© 1991 by Oxford University Press
AN ASYMPTOTIC SOLUTION FOR SHORT-TIME TRANSIENT HEAT CONDUCTION BETWEEN TWO DISSIMILAR BODIES IN CONTACT
(
Mechanics Division, Naval Academy of Greece 33–35 G. Papandreou Street, 16231 Athens, Greece
Department of Mechanical Engineering and Applied Mechanics, University of Michigan Ann Arbor, Michigan 48109-2125, USA
)
Present address: Mechanics Division, School of Technology, Box 422, The Aristotle University of Thessaloniki, 54006, Greece.
A solution is obtained for the heat-conduction problem of two half-spaces of dissimilar materials, initially at different temperatures, brought into contact over half of their common boundary, the remainder of the interface being insulated. The solution is obtained by taking Laplace transforms in time and one space dimension and utilizing the Wiener-Hopf technique.
The results describe the local asymptotic fields near the boundary of a more general shape of contact area between the two bodies, at small values of time. It is therefore possible to develop a two-term short-time asymptotic expression for the heat exchanged between the bodies, one term being proportional to the area of the contact region and the other to its perimeter. This expression is derived in closed form except for an integral which depends on two dimensionless parameters—the ratios of the material conductivities and diffusivities.
Numerical values of the integral are presented for a wide range of these parameters.