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

Abstract

In this paper, the solution of the problem of transient heat conduction in a thin circular plate subjected to some different types of boundary conditions is obtained in the form of infinite series by employing the integral transform technique. 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 a linear combination of temperature and its normal derivative is prescribed on the circular edge as well as on the plane surfaces of the plate. Using the expression for the temperature function, we determine the displacement function and stresses within the plate. The second type of boundary condition is that in which the upper surface is kept at arbitrary temperature, lower surface is kept at zero and circular edge is insulated. Two other problems involving boundary conditions similar to those of the second type are also discussed.

Keywords:

• Circular plate
• Plane state of stress
• Pseudo-steady temperature
• Transient heat conduction