MathematicalModeling of Transient Heat Conduction and Analysis of Thermal Stresses in a Thin Circular Plate

Abstract

In this paper, the solution of the problem of transient heat conduction in a thin circular plate subjected to two types of boundary conditions is obtained by employing the integral transform technique in the form of infinite series. It is assumed that the plate is in the plane state of stress and initially the temperature of the plate is kept at zero. The first type of boundary condition is that in which the upper surface is kept at arbitrary temperature, lower surface is kept at zero temperature and circular edge is insulated. In the literature, the origin of coordinates is taken to be the centre of the lower surface of the plate. The second type of boundary condition is that in which a linear combination of temperature and its normal derivatives is prescribed on the circular edge as well as on the plane surfaces of the plate. The true results are given in the form of figure.

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