An asymptotic solution for shorttime transient heat conduction between two similar contacting bodies
Abstract
A shorttime asymptotic solution is developed for the problem of a halfspace, part of the surface of which is raised to a prescribed temperature. A Green's function formulation is used to demonstrate that the heat flux at the surface can be determined from a onedimensional analysis of the local heat conduction problem, except in the immediate vicinity of the edge of the heated area, where there is a boundary layer, the thickness of which grows with time. This boundary layer is then analyzed in more detail, using Williams' asymptotic technique. In particular, the additional total heat flux to the halfspace due to the boundary layer is determined and hence a twoterm asymptotic expression for the transient thermal resistance is obtained. The results are compared with existing solutions for the case of a circular heated area and show good agreement up to Fourier numbers of the order of 0.3.
 Publication:

International Journal of Heat and Mass Transfer
 Pub Date:
 May 1989
 DOI:
 10.1016/00179310(89)902433
 Bibcode:
 1989IJHMT..32..943B
 Keywords:

 Asymptotic Methods;
 Conductive Heat Transfer;
 Half Spaces;
 Transient Heating;
 Edges;
 Green'S Functions;
 Heat Flux;
 Temperature Profiles;
 Three Dimensional Models;
 Fluid Mechanics and Heat Transfer