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TECHNICAL BRIEFS

Conjugate Heat Transfer Study of a Two-Dimensional Laminar Incompressible Wall Jet Over a Backward-Facing Step

[+] Author and Article Information
P. Rajesh Kanna1

Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati-781 039, Indiaprkanna@gmail.com

Manab Kumar Das2

Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati-781 039, Indiamanab@iitg.ernet.in

1

Present address: Post-Doctoral Fellow, Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan.

2

Corresponding author.

J. Heat Transfer 129(2), 220-231 (Jul 15, 2006) (12 pages) doi:10.1115/1.2424235 History: Received February 27, 2006; Revised July 15, 2006

Steady-state conjugate heat transfer study of a slab and a fluid is carried out for a two-dimensional laminar incompressible wall jet over a backward-facing step. Unsteady stream function-vorticity formulation is used to solve the governing equation in the fluid region. An explicit expression has been derived for the conjugate interface boundary. The energy equation in the fluid, interface boundary and the conduction equation in the solid are solved simultaneously. The conjugate heat transfer characteristics, Nusselt number are studied with flow property (Re), fluid property (Pr), and solid to fluid conductivity ratio (k). Average Nusselt number is compared with that of the nonconjugate case. As k is increased, average Nusselt number is increased, asymptotically approaching the non-conjugate value.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic diagram and boundary conditions in a wall jet over backward-facing step problem: (a) schematic of the problem and (b) computational domain

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Figure 2

Schematic diagram and boundary conditions in a wall jet problem

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Figure 3

Laminar wall jet results. Re=500, Pr=1.4(a)u-velocity and (b) temperature.

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Figure 4

Backward-facing step flow with upstream channel problem. (a) Schematic diagram. and (b) Reattachment length for different Reynolds number.

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Figure 5

Grid independence study. Variation of Local Nu for k=5 and 50. (a)k=5. (b)k=50.

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Figure 6

Clustered grids used for the computation. (a) Fluid region. (b) Solid region.

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Figure 7

Conjugate interface temperature: Effect of Re (Pr=1, k=5, l=2h, s=1h, w=1h). (a) Along AB. (b) Along CD. (c) Along BC.

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Figure 8

Conjugate interface temperature: Effect of Pr (Re=400, k=5, l=2h, s=1h, w=1h). (a) Along AB. (b) Along CD. (c) Along BC.

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Figure 9

Conjugate interface temperature: Effect of k (Re=400, Pr=1, l=2h, s=1h, w=1h). (a) Along AB. (b) Along CD. (c) Along BC.

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Figure 10

Local Nusselt number: Effect of Re (Pr=1, k=5, l=2h, s=1h, w=1h). (a) Along AB. (b) Along CD. (c) Along BC.

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Figure 11

Local Nusselt number: Effect of Pr (Re=400, k=5, l=2h, s=1h, w=1h). (a) Along AB. (b) Along CD. (c) Along BC.

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Figure 12

Local Nusselt number: Effect of k (Re=400, Pr=1, l=2h, s=1h, w=1h). Nonconjugate case. (a) Along AB. (b) Along CD. (c) Along BC.

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