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Research Papers

Thermal-Boundary-Layer Response to Convected Far-Field Fluid Temperature Changes

[+] Author and Article Information
Hongwei Li

School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907

M. Razi Nalim1

Department of Mechanical Engineering, Indiana University-Purdue University Indianapolis, Indianapolis, IN 46202mnalim@iupui.edu

1

Corresponding author.

J. Heat Transfer 130(10), 101001 (Aug 07, 2008) (6 pages) doi:10.1115/1.2953239 History: Received August 07, 2007; Revised December 23, 2007; Published August 07, 2008

Fluid flows of varying temperature occur in heat exchangers, nuclear reactors, nonsteady-flow devices, and combustion engines, among other applications with heat transfer processes that influence energy conversion efficiency. A general numerical method was developed with the capability to predict the transient laminar thermal-boundary-layer response for similar or nonsimilar flow and thermal behaviors. The method was tested for the step change in the far-field flow temperature of a two-dimensional semi-infinite flat plate with steady hydrodynamic boundary layer and constant wall temperature assumptions. Changes in the magnitude and sign of the fluid-wall temperature difference were considered, including flow with no initial temperature difference and built-up thermal boundary layer. The equations for momentum and energy were solved based on the Keller-box finite-difference method. The accuracy of the method was verified by comparing with related transient solutions, the steady-state solution, and by grid independence tests. The existence of a similarity solution is shown for a step change in the far-field temperature and is verified by the computed general solution. Transient heat transfer correlations are presented, which indicate that both magnitude and direction of heat transfer can be significantly different from predictions by quasisteady models commonly used. The deviation is greater and lasts longer for large Prandtl number fluids.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Finite-difference grid for the Keller-box scheme

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Figure 2

Present-method numerical (dots) and analytical (line) solutions of the heat equation for a range of τ+

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Figure 3

Temperature response to the step change in incoming fluid temperature, with no initial thermal boundary layer

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Figure 4

Temperature response to a step change in incoming fluid temperature, with an initial thermal boundary layer (R=0.5)

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Figure 5

Temperature response to a step change in incoming fluid temperature with an initial thermal boundary layer (R=2.0)

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Figure 6

Transitions of the local Nusselt number for step changes R=0.5 and R=2.0 at different Pr

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