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Research Papers: Radiative Heat Transfer

A Novel, Noniterative Inverse Boundary Design Regularized Solution Technique Using the Backward Monte Carlo Method

[+] Author and Article Information
M. Mosavati

Department of Mechanical Engineering,
Science and Research Branch,
Islamic Azad University,
Tehran, 1477893855, Iran
e-mail: Maziar_mosavati@yahoo.com

F. Kowsary

Department of Mechanical Engineering,
University College of Engineering,
University of Tehran,
Tehran, 1439957131, Iran
e-mail: fkowsari@ut.ac.ir

B. Mosavati

Department of Mechanical Engineering,
Science and Research Branch,
Islamic Azad University,
Tehran, 1477893855, Iran
e-mail: Babak_mosavati@yahoo.com

For example, if enclosure consisted of Nh heater elements and Nd design elements, the number of required distribution factors is merely Nh × Nd.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received July 5, 2011; final manuscript received October 22, 2012; published online March 20, 2013. Assoc. Editor: William P. Klinzing.

J. Heat Transfer 135(4), 042701 (Mar 20, 2013) (7 pages) Paper No: HT-11-1331; doi: 10.1115/1.4022994 History: Received July 05, 2011; Revised October 22, 2012

In this paper, the inverse radiation boundary problem is solved using a simplified backward Monte Carlo method (MCM) for cases in which radiation is the dominant mode of heat transfer (i.e., radiative equilibrium). For an N-surface enclosure, N2 radiative transfer factors are required to carry out the radiant exchange calculations. In this paper, it is shown that when the enclosure is comprised of some adiabatic surfaces (as is nearly always the case in radiative furnaces), this number can be reduced considerably. This reduction in the required number of distribution factors causes a clear simplification in the formulation of the inverse problem and a substantial reduction in the computational time. After presenting the formulation for the inverse problem, standard test cases are solved to demonstrate the efficiency and the accuracy of the proposed method.

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Figures

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Fig. 1

Schematic of a radiative furnace

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Fig. 2

Sketch of a furnace with reradiating surfaces

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Fig. 3

Nondimensional temperature distribution (Φ(τ) = (T4-T24)/(T14-T24)) for a gray medium at radiative equilibrium between isothermal plates in present work

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Fig. 4

Sketch of three-dimensional furnace used in first test case

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Fig. 5

Dimensionless temperature distribution on heater surface in the first test case for diffuse reflection and optical thickness of τ = 1

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Fig. 6

Comparison of design and the calculated heat flux over step surface for diffuse reflection and optical thickness of τ = 1

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Fig. 7

Geometry of the furnace used in the second test case

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Fig. 8

Dimensionless temperature distribution on heater surface in the second test case for diffuse reflection and various optical thicknesses for 0, 1, and 10

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Fig. 9

Comparison of design and the calculated heat flux values over a hemisphere surface for diffuse reflection and various optical thicknesses for 0, 1, and 10

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