Improving the accuracy of heat balance integral methods applied to thermal problems with time dependent boundary conditions


Autoria(s): Mitchell, Sarah L.; Myers, T.G.
Contribuinte(s)

Centre de Recerca Matemàtica

Data(s)

2011

Resumo

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.

Formato

26

316793 bytes

application/pdf

Identificador

http://hdl.handle.net/2072/169270

Idioma(s)

eng

Publicador

Centre de Recerca Matemàtica

Relação

Prepublicacions del Centre de Recerca Matemàtica;1013

Direitos

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Palavras-Chave #Calor -- Transmissió #Dinàmica de fluids #53 - Física
Tipo

info:eu-repo/semantics/preprint