THERMAL PROBLEMS WITH RADIATION BOUNDARY CONDITIONS

Abstract

Contact or crack problems in thermoelasticity are usually analysed with the idealised boundary conditions of perfect conduction or perfect insulation. These boundary conditions, while simplifying the mathematics, sometimes lead to unrealistic, singular thermoelastic fields. This paper formulates axisymmetric static thermal problems for a half-space when one boundary condition corresponds to partial insulation, either inside or outside the circle r = a, z = 0. Four important cases are considered and the problems are reduced to the solution of integro-differential equations of Abel type. In each case it is shown that the equation can be solved by using two simultaneous Fourier expansions of the unknown function.