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RESEARCH PAPERS: Natural and Mixed Convection

# Numerical Simulation of Mixed Convective Flow Over a Three-Dimensional Horizontal Backward Facing Step

[+] Author and Article Information
J. G. Saldana, N. K. Anand

Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA

V. Sarin

Department of Computer Science, Texas A&M University, College Station, TX 77843, USA

J. Heat Transfer 127(9), 1027-1036 (Apr 27, 2005) (10 pages) doi:10.1115/1.2005272 History: Received May 27, 2004; Revised April 27, 2005

## Abstract

Laminar mixed convective flow over a three-dimensional horizontal backward-facing step heated from below at a constant temperature was numerically simulated using a finite volume technique and the most relevant hydrodynamic and thermal features for air flowing through the channel are presented in this work. The channel considered in this work has an aspect ratio $AR=4$, and an expansion ratio $ER=2$, while the total length in the streamwise direction is 52 times the step height $(L=52s)$ and the step length is equal to 2 times the step height $(l=2s)$. The flow at the duct entrance was considered to be hydrodynamically fully developed and isothermal. The bottom wall of the channel was subjected to a constant high temperature while the other walls were treated to be adiabatic. The step was considered to be a thermally conducting block.

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## Figures

Figure 1

Schematic of the three-dimensional backward facing step

Figure 2

xu line for the stepped wall (z∕W=0 wall and z∕W=1 central plane)

Figure 3

Local Nusselt number distribution for the stepped wall at x∕s=6.6 (z∕W=0 wall and z∕W=1 central plane)

Figure 4

Average Nusselt number for a mixed convective flow through a straight rectangular channel Gr=1.55×106, Re=500 and Pr=6.5

Figure 5

xu-line distribution for mixed convection over a 3D backward facing step

Figure 6

Spanwise average of the streamwise shear stress component along the bottom wall

Figure 7

Spanwise averaged Nusselt number distribution for the mixed convective flow over a 3D backward facing step

Figure 8

u- velocity profiles at plane z=0.02 at different x positions (a) forced convection (b) Ri=3, (c) Ri=2, (d) Ri=1

Figure 9

v velocity at different x and y planes

Figure 10

w velocity component at different x and y planes

Figure 11

Temperature contours and velocity vectors at constant x planes (a) Ri=3, (b) Ri=2, (c) Ri=1, (d) forced convection

Figure 12

Temperature distribution inside the back-step for the central plane z=0.02 (a) ks=386 (copper) (b) ks=64 (carbon steel AISI 1010)

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