(a)–(c), the moisture ratio decreased with time and the total drying time reduced significantly as hot air temperature and speed increased. The increase of hot air temperature or speed gave rise to an enhancement of heat transfer in the thin layer, which caused the moisture ratio to decrease rapidly. Similar results were reported by Burmester and Eggers [38]. Temperature difference between hot air and lignite was high in the first falling rate period than the second falling rate period, which would conduct more heat flux through the thin layer, causing a rapid increase of average temperature in this stage. However, in the second falling rate period, the average temperature grew slightly due to the low temperature difference and gradually reached to a steady stage, in which the convective heat transfer balanced the heat transfer through conduction [20]. Besides, the drying rate in the first falling rate period was higher than the second one, which enhanced the mass transfer, causing the rapid increase in the average temperature during the first falling rate period. Similar results were reported by Barati et al. [39].

B.A. Fu et al. / Fuel 154 (2015) 132–139

1.0

0.8

MR

0.6

120 100

0.6 80

0.4 0.2 0.0

1

2

3

4

5

6

7

8

120 100

0.4

80

60

0.2

60

40

0.0

40 0

9

1

2

3

-3

t ×10 (s)

4

5

6

7

t ×10-3/s

(a) 0.6 m s-1.

(b) 1.4 m s-1. 1.0 100°C 110°C 120°C 130°C 140°C 150°C 160°C

0.8

MR

0.6 0.4 0.2 0.0

0

1

2

3

4

5

6

160 150 140 130 120 110 100 90 80 70 60 50 40

Ta /°C

0

140

100°C 110°C 120°C 130°C 140°C 150°C 160°C

0.8

Ta /°C

100°C 110°C 120°C 130°C 140°C 150°C 160°C

MR

1.0

Ta /°C

136

7

t ×10-3/s

(c) 2.0 m s-1. Fig. 2. Variation of the moisture ratios and average temperatures versus time.

100°C 110°C 120°C 130°C 140°C 150°C 160°C

5 4

80

3

70 2

60

Ts /°C

90

1

50 40

0 1

2

3

4

5

6

7

8

8

140 130 120 110 100 90 80 70 60 50 40

9

100°C 110°C 120°C 130°C 140°C 150°C 160°C

1 0 0

1

2

3 4 t ×10-3/s

(b) 1.4 m s-1. 10 9 8 7 6 5 4 3 2 1 0

100 °C 110 °C 120 °C 130 °C 140 °C 150 °C 160 °C

160 150 140 130 120 110 100 90 80 70 60 50 40 2

3

5

2

(a) 0.6 m s-1.

1

6

3

t ×10-3/s

0

7

4

4

5

6

dMR /dt ×10 4 /s-1

0

Ts /°C

Ts /°C

100

6

4

110

-1 dMR /dt ×10 /s

120

7

t ×10-3/s

(c) 2.0 m s-1. Fig. 3. Variation of the drying rates and surface temperatures versus time.

5

6

7

dMR / dt ×10 4 /s-1

7

130

137

B.A. Fu et al. / Fuel 154 (2015) 132–139

As can be seen in Fig. 2(a)–(c), the effect of wind speed on the average temperature was more important at the beginning of the process, in which free water was being removed. During this stage, average temperature increased rapidly. As the drying progressed, the rate of increment in the average temperature became slowly and almost stabilized regardless of the wind speed. From a boundary layer point of view, increment in hot air speed would lead to an increase of global heat and mass transfer coefficients, as the boundary layer got progressive thinning, which enhanced the heat transfer between the lignite and the hot air. In the second falling rate period, the internal resistances to heat transfer predominated and wind speed had weak influence on the heat transfer. Also, when the wind speed rose from 0.6 m s1 up to 2.0 m s1, the stabilized temperature within hot air temperatures of 100–160 °C increased by about 4.2% to 14.8%. In Figs. 2 and 3, the average and surface temperature profiles displayed the same tendency. The similar results were also observed by Wang et al. [40] during potato slice drying. The surface temperature tended more asymptotically towards the hot air temperature with the increase in wind speed. However, the surface temperature did not reach the hot air temperature within 2 h. The porosity of sample increased with the removal of water [41], which caused an increase in the thermal resistance, therefore, it would take much time to reach the hot air temperature. Similar results during mango slices drying were observed by PavonMelendez et al. [42]. Wang and Brennan [40] also observed that temperature of potato surface did not reach the air temperature within 12 h.

and second falling rate period with the hot air temperature and speed were shown in Fig. 4(d). As presented in Fig. 4(a)–(c), the surface heat transfer coefficient increased with the increasing hot air temperature and wind speed. Meanwhile, during the drying process, lignite sample successively experienced the removal of internal water, which can destroy and cause the pore structure to collapse [43]. The pore volume and surface area increased with the rising of temperature [41], which could lead to water removal more easily. Also, the evaporation rate increased with the increase of the hot air temperature and speed, enlarging the moisture content difference between the internal water and the surface water of the thin layer, which enhanced the mass transfer. In the falling rate period, the seven heat transfer coefficients curves became closer as the internal resistance to mass and heat transfer began to dominate the drying process. Similar results in the drying of coffee fruits were found in literature [44]. As can be seen in Fig. 4(d), the average heat transfer coefficients of the first and second falling rate period increased with the increasing hot air temperature and speed. Similar results were reported in literatures [45,46]. When the hot air temperature increased from 100 to 160 °C, the average surface heat transfer coefficients of the first falling rate period increased by about 71.9%, 80.9%, and 75.6%, respectively, at the hot air speeds of 0.6 m s1, 1.4 m s1 and 2.0 m s1. However, the average surface heat transfer coefficients of the second falling rate period increased by about 56.8%, 113.3%, and 146.0%, respectively. Within hot air speeds of 0.6 –2.0 m s1 and hot air temperatures of 100–160 °C, the average surface heat transfer coefficients in the first falling rate period were about 2–3 times of those in the second falling rate period. That could be resulted from less moisture ratio and higher temperature within the thin layer in the second falling rate period, meaning that would lead to a weakening of the heat transfer in this stage.

4.2. Surface heat transfer coefficient

14

100°C 110°C 120°C 130°C 140°C 150°C 160°C

100 °C 110 °C 120 °C 130 °C 140 °C 150 °C 160 °C

12 10 -2

10 9 8 7 6 5 4 3 2 1 0 0.0

h /W m K-1

h /W m-2 K-1

Variations of the surface heat transfer coefficients versus moisture ratios of the lignite thin layer were shown in Fig. 4(a)–(c). The variations of average surface heat transfer coefficients in the first

8 6 4 2

0.2

0.4

0.6

0.8

0 0.0

1.0

0.2

0.4

(a) 0.6 m s-1.

-2 -1 h /W m K

12 10

12

100°C 110°C 120°C 130°C 140°C 150°C 160°C

10 -1

14

0.8

1.0

(b) 1.4 m s-1.

hm/W m-2 K

16

0.6

MR

MR

8 6

8

0.6 m s-1 2nd falling rate period 1.4 m s-1 2nd falling rate period 2.0 m s-1 2nd falling rate period 0.6 m s-1 1st falling rate period 1.4 m s-1 1st falling rate period 2.0 m s-1 1st falling rate period

6 4

4 2

2

0 0.0

0.2

0.4

0.6

MR

(c) 2.0 m s-1.

0.8

1.0

100

110

120

130

140

150

160

T /°C

(d) hm in two falling rate periods.

Fig. 4. Variations of the surface heat transfer coefficients.

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B.A. Fu et al. / Fuel 154 (2015) 132–139

Table 2 Analyses of variance for lignite thin-layer drying. Source of variation

SS

Df

MS

F

P-value

Fcrit

1 falling rate period

Air speed Temperature Error Total

29.94 54.52 2.891 87.36

2 6 12 20

4.990 27.26 0.240

20.71 113.2

1.120E5 1.630E08

2.996 3.885

2nd falling rate period

Air speed Temperature Error Total

12.23 11.50 5.820E17 3.510E15

2 6 12 20

6.119 1.917 5.330E18

26.23 8.219

4.160E5 1.091E3

2.996 3.885

st

The effects of the hot air temperatures and speeds on the average surface heat transfer coefficients of the first and second falling rate period were analyzed by applying two-way ANOVA [46,47], as shown in Table 2. From Table 2, the effects of both the hot air temperatures and wind speeds on the average heat transfer coefficients of the thin layer in the first and second falling rate period were significant (P < 0.05). The effect of hot air temperature was larger than that of wind speed due to its higher F value in the first falling rate period, whereas the effect of wind speed was larger than that of hot air temperature in the second falling rate period.

Table 3 Values of n and a in Eq. (15) under different drying conditions. Hot air wind (m s1)

Hot air temperatures (°C) 100

110

120

130

140

150

160

0.6

n a R

0.740 0.751 0.969

0.602 1.030 0.979

0.530 0.915 0.989

0.458 0.942 0.975

0.492 0.911 0.995

0.439 0.906 0.960

0.402 0.937 0.977

1.4

n a R

0.650 0.898 0.948

0.644 1.030 0.938

0.621 1.050 0.947

0.586 0.934 0.971

0.498 0.882 0.965

0.423 0.927 0.977

0.302 0.833 0.967

2.0

n a R

0.459 0.989 0.959

0.323 0.813 0.854

0.540 0.848 0.948

0.672 0.944 0.983

0.431 0.817 0.914

0.401 0.724 0.950

0.363 0.651 0.987

4.3. Heat transfer correlation Based on Eq. (14), the attempt to obtain the heat transfer correlation of the thin layer in the first falling rate period was available. Fig. 5 presented the linear fitting of the first falling rate period by plotting fitting of the first falling rate period by plotting   2

T þ273 ln Nu Re0:5 Tgs þ273 versus ln MR for the thin layer drying at 0.6 m s1 wind speed and 100 °C hot air temperature. The n and a were determined to be 0.740 and 0.751, respectively. The method might also be applied to other drying conditions. The results were presented in Table 3. The widely used parameters for global assessment are the mean absolute percentage error (MAE) defined by Eq. (16), and the percentage of experimental data (b) within error bands [48,49]. N 1X jNupre;i  Nuexp;i j MAE ¼ N i¼1 Nuexp

ð16Þ

Based on the optimization method, the best correlation for the drying conditions can be determined by minimizing the MAE. The mean values of n and a were set to be the initial point (0.5, 0.9) for the restricted search. The searching range is set to be within the experimental n and a in Table 3, and the searching step size is 0.01. The optimum design problem was established as follows,

Find n and a to minimize MAE subject to 0.363 < n < 0.740 0.651 < a < 1.03 b > 85%

Based on the optimization toolbox of Matlab R2012b, the optimization point is (0.51, 0.93), therefore, therefore, the heat transfer correlation can be determined as follows,

Nu ¼ 0:93Re0:5

0.6m/s 100 °C 0.6m/s 120 °C 0.6m/s 140 °C 0.6m/s 160 °C 1.4m/s 110 °C 1.4m/s 130 °C 1.4m/s 150 °C 2.0m/s 100 °C 2.0m/s 120 °C 2.0m/s 140 °C 2.0m/s 160 °C

100

80

Nupre

experiment value linear fitting -0.4 0.5 2 Ln{Nu/[Re (Tg+273/Ts+273) ]} -0.6 =0.740lnMR-0.287 R 2 =0.939

-0.8

ð17Þ

Fig. 6 showed the comparison of Nu from Eq. (17) with the experimental values. The modified correlation predicted 88.2% of the all data in the first falling rate period within the ±30% error band at a MAE valued of 14.7%.

-0.2 2 0.5 ln{Nu/[Re (Tg+273/Ts+273) ]}

 2 T g þ 273 ðMRÞ0:51 T s þ 273

+30%

0.6m/s 110 °C 0.6m/s 130 °C 0.6m/s 150 °C 1.4m/s 100 °C 1.4m/s 120 °C 1.4m/s 140 °C 1.4m/s 160 °C 2.0m/s 110 °C 2.0m/s 130 °C 2.0m/s 150 °C

60

-30%

β =88.2%

40

-1.0

MAE=14.7%

-1.2

20

-1.4 -1.6

-1.5

-1.0

-0.5

0.0

lnMR  2

T þ273 Fig. 5. ln Nu= Re0:5 Tgs þ273 versus ln MR at 100 °C and 0.6 m s1.

0 0

20

40

60

80

100

Nuexp Fig. 6. Comparison of Nu values from Eq. (17) with experimental values.

B.A. Fu et al. / Fuel 154 (2015) 132–139

5. Conclusions The temperature profiles, moisture ration and heat transfer coefficients of the lignite thin layer were obtained during hot air convective drying. The surface heat transfer coefficients of the lignite thin layer increased with the increase of the hot air temperatures and speeds. The increase of hot air temperatures and speeds reduced the moisture ratio corresponding to maximum surface heat transfer coefficient of the thin layer. The average surface heat transfer coefficients of the thin layer in the first falling rate period varied from 3.48 to 11.26 W m2 K1 under the experimental conditions, however, that in the second falling rate period varied from 1.50 to 5.24 W m2 K1. Hot air temperatures and wind speeds were the significant factors on the average surface heat transfer coefficients of the first and second falling rate period (P < 0.05), the effect of the hot air temperature was larger than that of the hot air speed in the first falling rate period, however, the effect of wind speed was larger than that of hot air temperature in the second falling rate period. The modified dimensionless correlation,  2 T þ273 Nu ¼ 0:93Re0:5 Tgs þ273 ðMRÞ0:51 , was obtained for predicting the surface heat transfer coefficients of the lignite thin layer drying in the first falling rate period. Acknowledgment This work was supported by the National Natural Science Foundation of China under No. 51376017 and the Fundamental Research Funds of China for the Central Universities under No. 2015YJS142. References [1] Yu J, Tahmasebi A, Han Y, Yin F, Li X. A review on water in low rank coals: the existence, interaction with coal structure and effects on coal utilization. Fuel Process Technol 2013;106:9–20. [2] Selvakumaran P, Lawerence A, Bakthavatsalam AK. Effect of additives on sintering of lignites during cfb combustion. Appl Therm Eng 2014;67:480–8. [3] Katalambula H, Gupta R. Low-grade coals: a review of some prospective upgrading technologies . Energy Fuels 2009;23:3392–405. [4] Bergins C. Kinetics and mechanism during mechanical/thermal dewatering of ligniteq. Fuel 2003;82:355–64. [5] Zheng H-J, Zhang S-Y, Guo X, Lu J-F, Dong A-X, Deng W-X, et al. An experimental study on the drying kinetics of lignite in high temperature nitrogen atmosphere. Fuel Process Technol 2014;126:259–65. [6] Agraniotis M, Koumanakos A, Doukelis A, Karellas S, Kakaras E. Investigation of technical and economic aspects of pre-dried lignite utilisation in a modern lignite power plant towards zero CO2 emissions. Energy 2012;45:134–41. [7] Pickles CA, Gao F, Kelebek S. Microwave drying of a low-rank sub-bituminous coal. Miner Eng 2014;62:31–42. [8] Tahmasebi A, Yu J, Han Y, Li X. A study of chemical structure changes of Chinese lignite during fluidized-bed drying in nitrogen and air. Fuel Process Technol 2012;101:85–93. [9] Evans DG. The brown-coal/water system: Part 4. Shrinkage on drying. Fuel 1973;52:186–90. [10] Delgado JMPQ. Heat and mass transfer in porous media. Berlin: Springer; 2012. [11] Duc LA, Han JW, Keum DH. Thin layer drying characteristics of rapeseed (brassica napus l.). J Stored Prod Res 2011;47:32–8. [12] Hemis M, Bettahar A, Singh CB, Bruneau D, Jayas DS. An experimental study of wheat drying in thin layer and mathematical simulation of a fixed-bed convective dryer. Drying Technol 2009;27:1142–51. [13] Dissa AO, Bathiebo DJ, Desmorieux H, Coulibaly O, Koulidiati J. Experimental characterisation and modelling of thin layer direct solar drying of amelie and brooks mangoes. Energy 2011;36:2517–27. [14] Celma AR, Rojas S, López F, Montero I, Miranda T. Thin-layer drying behaviour of sludge of olive oil extraction. J Food Eng 2007;80:1261–71. [15] Gómez-de la Cruz FJ, Casanova-Peláez PJ, Palomar-Carnicero JM, Cruz-Peragón F. Drying kinetics of olive stone: a valuable source of biomass obtained in the olive oil extraction. Energy 2014;75:146–52. [16] Rahman SMA, Islam MR, Mujumdar AS. A study of coupled heat and mass transfer in composite food products during convective drying. Drying Technol 2007;25:1359–68.

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