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Computation of conjugate heat transfer in the turbulent mixed convection regime in a vertical channel with multiple heat sources

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Abstract

This paper presents the results of a comprehensive numerical study to analyze conjugate, turbulent mixed convection heat transfer from a vertical channel with four heat sources, uniformly flush-mounted to one of the channel walls. The results are presented to study the effect of various parameters like thermal conductivity of wall material (k s), thermal conductivity of flush-mounted discrete heat source (k c), Reynolds number of fluid flow (Re s), modified Richardson number (Ri +) and aspect ratio (AR) of the channel. The standard k-ε turbulence model, modified by including buoyancy effects with physical boundary conditions, i.e. without wall functions, has been used for the analysis. Semi-staggered, non-uniform grids are used to discretise the two dimensional governing equations, using finite volume method. A correlation, encompassing a wide range of parameters, is developed for the non-dimensional maximum temperature (T *) using the asymptotic computational fluid dynamics (ACFD) technique.

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Abbreviations

AR:

aspect ratio of the channel (H/S)

Gr +s :

modified Grashof number, based on volumetric heat generation (β gS3ΔT ref/ν2)

H :

height of the channel (m)

H 1 :

height of the heat source (m)

k :

turbulent kinetic energy (m2/s2)

k c :

thermal conductivity of heat source (W/m K)

k f :

thermal conductivity of fluid (W/m K)

k * :

non-dimensional turbulent kinetic energy (k/(V ∞)2)

k s :

thermal conductivity of channel wall (W/m K)

p * :

non-dimensional pressure ( \({\overline{p}} \mathord{\left/ {\vphantom {{\overline{p}} {\rho V_{\infty}^{2}}}} \right. \kern-\nulldelimiterspace} {\rho V_{\infty}^{2}}\))

\(\bar{p}\) :

time averaged pressure (N/m2)

\({\dot{q}}^{\prime\prime\prime}\) :

rate of volumetric heat generation from heat source (W/m3)

Re s :

Reynolds number based on S (V ∞ S/υ)

Ri :

Richardson number (Gr/Re 2)

Ri + :

modified Richardson number (Gr +s /Re 2s )

S :

spacing between two channel walls or width of the square enclosure (m)

T :

temperature at any point (K)

T * :

non-dimensional temperature (T − T ∞/ΔT ref)

T * C :

non-dimensional maximum temperature on the conducting wall

T * C :

temperature on the conducting wall (K)

T max :

maximum temperature (K)

T *max :

maximum non-dimensional temperature

T w :

wall temperature (K)

T ∞ :

uniform inlet temperature (K)

t * :

non-dimensional time (t v ∞/S)

ΔT ref :

reference temperature difference ( \({\dot{q}}^{\prime\prime\prime} 4{H}_{1}\delta/{k}_{\rm f}\))

\(\bar{u}\) :

time averaged x-component of velocity (m/s)

u * :

non-dimensional horizontal velocity ( \({\overline{u}} \mathord{\left/ {\vphantom {{\overline{u}} {V_{\infty}}}} \right. \kern-\nulldelimiterspace} {V_{\infty}}\))

\(\bar{v}\) :

time averaged y-component of velocity (m/s)

v * :

non-dimensional vertical velocity ( \({\overline{v}} \mathord{\left/ {\vphantom {{\overline{v}} {V_{\infty}}}} \right. \kern-\nulldelimiterspace} {V_{\infty}}\))

V ∞ :

uniform inlet velocity (m/s)

x * :

non-dimensional horizontal coordinate (x/S)

y * :

non-dimensional vertical coordinate (y/S)

β:

coefficient of volume expansion (K−1)

δ:

thickness of channel wall (m)

ɛ:

dissipation rate of k (m2/s3)

ɛ* :

non-dimensional dissipation rate (ɛ S/(V ∞)3)

υ:

kinematic viscosity (m2/s)

υ * t :

turbulent eddy viscosity (m2/s)

References

  1. Kuyper RA, Meer ThH van der, Hoogendoorn CJ, Henkes RAWM (1993) Numerical study of laminar and turbulent natural convection in an inclined square cavity. Int J Heat Mass Transf 36:2899–2900

  2. Velusamy K, Sundararajan T, Seetharamu KN (2001) Interaction effects between surface radiation and turbulent natural convection in square and rectangular enclosures. ASME J Heat Transf 123:1062–1070

    Article  Google Scholar 

  3. Carr AD, Connor MA, Buhr HO (1973) Velocity, temperature and turbulence measurements in air for pipe flow with combined free and forced convection. ASME J Heat Transf 95:445–452

    Google Scholar 

  4. Pokas P, Pokas R (2003) Local turbulent opposing mixed convection heat transfer in inclined flat channel for stably stratified airflow. Int J Heat Mass Transf 46:4023–4032

    Article  Google Scholar 

  5. Zhang X, Dutta S (1998) Heat transfer analysis of buoyancy-assisted mixed convection with asymmetric heating conditions. Int J Heat Mass Transf 41:3255–3264

    Article  Google Scholar 

  6. Nakajima M, Fukui K, Ueda H, Mizushina T (1980) Buoyancy effects on turbulent transport in combined free and forced convection between parallel plates. Int J Heat Mass Transf 23:1325–1336

    Article  Google Scholar 

  7. Inagaki T, Komori K (1995) Numerical modeling on turbulent transport with combined forced and natural convection between two vertical parallel plates. Numer Heat Transf A 27:417–431

    Google Scholar 

  8. Anand NK, Kim SH, Aung W (1990) Effect of wall conduction on free convection between asymmetrically heated vertical plates: uniform wall temperature. Int J Heat Mass Transf 33:1025–1028

    Article  Google Scholar 

  9. Kim SH, Anand NK, Aung W (1990) Effect of wall conduction on free convection between asymmetrically heated vertical plates: uniform wall heat flux. Int J Heat Mass Transf 33:1013–1023

    Article  Google Scholar 

  10. Lee S, Culham JR, Yovanovich MM (1991) Parametric investigation of conjugate heat transfer from microelectronic circuit boards under mixed convection cooling. In: International electronic packaging conference, San Diego, September 15–19, pp 421–446

  11. Gururaja Rao C, Balaji C, Venkateshan SP (2002) Effect of surface radiation on conjugate mixed convection in a vertical channel with a discrete heat source in each wall. Int J Heat Mass Transf 45:3331–3347

    Article  MATH  Google Scholar 

  12. Herwig H (1992) Combining asymptotic und numerical methods: the ACFD-approach in heat and mass transfer. Trends Heat Mass Moment Transf 2:43–54

    Google Scholar 

  13. Balaji C, Herwig H (2003) The use of ACFD approach in problems involving surface radiation and free convection. Int Commun Heat Mass Transf 30:251–259

    Article  Google Scholar 

  14. Premachandran B, Balaji C (2005) Mixed convection Heat transfer from a horizontal channel with protruding heat sources. Heat Mass Transf 41(6):510–518

    Article  Google Scholar 

  15. Bautista O, Mendez F, Trevino C (2001) The conjugate heat transfer from an internal heated small strip in a forced laminar flow. Heat Mass Transf 37:485–491

    Article  Google Scholar 

  16. Sathe SB, Joshi Y (1991) Natural convection from a heat generating substrate-mounted protrusion in a liquid-filled two dimensional enclosure. Int J Heat Mass Transf 34:2149–2163

    Article  Google Scholar 

  17. Mendez F, Trevino C (2000) The conjugate conduction-natural convection heat transfer along a thin vertical plate with non-uniform heat generation. Int J Heat Mass Transf 43:2149–2163

    Google Scholar 

  18. Rizk TA, Kleinstreuer C, Ozisik MN (1992) Analytical solution to the conjugate heat transfer problem of flow past a heated block. Int J Heat Mass Transf 35:1519–1525

    Article  Google Scholar 

  19. Markatos NC, Pericleous KA (1984) Laminar and turbulent natural convection in an enclosed cavity. Int J Heat Mass Transf 27:755–772

    Article  MATH  Google Scholar 

  20. Elsherbiny SM, Raithby GD, Hollands KGT (1982) Heat transfer by natural convection across vertical and inclined air layers. ASME J Heat Mass Transf 104:96–102

    Google Scholar 

  21. De Vahl Davis G (1983) Natural convection of air in a square cavity: a bench mark numerical solution. Int J Numer Methods Fluids 3:249–264

    Article  Google Scholar 

  22. Aung W, Worku G (1986) Developing flow and flow reversal in a vertical channel with asymmetric wall temperatures. ASME J Heat Transf 108:299–304

    Article  Google Scholar 

  23. Roy N. Mathews, Balaji C (2005) Numerical Simulation of conjugate, turbulent mixed convection in a vertical channel. In: 4th international conference on computational heat and mass transfer, Paris-Cachan, France vol 1, pp 257

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, 600 036, India

    Roy N. Mathews, C. Balaji & T. Sundararajan

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  1. Roy N. Mathews
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  2. C. Balaji
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  3. T. Sundararajan
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Correspondence to C. Balaji.

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Mathews, R.N., Balaji, C. & Sundararajan, T. Computation of conjugate heat transfer in the turbulent mixed convection regime in a vertical channel with multiple heat sources. Heat Mass Transfer 43, 1063–1074 (2007). https://doi.org/10.1007/s00231-006-0192-9

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