Effect of pin inclination angle on flow and heat transfer characteristics for a row of pins in a flow channel

International Communications in Heat and Mass Transfer 110 (2020) 104396

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Effect of pin inclination angle on flow and heat transfer characteristics for a row of pins in a flow channel Pathomporn Naratoa, Makatar Wae-hayeea, Mohd Z. Abdullahb, Chayut Nuntadusita, a b

T

⁎

Department of Mechanical Engineering, Faculty of Engineering, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand School of Mechanical Engineering, Engineering Campus, Universiti Sains Malaysia, Nibong Tebal, Penang 14300, Malaysia

A R T I C LE I N FO

A B S T R A C T

Keywords: Cylindrical pin Flow and heat transfer characteristics Pin inclination Short and long pins CFD Thermal performance factor

The aim of this research was to study flow and heat transfer characteristics with a row of inclined pins in a rectangular channel. The cylindrical pins of diameter D = 10 mm were mounted on the heat transfer surface in spanwise direction of the channel. The pin-to-pin distance was fixed at S = 2D. Two of pin heights H were studied, namely short pins or long pins with H = 2D or H = 3.2D, respectively. The effects of pin inclination angle were investigated for θ=30o, 45o, 60o, 90o, 120o, 135o, and 150o in the range of Reynolds number from 14,000 to 32,860. The local temperature on endwall surface was measured using a thermochromic liquid crystal sheet coupled with image processing. Numerical simulations were used to obtain three-dimensional flow fields and heat transfer rates on pin surfaces and endwall surface. Results for the case H/D = 2 show that pins inclined by θ=30o, 45o and 60o can enhance heat transfer downstream of the pin row, from the baseline case of pins with θ=90o. The heat transfer was improved by a pair of counter-rotating vortices near the heat transfer surface. These vortices induced the main flow to attach on the heat transfer surface. The pin inclinations θ=120o and 135o somewhat improved heat transfer behind the pins. However, the inclination θ=150o gave the lowest heat transfer rate on the endwall surface. The heat transfer on endwall surface with H/D = 3.2 was poorer than with H/D = 2 because the counter-rotating vortices did not reach the heat transfer surface. The inclination θ=30o with H/D = 2 gave the best thermal performance. The local Nusselt number on the rear side of pin surfaces with H/D = 3.2 and inclinations θ=30o, 120o, 135o and 150o tended to increase from the case H/D = 2, due to a jetlike flow attachment on the pin surfaces. However, the local Nusselt number on pin surfaces with H/D = 3.2 and inclinations θ=45o and 60o tended to be lesser than with H/D = 2, due flow separation downstream far from the pins.

1. Introduction Pin arrays are typically used to improve surface heat transfer in a variety of engineering applications, as in cooling of gas turbine blades, cooling of electronic devices, and heat transfer enhancement in compact heat exchangers. The pins used in turbine blade cooling have pin height-to-diameter ratio H/D between 0.5 and 4 [1]. Arrays of pins with pin height-to-diameter ratio H/D over 8 are used in heat exchangers. Low aspect ratio pins with small H/D below 0.5 are applied in some types of plate-fin heat exchangers. The heat transfer improvement by a pin array is due to two factors. The first is increase of heat transfer surface by area of the pins. The second is increase of heat transfer coefficient on the endwall by the pins [2]. The heat transfer enhancement on the endwall surface in a pin fins channel caused by the convection combined the high thermal conductivity material of the pins

⁎

Corresponding author. E-mail address: [email protected] (C. Nuntadusit).

https://doi.org/10.1016/j.icheatmasstransfer.2019.104396

0735-1933/ © 2019 Elsevier Ltd. All rights reserved.

more than alone convection [3]. Pins are generally cylindrical in shape, protruding from the heat transfer surface. The heat transfer fluid is forced to flow pass an array of pins for cooling. Fig. 1 shows the flow pattern on the endwall of a vertical pin. A horseshoe vortex that improves heat transfer is generated on the endwall in front of the pin. Wake flow and a region of high mixing are observed behind the pin [4]. These disturb the boundary layer and promote turbulence behind the pin, improving heat transfer. Multiple investigations have been conducted focusing on the effects of vertical pins of cylindrical shape on heat transfer and pressure drop in flow channel. Chyu et al. [5] and Axtmann et al. [6] investigated the effects of the shorter pins and the longer pins on heat transfer surface in a flow channel. The shorter pins provided better heat transfer on the endwall than the longer pins. Lyall et al. [7] and Lawson et al. [8] determined the effect of spacing between the pins on the heat transfer

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circular pin. The average Nusselt number for the fan shaped pin was greater than for circular pin for all Reynolds numbers, and the friction factor with the new fan-shaped pin was similar to with circular pin. Tarchi et al. [22] studied heat transfer coefficients and pressure drop by mounting four types of pin arrays: streamwise staggered elliptical pin configuration, spanwise staggered elliptical pin configuration, and circular pin geometries with staggered and pentagonal arrangement. Results showed that heat transfer and pressure drop with spanwise staggered elliptical pin configuration was higher than with streamwise staggered elliptical pin configuration. Eren et al. [23] studied inlined and staggered arrays of cylindrical grooved pin-fins (C-GPFs) and triangular grooved pin-fins (T-GPFs) on heat transfer in a flow channel. The thermal performance with inline and staggered arrangements in the case of T-GPFs was better than with C-GPFs at all Reynolds numbers. Du et al. [24] studied the effect of low and high clearance on the heat transfer characteristics in a detached latticework duct by a numerical method. They found that heat transfer in the static channel with low clearance was higher than the case of high clearance in a detached latticework duct at the same Reynolds number. The diamond pins gave better heat transfer than the square or circular pins. Although noncircular pins or circular pins mixed the dimple show better heat transfer, the manufacturing process is difficult and expensive. Choi et al. [25] investigated the influence of cylinder inclination on heat transfer and the flow field around a cylinder. Heat transfer on the upper endwall was enhanced by inclined cylinders due to impingement interaction between a horseshoe vortex and a jet-like flow. Chyu et al. [26] and Takeishi et al. [27] studied heat transfer on a surface with inclined pin arrays in staggered arrangement. The height of pins was identical to the height of channel. They found that heat transfer and pressure drop were reduced by inclined pins when compared to vertical pins. As shown in the above review, cylindrical pin arrays and pin arrays with different cross section shapes on heat transfer surface in staggered and inline arrangement generate high pressure drop in the flow channel when the pin height equals the channel height. The heat transfer and pressure drop were reduced by mounting inclined pin arrays with the pin height equal to the channel height, when compared to case of vertical pin arrays. In the past, most studies have investigated pins of channel height or short pins. There is no prior study comparing pins of channel height with short pins. This study experimentally explored the effects of inclination of pin on heat transfer and flow characteristics with the pin heights H/D = 2 and 3.2. The effects of pin inclination on heat transfer were investigated for θ=30o, 45o, 60o, 90o, 120o, 135o, and 150o. The experiments were conducted in the range of Reynolds numbers between 14,000 and 32,860. Numerical simulations were also carried out to investigate the flow and heat transfer characteristics at Re = 27,000. The details of local Nusselt number on pin surface were also investigated by simulations.

Wake flow

Horseshoe vortex Region of high mixing

Y

Z X

Fig. 1. Schematic of flow pattern on the endwall surface with a mounted pin.

surface. They found that heat transfer and pressure drop in flow channel with the small spacing was the highest. Hung et al. [9] studied the heat transfer on surface with non-uniform (small pin mixed uniform pin, and big pin mixed uniform pin) pin fin arrays for both stationary and rotating conditions. In the static channel, the non-uniform pins gave better heat transfer than the uniform (6 mm-diameter of pin) pins at the same Reynolds number. Rao et al. [10] and Du et al. [11] studied the pin array mixed the dimple on the heat transfer surface in a flow channel. The heat transfer on endwall surface is enhanced by mounting pin arrays combined dimple when compared to case of a pure pin arrays in a flow channel. The friction factor was low for pin arrays on dimpled surface compared to pin arrays on smooth surface. Singh et al. [12] investigated the effects of rib combined cylindrical dimple on heat transfer surface. They found that, the heat transfer and thermal hydraulic performance in case of the rib combined dimple was higher than the case of ribs alone and dimples alone configurations. Xie et al. [13] presented the effect of pin-fin-dimple/protrusions and dimple/protrusion on the tip cap surface. The mounting of dimple/protrusions and pin-fin-dimple/protrusions on the tip surface inside the blade could enhance the heat transfer with small increases in friction. Numerous studies have focused on the effects of pin shape on heat transfer and flow friction in a flow channel. Chyu [14] studied the effects of pin shape on heat and mass transfer focusing only on the case of pins normal to the heat transfer surface. Inlined and staggered arrays of pins with and without base fillet were studied. The heat and mass transfer performance of vertical pin without fillet was better than that of fillet cylinders in staggered arrays. The friction factor was lowest in the case of vertical pins with inline arrays. Chen et al. [15] studied heat transfer and pressure drop characteristics with staggered arrays of dropshaped pins. The experimental results showed that heat transfer with drop-shaped pins is higher than with circular pins. Goldstein and Chen [16] studied mass transfer and pressure drop characteristics with uniform diameter circular pins and stepped circular pins. Their results showed stepped circular pins produced higher heat transfer than uniform diameter circular pins. The stepped circular pin arrays gave the best mass transfer performance. Hwang et al. [17] and Chyu et al. [18] studied heat transfer and pressure drop with cubic pins, diamond pins and circular pins in staggered arrangement. They found that heat transfer with cubic pin arrays and diamond pin arrays was higher than with circular pin arrays at the same Reynolds number, and the pressure drop with the circular pin arrays was the lowest. Wang et al. [19] presented heat transfer characteristics on endwall surface with circular pins, elliptical pins, and drop-shaped pins. The average Nusselt number with elliptical pins and drop-shaped pins was below that with circular pins. The pressure drop of circular pins was larger than with elliptical pins and drop-shaped pins. Pandit et al. [20] investigated staggered arrays of circular, triangular, hexagonal and diamond shapes on heat transfer in a flow channel. The results show that heat transfer with diamond pins was the highest among the shapes tested. Moon et al. [21] studied heat transfer from a new fan-shaped pin in comparison with a

2. Experimental model and parameters The details of experimental model are shown in Fig. 2. A row of cylindrical pins with diameter of D = 10 mm was mounted in spanwise direction in a flow channel. The cylindrical pins and the wind tunnel were made of acrylic glass (k = 0.2 W/m K at 25 °C). The pin heights tested were H = 2D (62.5% of the channel height) and 3.2D (equivalent the channel height). The pin-to-pin distance (S) was fixed at S = 2D. In Fig. 2, the origin of the Cartesian coordinates was located at center of the pin in the flow channel. The X-, Y- and Z-axes are in streamwise, spanwise, and direction normal to the heat transfer surface, respectively. The heat transfer characteristics were considered only for three pitches of pins in the dotted area, as shown in Fig. 2(c). In this work, the effects of pin inclination angle were investigated for θ= 30o, 45o, 60o, 90o, 120o, 135o and 150o, as shown in Fig. 2(d).

2

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q Flow

Pin

Z

Flow

Pin

Z

Heat transfer surface H=3.2D

(b) For case of H/D=3.2

(a) For case of H/D=2

Y

X

q

X H=2D Heat transfer surface

Considered region

Flow 18D

X S=2D 13.5D 27D Pin model on heat transfer surface

(d) Inclination of pin in case of H/D=3.2

(c) Pin arrangement

Fig. 2. Inclination of pin mounted on the heat transfer surface and their locations in the test section.

3. Experimental setup and method

(53.3D) connected the wind tunnel to an air chamber with an orifice flow meter and blower. The air flow was forced through the wind tunnel passing the upstream section with heater chamber, the test section and the downstream section by a blower. The inlet was equipped with two layers of mesh plates and flow straightener to ensure a uniform flow field. The mean temperature (Tin) of the air inlet flow was kept constant at 26.0 ± 0.1 °C with temperature regulated power controllers (3-kW heater). The environmental temperature (Ts) was kept constant at 25.0 ± 0.1 °C with an air conditioner. The environment temperature near the heat transfer surface was measured with calibrated Type-K thermocouples. The mean temperature of the air entering and leaving the test section was measured with four calibrated Type-K thermocouples located across the cross section at immersion depth of about half of the channel height. The average of four thermocouple reading as was recorded as the inlet mean temperature (Tin) and the outlet mean temperature (Tout) was similar.

3.1. Experimental setup A schematic diagram of the experimental apparatus is show in Fig. 3. The wind tunnel has rectangular cross section with 300 mm width and 32 mm height. The wind tunnel can be divided into three parts; upstream section (before the test section), test section, and downstream section (after the test section). The upstream section with length of 1535 mm (153.5D) had sufficient length for fully developed flow before it entered the test section. A static Pitot tube was located in the center of the wind tunnel, in the upstream section, to measure the flow velocity. The test section with a length of 500 mm (50D) had the heat transfer surface with inclined pins. The pressure drop was measured between upstream and downstream locations with using differential pressure transducer (OmegaPX277-01D5V). The downstream section with a length of 533 mm

Digital camera

Acrylic Screw TLC

Computer

Light

Copper bus bar SUS304 foil Mesh plate

Ts

1,535 mm

Flow

500 mm

q

Wind tunnel Type-K Heater Movable thermocouple chamber pitot tube Temperature controller

Tin

Power supply 533 mm

Pins

L Pressure drop

Tout Orifice

Inverter

Z Out Flow

Blower

X Pressure transducer

V

Manometer

Volt meter

Fig. 3. Schematic diagram of the experimental apparatus. 3

Digital Thermometer

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Velocity inlet Heat transfer surface q D

H

Symmetry Z

Y X

Symmetry

3.2D Pressure outlet

Fig. 4. Computational domain and grid system.

flow temperature (Tam) was:

The details of heat transfer surface in the test section are also shown in Fig. 3. The heat transfer surface was made of a stainless steel foil with 30 μm thickness. The stainless steel foil was stretched between copper bus bars. The heat transfer surface with constant heat flux was heated by supplying an electric current from a DC power source through the copper bus bars. For temperature measurement on heat transfer surface, a thermochromic liquid crystal (TLC, Omega-LCS-95) sheet was attached on the back side of the heat transfer surface with inclined pins. The TLC sheet indicated by color the temperatures in range from 30 °C to 35 °C. The calibration was done similarly as in Nuntadusit et al. [28] and Wae-hayee et al. [29] using some thermocouples under experimental conditions and fixed lighting and camera setting. The color information from TLC sheet was converted to temperature by image processing.

Tam =

Tin + Tout 2

(6)

Here Tin and Tout are the average air temperatures at inlet and exit of the test section. To obtain the local Nusselt number on heat transfer surface with row of inclined pins, Nu, the following equation was used

Nu =

hDh k

(7)

Here, Dh and k are the channel hydraulic diameter (= 57.8 mm) and the thermal conductivity of air at Tam. For the air flow in the inclined pin channel, the Reynolds number was defined by:

Vc Dh ν

3.2. Data reduction

Re =

The local heat transfer coefficient (h) for forced convection on the heat transfer surface can be evaluated from:

where Vc and ν are the air velocity at the center of wind tunnel in the upstream section and the kinetic viscosity of air. The pressure drop in test section was obtained as difference between pressure transducers and was then converted to a friction coefficient:

̇ qinput =

IV A

̇ , losses = qloss ̇ , conv + qloss ̇ , rad qtotal h=

(1)

2ΔP D f = ⎜⎛ 2 ⎟⎞ ⎛ h ⎞ ⎝ ρVc ⎠ ⎝ L ⎠

(2)

̇ ̇ , losses qinput ‐qtotal (Tw ‐Tam )

(8)

(3)

(9)

Here q̇input , I, A and V are the heat flux supplied from supplier unit, the electric current from supplier unit, the heat transfer area on stainless steel foil, and the electric voltage across the bus bars, respectively. q̇loss, conv and q̇loss, rad are the heat losses from the back side of TLC sheet to the environment by free convection and radiation, and can be calculated from:

Here L is the length (=253 mm) between pressure measurement points. The average Nusselt number of the smooth circular duct with fullydeveloped turbulent flow was calculated by the Dittus-Boelter correlation in Eq. (10) [31]. The friction factor in a smooth pipe with fullydeveloped flow was calculated from experimental data. The overall thermal performance factor (η) was calculated by Webb and Eckert Eq. (11) [32]. Pr is the Prandtl number of air flow.

̇ , conv = hc (Tw − Ts ) qloss

(4)

Nu 0 = 0.023Re0.8Pr 0.4

̇ , rad = σεTLC (T w4 − Ts4 ) qloss

(5)

(10)

1/3

Nu ⎤ ⎡ f ⎤ / η=⎡ ⎢ Nu 0 ⎥ ⎢ f0 ⎥ ⎦ ⎣ ⎦ ⎣

Here hc is the natural convection coefficient from a heated horizontal plate to the environment by natural convection [30], Tw is the overall average wall temperature obtained from color images of TLC sheet, σ is the Stefan-Boltzmann constant, and εTLC is the emissivity of TLC sheet that was 0.9 [29]. The local wall temperature (Tw) on heat transfer surface was obtained from color imaging of TLC sheet. The air mean

(11)

The experimental uncertainty was assessed according to Kline and McClintock [33]. The Nusselt number uncertainty is between 3.3% and 4.0%, similar to previous studies [28,29]. The uncertainty of friction factor is between 3.5% and 7.5%. 4

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3.3. Numerical setup and validation Fig. 4 shows the computational domain and grid system with only 4 pitches of inclined pins, for simulations of flow field and heat transfer on surface in the wind tunnel. The computational domain and flow conditions represented the experimental conditions. As boundary conditions, uniform velocity profile was specified at the inlet section and atmospheric pressure was specified at outlet section. The symmetry planes at which the normal gradients of all flow variables are zero formed sides of the computational domain. No-slip condition was imposed at the pin surface, the up and down walls in flow channel. A uniform heat flux was applied at the heat transfer surface and the pin surfaces. Numerical simulations with ANSYS ver. 15 (FLUENT) solved the Reynolds averaged continuity equation, the Navier-Stokes equations, and energy equation, to obtain the three-dimensional flow field and the heat transfer characteristics on the endwall surface and the pin surfaces. The continuity, momentum and energy equations for simulation refer according to Kim and Moon [34]. The solution method for velocity and pressure fields was Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) with second order upwind, for all spatial discretization. Convergence was assessed from the root mean square (RSM) relative residual with thresholds: 10−4 for the three components of the velocity, 10−7 for the energy, 10−4 for the continuity equation, 10−5 for specific dissipation rate, and 10−4 for turbulent kinetic energy. The grid system for the SST k-ω turbulence model had about 3.5 million nodes. The grid system was tested so that the dimensionless wall distance (y+) of computational domains was less than 1.0 [10,21,35,and], as shown in Fig. 5. The shear stress transport (SST) k-ω turbulence model was used. It combines the advantages of standard k-εturbulence model and k-ω turbulence model by using a blending function. Kim and Moon [34] showed that the overall average Nusselt number on a heat transfer surface, on using the SST k-ω turbulence model, matched the experiments with stepped circular pin arrays in the flow channel. The SST k-ω turbulence model works well for problems with adverse pressure gradient, separation zones, and vortexes [36–39,and]. Fig. 6 shows a comparison of the numerical and experimental overall average Nusselt number on endwall surface in the range of Reynolds numbers between 14,000 and 32,860 at H/D = 2. It is found that the overall average Nusselt number from numerical simulation of a row of inclined pins was in good agreement with experimental data. At Re = 27,000, the numerical average Nusselt number with pin inclinations θ= 30o, 45o, 60o and 90o was about 0.83%, 6.21%, 12.24% and 10.6% higher than that the experimental data, respectively. On the

2

Fig. 6. Overall average Nusselt number on endwall surface compared between simulations and experimental data for H/D = 2.

Fig. 7. The numerical and experimental local Nusselt number on endwall surface along X-axis at Y/D = 0 for case of inclination θ= 30o with various the Reynolds number.

other hand, the numerical average Nusselt number with inclinations θ= 120o, 135o and 150o was about 12%, 8.6% and 1.9% below the experimental data. Fig. 7 shows the numerical and experimental local Nusselt number in downstream of the pin on endwall surface along Xaxis at Y/D = 0 for case of inclination θ= 30o with various the Reynolds number. The numerical model was enough to predict the local Nusselt number at downstream of the pin. This agrees with the result of Du et al. [40]. Fig. 8 shows a comparison of the numerical and experimental

1

3 Z

Y X

1

2

Fig. 5. Rectangular mesh in the flow domain. 5

3

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upstream (θ= 30o, 45o and 60o), the local Nusselt number upstream of a pin tends to increase and the local Nusselt number downstream of the pin tends to significantly increase, with a large area compared to the case with θ= 90o. The inclined pins with θ= 45o give the largest local Nusselt number contour downstream of the pin row. For pins inclined downstream (θ = 120o, 135o and 150o), the local Nusselt number downstream of a pin tends to decrease with inclination angle, from θ = 90o to 120o, 135o and 150o. The effects of a horseshoe vortex upstream of the pin cannot be seen in the Nusselt number. Fig. 10 shows Nusselt number distributions for different pin inclinations with H/D = 3.2 at Re = 27,000. As can be seen from the contours, the local Nusselt number contours for case of pin inclination θ= 90o are similar to those with θ= 90o at H/D = 2. However, the local Nusselt number contour downstream is larger and covers a larger area than with H/D = 2. For pins inclined upstream (θ= 30o, 45o and 60o), the local Nusselt number upstream and downstream of a pin tends to decrease with the inclination angle moving from θ= 90o to 60o, 45o and 30o. The pins with θ= 90o give the largest heat transfer downstream of the pin row. In the case H/D = 2, the local Nusselt number downstream with inclinations θ= 30o, 45o and 60o tends to significantly decrease because there is a pair of counter-rotating vortices behind the pin extending further on the heat transfer surface in comparison to the case of H/D = 2, in Figs. 23 and 24. The heat transfer enhancement downstream of the pins may be caused by the counterrotating vortex. The local Nusselt number contours downstream with pin inclination θ= 90o tends to increase slightly. The local Nusselt number with pin inclinations θ= 120o, 135o and 150o does not increase downstream. The mechanisms of heat transfer enhancement and deterioration will be further discussed with numerical results later.

Fig. 8. Friction factor in test section compared between simulations and experimental data for H/D = 2.

friction factor in flow channel with various the Reynolds number at H/ D = 2. It was found that the friction factor in flow channel from numerical result of a row of inclined pins was in good agreement with experimental result. The different value of friction factor from numerical data and experimental data were similar as with in Rao et al. [41]. The trends of overall average Nusselt number on endwall surface and friction factor in a flow channel in numerical results were similar to the experimental ones. 4. Results and discussion 4.1. Nusselt number distribution The local Nusselt number contours on heat transfer surface, from heat transfer measurements using TLC sheet, with different pin inclinations at Re = 27,000, are shown in Figs. 9 and 10 for only 3 pitches of the inclined pins in center of a flow channel. The air flows from left to right, in the increasing X/D direction. Fig. 9 shows Nusselt number distributions for different pin inclinations with H/D = 2 at Re = 27,000. As can be seen from the contours, the local Nusselt number upstream for case of inclination θ= 90o is high around the pin. This is due to the horseshoe vortex around the pin upstream of it. The Nusselt number downstream is higher and covers a larger area. This is due to wake flow and separating flow that disturb the boundary layer and promote turbulence downstream. This agrees with the results from other studies [8,19,42]. For pins inclined

4.2. Local Nusselt number and spanwise average Nusselt number Figs. 11 and 12 show local Nusselt number along the X-axis at Y/ D = 0 and Re = 27,000, obtained from Fig. 9 and Fig. 10 with H/D = 2 and 3.2, respectively. The local Nusselt number is not shown on heat surface under the pin. For inclination θ= 90o with H/D = 2 and 3.2, the local Nusselt number upstream tends to increase on approaching the pin. The local Nusselt number downstream tends to increase away from the pin reaching its maximum at X/D≈2.2, and then decreasing further downstream. The local Nusselt number from X/D = 2.2 to 7 with H/ D = 2 decreased more quickly than with H/D = 3.2. In case H/D = 2, with inclinations θ= 30o, 45o and 60o, the local

Fig. 9. Nusselt number distributions with H/D = 2 for different pin inclinations, at Re = 27,000. 6

International Communications in Heat and Mass Transfer 110 (2020) 104396

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Fig. 10. Nusselt number distributions with H/D = 3.2 for different pin inclinations, at Re = 27,000. o

30 120o

45o 135o

60o 150o

30 120o

450 400 350 300 250 200 150 100 50

450 400 350 300 250 200 150 100 50 -2

-1

0

1

2

3

4

45o 135o

o

90o

5

6

-2

7

-1

0

1

2

450 400 350 300 250 200 150 100 50 -2

-1

0

o

1

2

60o 150o

3

4

90

30 o 120

o

450 400 350 300 250 200 150 100 50

5

6

4

5

6

7

Fig. 13. Spanwise average Nusselt number along X-axis for different pin inclinations at Re = 27,000 and H/D = 2.

Fig. 11. Local Nusselt number along X-axis at Y/D = 0 for different pin inclinations, at Re = 27,000 and H/D = 2. 45o 135o

3

90o

X/D

X/D

30o 120o

60o 150o

-2

7

-1

0

1

o

60o o 150

45 135o

2

X/D

3

4

90o

5

6

7

X/D Fig. 14. Spanwise average Nusselt number along X-axis for different pin inclinations at Re = 27,000 and H/D = 3.2.

Fig. 12. Local Nusselt number along X-axis at Y/D = 0 for different pin inclinations at Re = 27,000 and H/D = 3.2.

For inclinations θ= 120o, 135o and 150o, the local Nusselt number upstream of a pin was similar to that with θ= 90o, but downstream it was lesser than with θ= 90o. Figs. 13 and 14 show spanwise average Nusselt number along the Xaxis for different pin inclinations at Re = 27,000, obtained from Figs. 9 and 10 with H/D = 2 and 3.2, respectively. This spanwise average Nusselt number was calculated by averaging the local Nusselt number in spanwise direction in Figs. 9 and 10, at different X distances. The local Nusselt numbers under the pins were not accounted for. In case H/D = 2, for inclinations θ= 30o, 45o and 60o, the spanwise average Nusselt number downstream of a pin was highest at X/D≈1,

Nusselt number downstream was largest at X/D≈1, with the local Nusselt number more than two-fold that with inclination θ= 90o; and then the local Nusselt number decreased downstream but stayed larger than with θ= 90o. For inclinations θ= 120o, 135o and 150o, the local Nusselt number upstream of a pin was similar as with θ= 90o, but the local Nusselt number downstream was smaller. In case H/D = 3.2, with inclinations θ= 30o and 45o, the local Nusselt number downstream was high from X/D≈1 to 2, and then decreased downstream with values below those with θ= 90o. The local Nusselt number downstream with θ= 60o was below that with θ= 90o. 7

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Fig. 17. Friction factor versus Reynolds number with H/D = 2 for different pin inclinations.

Fig. 15. Average endwall Nusselt number versus Reynolds number with H/ D = 2 for different pin inclinations.

and then the spanwise average Nusselt number decreased downstream but was larger than that with θ= 90o. For inclinations θ= 120o, 135o and 150o, the spanwise average Nusselt number downstream of a pin was lesser than with θ= 90o. In case H/D = 3.2, for inclinations θ= 30o and 45o, the spanwise average Nusselt number downstream of a pin was high from X/D≈0.6 to 2.4 when compared to θ= 90o, and then it decreased from X/ D = 2.4 to 7. For inclinations θ= 60o, 120o, 135o and 150o, the spanwise average Nusselt numbers upstream and downstream of a pin were below those with θ= 90o. 4.3. Average endwall Nusselt number, friction factor and thermal performance factor

Fig. 18. Friction factor versus Reynolds number with H/D = 3.2 for different pin inclinations.

The overall average Nusselt number versus the Reynolds number is shown in Figs. 15 and 16 for H/D = 2 and 3.2, respectively. This overall average Nusselt number was calculated by averaging the local Nusselt number on the heat transfer surface. In case H/D = 2, for inclinations θ= 30o, 45o, 60o, 90o, 120o and 135o, the overall average Nusselt number increased with Reynolds number, while with θ= 150o it appeared independent of the Reynolds number. The inclinations θ= 30o, 45o and 60o can enhance the overall average Nusselt number over the baseline θ= 90o case at any Reynolds number tested. At Re = 32,860, the overall average Nusselt number with θ= 30o, 45o and 60o was about 21.6%, 28.9% and 32.6% higher than with θ= 90o, respectively. On the other hand, with θ= 120o and the overall average Nusselt number was not improved, and θ= 150o gave the lowest overall average Nusselt number. In case H/D = 3.2 with θ= 30o, 45o, 60o, 90o, 120o and 135o, the average Nusselt number increased with Reynolds number, but with θ= 150o it did not depend on the Reynolds number. The inclinations θ= 30o, 45o, 60o, 120o, 135o and 150o did not improve the overall average Nusselt number when compared to baseline θ= 90o. The inclination θ= 150o gave the lowest overall average Nusselt number. The pin inclination upstream or downstream with H/D = 3.2 did not enhance

heat transfer on endwall surface from that with θ= 90o. The friction factor was also considered and is shown in Figs. 17 and 18 over the studied Reynolds number range for different pin inclinations with H/D = 2 and 3.2, respectively. The dimensionless friction factor was obtained from the pressure drop in the test section. With any pin inclination, the friction factor increased with Reynolds numbers between 8000 and 20,000, was stable for Reynolds numbers between 20,000 and 32,860. In case H/D = 2 and any Reynolds number, the trends in friction factor with θ = 30o were similar as with θ = 150o, and the trends with θ= 45o were similar as with θ = 135o. The inclination θ = 90o gave the highest friction factor. The inclinations θ= 60o and 120o gave somewhat larger friction factors than θ= 30o, 45o, 135o and 150o. In case H/D = 3.2 and any Reynolds number, the trends of friction factor were similar to those with H/D = 2, but the values of the former were larger. The pressure drop in test section was smaller with inclined pins than with θ = 90o, with either H/D = 2 or 3.2. Figs. 19 and 20 show thermal performance factor versus Reynolds number for different pin inclinations with H/D = 2 and 3.2, respectively. The thermal performance factor was obtained from heat transfer

Fig. 16. Average endwall Nusselt number versus Reynolds number with H/ D = 3.2 for different pin inclinations.

Fig. 19. Thermal performance factor versus Reynolds number with H/D = 2 for different pin inclinations. 8

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4.4. Flow structure Fig. 21 shows the velocity contours on Z-X plane passing the pin center, from numerical simulations, for different pin inclinations with H/D = 2. The air flows from left to right of in X/D direction. In case θ=90o, there are acceleration flow regions near the head of pins at X/ D = 0. The low velocity wake flow near the heat transfer surface can be obviously detected behind the pin [40]. Flow separation occurs on the head of pin and the flow reattaches to the heat transfer surface at X/ D = 6. With inclinations θ=30o, 45o and 60o, the region with wake flow behind the pin cannot be seen. The separated flow from the head of pin along the rear side of the pin is jet-like and attaches to the pin surface and flows to the heat transfer surface [25]. The inclinations θ=120o and 135o gave a region of wake flow behind the pin. However, with θ=150o flow attachment near the pin surface reduced the wake region downstream of the pin. Fig. 22 shows the velocity contours on Z-X plane passing through the pin center, from numerical simulations with different pin inclinations and H/D = 3.2. In case θ=90o, the wake region with low velocity can be seen downstream of the pin from X/D = 0.5 to 3. The wake flow fully covers the cross-sectional area of flow channel downstream of the pins. The velocity of flow downstream increased again from X/D = 3 to 7. The wake flow behind the pin near the heat transfer surface cannot be seen in case θ=30o, and attachment of the jet-like flow occurs downstream of the pin. The wake flow occurs downstream of the pin with θ=45o and 60o. This is different from H/D = 2 that had jet-like flow behind the pin. With θ=120o, 135o and 150o, the wake flow downstream of the pin near the heat transfer surface can be seen for θ=120o, but with θ=135o and 150o wake flow did not occur due to flow attachment on the rear side of pin. The flow characteristics from mounting the inclined pins in the case of H/D = 3.2 agrees with the results from other studies [25,44]. Figs. 23 and 24 show the streamlines from numerical simulations with H/D = 2 and 3.2 at Re = 27,000. The figures show streamlines

Fig. 20. Thermal performance factor versus Reynolds number with H/D = 3.2 for different pin inclinations.

on endwall surface per pressure drop. The thermal performance factor decreased with Reynolds number. This agrees with the results from other studies [12,42,43,and]. In case H/D = 2, the inclinations θ= 30o, 45o and 60o can enhance the thermal performance factor when compared to θ= 90o, at any Reynolds number. At Re = 14,000, the thermal performance with inclinations θ= 30o, 45o and 60o was about 45.8%, 36.1% and 9.8% higher than with θ= 90o, respectively. On the other hand, the inclinations θ= 120o, 135o and 150o did not improve thermal performance factor from that with θ= 90o. In case H/D = 3.2, the inclinations θ= 30o and 45o can enhance the thermal performance factor from that with θ= 90o at any Reynolds number. At Re = 14,000, the thermal performance with θ= 30o or 45o was about 29.9% or 11.4% better than with θ= 90o. In the Reynolds number range 24,000–32,860 the inclinations θ= 60o, 120o, 135o and 150o did not improve thermal performance. The inclinations θ= 30o and 45o significantly increased the thermal performance factor with H/D = 2 and 3.2 relative to vertical pins, at all Reynolds numbers tested. The thermal performance factor in case H/ D = 2 were higher than with H/D = 3.2, at any fixed Reynolds number.

Fig. 21. Velocity contours with H/D = 2 in Z-X plane at the center of wind tunnel for various pin inclinations at Re = 27,000. 9

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Fig. 22. Velocity contours with H/D = 3.2 in Z-X plane at center of the wind tunnel for various pin inclinations at Re = 27,000.

D = 3.2. With the inclination θ= 90o, the air flow across the pin generates a larger area wake flow, which gives the highest-pressure drop (Fig. 18) in the downstream region. The region of wake flow in case H/D = 3.2 behind the pin was larger than for H/D = 2. No jet-like flow with counter-rotating vortices can be found in this case. With the inclinations θ= 30o, 45o and 60o, there is jet-like flow with counter-rotating vortices behind the pin see in top and side views. The counter-rotating vortices behind the pin cannot attach to the heat transfer surface as they did with H/D = 2. The heat transfer enhancement by the counter-rotating vortices was smaller than with H/ D = 2, as seen in Figs. 9 and 10. On the other hand, no wake vortices downstream of the pin can be found in this case. The counter-rotating vortices downstream with θ= 30o, 45o and 60o may destroy the wake flow. Among the inclinations θ= 120o, 135o and 150o, no wake flow behind the pin is found for θ= 150o. The size of wake region behind the pin decreased as inclination increased from 90o to 135o. The counterrotating vortices in jet-like flow behind the pin turned away from the heat transfer surface in side view. No heat transfer enhancement by counter-rotating vortex on heat transfer surface downstream of pins took place. The counter-rotating vortices improved heat transfer on rear side of the pin.

across the inclined pin at center of the flow channel. The 3-D streamlines around the inclined pin are shown in top and side views. The flow characteristics of air flow across are strongly affected by pin inclination. The air flow across an inclined pin generates a horseshoe vortex upstream with all inclination angles. The heat transfer upstream may be enhanced by the horseshoe vortices [21,45]. Fig. 23 shows the streamlines around an inclined pin with H/D = 2. With θ= 90o, there is a pair of wake regions with low velocity downstream of the pin, as seen in the top view, but no counter-rotating vortices downstream of the pin can be found in this case. The air flow downstream in side view shows that the wake flow prevails from X/ D = 0.5 to 3. The flow characteristics in the case of vertical pin with H/ D = 2 show that a leakage flow and a leakage vortex (LV) are found in downstream of the pin. This agrees with the results from other studies [40]. For the inclinations θ= 30o, 45o and 60o, air flow from the head of the pin surface at Z/D = 2 has separation with jet-like flow in the downstream region. A pair of jet-like flows generates a pair of counterrotating vortices behind the pin, near the heat transfer surface, seen in top and side views. The counter-rotating vortexes will attach to the heat transfer surface and grow larger downstream. The heat transfer increase seen in Fig. 9 downstream of the pins may be caused by the counterrotating vortexes that induce air flow attachment to the heat transfer surface downstream. On the other hand, no wake region downstream of pin can be found in this case. The counter-rotating vortices downstream with inclinations θ= 30o, 45o and 60o may destroy the wake flow and reduce the pressure drop in the flow channel [10]. For inclinations θ= 120o, 135o and 150o, wake flow formed behind the pin is seen in the top view, and the wake region downstream became smaller on increasing the inclination from 120o to 135o and 150o. The air flow across the pin generates wake flow downstream with θ= 120o and 135o and jet-like flow downstream with θ= 120o. With θ= 135o and 150o, jet-like flow and counter-rotating vortices near the pin surface can be found downstream with flow away from the heat transfer surface. The effect of counter-rotating vortices on heat transfer becomes small on the endwall surface. Fig. 24 shows the streamlines around the inclined pin with H/

4.5. Heat transfer characteristics on pin surface The local Nusselt number contours on pin surface, from numerical simulations, for different pin inclinations with H/D = 2 and 3.2 at Re = 27,000, are shown in Figs. 25 and 26. Constant heat flux was applied on the pin surface. The contours of local Nusselt number are shown in Z-X and Y-Z planes for only three pitches of inclined pins in the center of flow channel. The local Nusselt number contours on pin surface are shown in front view (first column), back view (second column), and side view (third column). Fig. 25 shows local Nusselt number distribution on pin surface for different pin inclinations with H/D = 2. In the front view, the local Nusselt number for inclinations θ= 30o, 45o and 60o is higher than with θ= 120o, 135o and 150o, and the local Nusselt numbers with θ= 90o, 10

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Fig. 23. The 3-D streamlines around the inclined pin on a heat transfer surface, with H/D = 2 at Re = 27,000.

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Fig. 24. The 3-D streamlines around the inclined pin on heat transfer surface, with H/D = 3.2 at Re = 27,000.

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In the side view, the local Nusselt number in front of the pin was high due to flow impinging on the pin surface. The local Nusselt number on back side of the pin with θ= 120o, 135o and 150o was lower than with θ= 90o, may be due to development of a thermal boundary layer at the pin surface. Fig. 26 shows local Nusselt number distribution on pin surface for different pin inclinations with H/D = 3.2. In the front view, the local Nusselt number with θ= 90o is higher on the pin surface than for H/ D = 2. The local Nusselt number on pin surface with θ=30o, 45o and 60o on head of the pin was lesser than with 90o. However, it is smallish at bottom of the pin in case H/D = 2. The local Nusselt number on pin surface with θ=120o, 135o and 150o is reduced at bottom of the pin. In the back view, the local Nusselt number with θ=90o in center on the pin surface tend to increase from that with H/D = 2. The local Nusselt number on pin surface with θ=30o, 120o, 135o and 150o tends to increase relative to H/D = 2 due to flow attachment near the pin surface, in Fig. 24. But the local Nusselt number on pin surface with θ=45o and 60o tends to be lesser than with H/D = 2, due to flow separation downstream on the pin surface. In the side view, the local Nusselt number in front of the pin was high due to impinging of main flow. The best distribution of local Nusselt number on pin surface on front side of the pin is seen with θ=90o. The heat transfer on back side of the pin with θ= 30o, 45o, 60o, 120o, 135o and 150o was affected by flow attachment. The overall average Nusselt number on endwall and pin surface from numerical result versus pin inclination angle is shown in Figs. 27 and 28 at Re = 27,000, obtained from Fig. 25 and Fig. 26 with H/D = 2 and 3.2, respectively. This overall average Nusselt number was calculated by averaging the local Nusselt number on the endwall surface and the pin surface. The results show that the Nusselt number on the pin surfaces was higher than the endwall Nusselt number at any pin inclination angle tested due to the air flow in a flow channel clash directly the pin surface. This agrees with the results from other studies [7,8]. The trends of overall average Nusselt number on endwall surface in case H/D = 2 and 3.2 were similar to with the experimental result. In case H/D = 2, the inclinations θ= 45o and 60o can enhance the overall average Nusselt number on pin surface over the baseline θ= 90o. The overall average Nusselt number on pin surface with θ= 45o and 60o was about 0.5%, and 6.5% higher than with θ= 90o, respectively. The inclinations θ=30o, 120o, 135o and 150o did not improve the overall average Nusselt number on pin surface when compared to baseline θ= 90o. The inclination θ= 120o gave the lowest overall average Nusselt number on pin surface. In case H/D = 3.2, the inclinations θ= 30o, 45o, 60o, 120o, 135o and 150o did not improve the overall average Nusselt number on pin surface when compared to baseline θ= 90o. The inclination θ= 150o gave the lowest overall average Nusselt number on pin surface.

Nu 0

52.6 105.3 157.9

210.5 263.1 315.7 368.4 Back View

421

474 500

Side View

3

Z/D 2 1

03

Z/D 2 1

03

Z/D 2 1

03

Z/D 2 1

03

Z/D 2 1

03

Z/D 2 1

03

Z/D 2 1

0

Front View

3

2

1

0 -1 -2 -3-3 -2 -1 0 1 Y/D Y/D

2

3-5 -4 -3 -2 -1 0 1 X/D

2

3

4

5

Fig. 25. Local Nusselt number distributions on pin surface in case H/D = 2 for different pin inclinations at Re = 27,000.

Nu 0

52.6 105.3 157.9 210.5 263.1 315.7 368.4 Back View

421

474 500

Side View

Z/D 2 1

03

Z/D 2 1

03

Z/D 2 1

03

Z/D 2 1

03

Z/D 2 1

03

Z/D 2 1

0

Front View

03

5. Conclusions

3

Z/D 2 1

In this study, the flow and heat transfer for a row of pins attached on a heat transfer surface in wind tunnel were studied in the range of

3

2

1

0 -1 -2 -3-3 -2 -1 0 1 Y/D Y/D

2

3-5 -4 -3 -2 -1

0 1 X/D

2

3

4

5

250 Endwall surface Pin surface

200

Fig. 26. Local Nusselt number distributions on pin surface in case H/D = 3.2 for different pin inclinations at Re = 27,000.

150 100

60o and 45o were significantly high on head of the pin due to the high velocity in center of the flow channel. In the back view, the local Nusselt number on pin surface with θ= 30o, 45o and 60o was obviously higher than with θ= 90o. This is due to flow attachment near the pin surface with flow separation on the head of the pin in Fig. 23. The local Nusselt number on pin surface with θ= 120o, 135o and 150o was lower than with θ= 90o.

50 0 30o

45o

60o 90o 120o Pin inclination angle (θ)

135o

150o

Fig. 27. Overall average Nusselt number on enwall and pin surface in case of H/D = 2, Re = 27,000. 13

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to impingement at high velocity in center of the flow channel. The local Nusselt number on the rear side of pin surface with θ= 30o, 45o and 60o was obviously higher than with θ= 90o. This is due to the jet-like flow attachment near the pin surface with flow separation at head of the pin. In case H/D = 3.2, the local Nusselt number in front side of the pin with θ=30o, 45o and 60o decreased from that with θ= 90o. The local Nusselt number on rear side of the pin with θ=30o, 120o, 135o and 150o tended to be larger than with H/D = 2 due to flow attachment near the pin surface. However, the local Nusselt number on pin surface with θ=45o and 60o tends to be smaller than with H/D = 2, due to flow separation downstream.

250 Endwall surface Pin surface

200 150 100 50 0

30o

45o

60o 120o 90o Pin inclination angle (θ)

135o

150o

Fig. 28. Overall average Nusselt number on enwall and pin surface in case of H/D = 3.2, Re = 27,000.

Nomenclature Reynolds numbers between 14,000 and 32,860. The effects of pin inclination were investigated for the angles θ= 30o, 45o, 60o, 90o, 120o, 135o, and 150o. The pin height was either H = 2D (62.5% of the channel height) or 3.2D (equal to channel height). The pin-to-pin distance (S) was fixed at S = 2D. Numerical simulations were used to investigate fluid flow and heat transfer characteristics. The main results obtained from this study are as follows: 1. In case H/D = 2, the pin inclination affects strongly the heat transfer characteristics on endwall surface. The local Nusselt number upstream of the pins with θ= 30o, 45o and 60o tends to increase with inclination and the local Nusselt number downstream of the pin tends to significantly increase with larger area than with θ= 90o. The heat transfer is improved by a counter-rotating vortex pair near the heat transfer surface. These vortices will induce air flow to impinge the heat transfer surface downstream. The local Nusselt number downstream of pins tends to decrease with increasing pin inclination among θ= 90o to 120o, 135o and 150o. The jet-like flow on the pin surface turns away from the heat transfer surface. The heat transfer contribution of counter-rotating vortices then becomes small on endwall surface. In case H/D3.2, the trends of local Nusselt number from pin inclination were similar to those with H/D = 2. Nevertheless, the heat transfer was lower than for H/D = 2. The counter-rotating vortices behind the pin cannot approach the heat transfer surface as close as they did with H/ D = 2. 2. In case of H/D = 2, the overall average Nusselt number with θ= 30o, 45o and 60o was higher than with θ= 90o, for any Reynolds number tested. On the other hand, the inclinations θ= 120o, 135o and 150o did not improve the overall average Nusselt number. In case H/ D = 3.2, the pin inclination could not improve the overall average Nusselt number on endwall surface from that with θ= 90o. The friction factor for H/D = 2 and 3.2 was largest with θ= 90o, but inclinations θ=30o and 45o strongly enhanced the thermal performance over that with θ= 90o for all Reynolds numbers. At Re = 14,000 in case H/ D = 2, the thermal performance with θ= 30o and 45o was about 45.8% and 36.1% higher, respectively, than that with θ= 90o. At Re = 14,000 in case of H/D = 3.2, the thermal performance with θ= 30o and 45o was about 29.9% and 11.4% higher, respectively, than that with θ= 90o. 3. With θ= 90o, the region of wake flow for H/D = 3.2 behind the pin was larger than for H/D = 2. With θ= 30o, 45o and 60o, jet-like flow generates a pair of counter-rotating vortices behind the pin near the heat transfer surface for H/D = 2, but the counter-rotating vortices behind the pin with H/D = 3.2 cannot attach to the heat transfer surface as closely as with H/D = 2. Then the heat transfer contribution of counter-rotating vortices becomes smaller than with H/D = 2. The counter-rotating vortices downstream of inclined pins with H/D = 2 and 3.2 may destroy the wake flow. With θ= 120o, 135o and 150o, wake flow formed behind the pin and its size decreased with inclination among these cases. The effect of counter-rotating vortices was small on heat transfer from the endwall surface. The counter-rotating vortices improved heat transfer on the pin surface. 4. In case H/D = 2, the local Nusselt number in front of the pins with θ= 90o, 60o and 45o was significantly high at head of the pin due

A D Dh f h hc H I k L Nu Nu y Nu Nu 0 ΔP q̇loss, conv q̇input q̇loss, rad Re S Tam Tin Tout Ts Tw, Tw V Vc

heat transfer area, (m2) pin diameter, (m) hydraulic diameter of wind tunnel, (m) friction factor, (−) local heat transfer coefficient, (W/m2 K) natural convection coefficient, (W/m2 K) pin height, (m) electrical current, (Ampere) thermal conductivity, (W/m K) the length between pressure measurement points, (m) local Nusselt number, (−) spanwise average Nusselt number, (−) overall average Nusselt number, (−) Nusselt number of the smooth rectangular channel, (−) pressure drop in test section, (Pa) heat loss due to natural convection, (W/m2) heat flux input, (W/m2) heat loss due to radiation, (W/m2) Reynolds number, (−) pin-to-pin distance, (m) air mean flow temperature, (°C) inlet mean temperature, (°C) outlet mean temperature, (°C) environmental temperature, (°C) local wall temperature and average wall temperature, (°C) electrical voltage, (Volt) air velocity at the center of wind tunnel, (m/s)

Greek symbol θ υ ρ σ εTLC η

pin inclined angle, (o) kinematic viscosity, (m2/s) density, (kg/m3) stefan-Boltzmann constant, (W/m2K4) emissivity coefficient of TLC sheet, (−) thermal performance factor, (−)

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