Journal
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
Volume 53, Issue 17-18, Pages 3540-3551Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijheatmasstransfer.2010.04.015
Keywords
Heat balance integral method; Refined integral method; Heat flow; Time dependent boundary conditions
Categories
Funding
- Science Foundation Ireland Mathematics Initiative [06/MI/005]
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In this paper the two main drawbacks of the heat balance integral methods are examined. Firstly we investigate the choice of approximating function. For a standard polynomial form it is shown that combining the heat balance and refined integral methods to determine the power of the highest order term will either lead to the same, or more often, greatly improved accuracy on standard methods. Secondly we examine thermal problems with a time-dependent boundary condition. In doing so we develop a logarithmic approximating function. This new function allows us to model moving peaks in the temperature profile, a feature that previous heat balance methods cannot capture. If the boundary temperature varies so that at some time t > 0 it equals the far-field temperature, then standard methods predict that the temperature is everywhere at this constant value. The new method predicts the correct behaviour. It is also shown that this function provides even more accurate results, when coupled with the new CIM, than the polynomial profile. Analysis primarily focuses on a specified constant boundary temperature and is then extended to constant flux, Newton cooling and time dependent boundary conditions. (C) 2010 Elsevier Ltd. All rights reserved.
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