TY - JOUR
T1 - Improving the accuracy of heat balance integral methods applied to thermal problems with time dependent boundary conditions
AU - Mitchell, S. L.
AU - Myers, T. G.
PY - 2010/9
Y1 - 2010/9
N2 - 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.
AB - 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.
KW - Heat balance integral method
KW - Heat flow
KW - Refined integral method
KW - Time dependent boundary conditions
UR - http://www.scopus.com/inward/record.url?scp=79960715789&partnerID=8YFLogxK
U2 - 10.1016/j.ijheatmasstransfer.2010.04.015
DO - 10.1016/j.ijheatmasstransfer.2010.04.015
M3 - Article
AN - SCOPUS:79960715789
SN - 0017-9310
VL - 53
SP - 3540
EP - 3551
JO - International Journal of Heat and Mass Transfer
JF - International Journal of Heat and Mass Transfer
IS - 17-18
ER -