Combined Laminar Mixed Convection and Surface Radiation using Asymptotic Computational Fluid Dynamics (ACFD) |
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Authors: | C Balaji M Hölling H Herwig |
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Institution: | (1) Department of Applied Thermodynamics, Hamburg University of Technology, Denickestrasse 17, 21073 Hamburg, Germany |
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Abstract: | This paper reports the use of the technique of combining asymptotics with computational fluid dynamics (CFD), known as asymptotic
computational fluid dynamics (ACFD), to handle the problem of combined laminar mixed convection and surface radiation from
a two dimensional, differentially heated lid driven cavity. The fluid under consideration is air, which is radiatively transparent,
and all the walls are assumed to be gray and diffuse and having the same hemispherical, total emissivity (ɛ). The computations
have been performed on FLUENT 6.2. The full radiation problem (i.e. all the walls are radiatively black corresponding to ɛ
= 1) is first taken up and the method of “perturbing and blending” is used wherein, first, limiting solutions of natural and
forced convection are perturbed, to obtain correlations for the weighted average convective Nusselt numbers for the full radiation case. These correlations are then blended suitably in order to obtain a composite
correlation for the weighted average convective Nusselt number that is valid for the entire mixed convection range, i.e., 0 ≤ Ri ≤ ∞. This correlation is then expanded in terms of ɛ to obtain an expression for the average convective Nusselt number that is valid for any ɛ in the range 0 ≤ ɛ ≤ 1. In so far as radiation heat transfer is concerned, using asymptotic
arguments, a new weighted average radiation Nusselt number is defined such that this quantity can be expanded just in terms of ɛ. Hence, by the use of ACFD, the number
of solutions required to obtain reasonably accurate correlations for both the convective and radiative heat transfer rates
and hence the total heat transfer rate (Nu
total = Nu
C + Nu
R), is substantially reduced. More importantly, the correlations for convection and radiation are asymptotically correct at
their ends. The effect of secondary variables like aspect ratio and the case of unequal wall emissivities can also be included
without significant additional effort. |
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Keywords: | |
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