APPLIED MECHANICS Non-Steady State Thermal Stresses in an Infinite Cylinder oi Rectangular or Circular Cross-Section

Let us consider an infinite cylinder whose cross-section has the form of a rectangle with sides a and b (Fig. 1). Let the temperature To of the cylinder be uniform To> 0 at a time t = 0. For t> 0, let the temperature.at the lateral surface be T = 0. Such a state will be realized if the cylinder with temperature To is immersed at the time t = 0 in a medium with a lower (T B = 0) temperature. The temperature field is described by the differential equation with the boundary conditions = 0, T and the initial condition (3) T(x,,a;a,0) = T0 = const, Fig. 1 where X is the coefficient of heat conduction, c — specific heat and o density. The double series x[n-|- m—2),2 m O.n e a>*+P'"'x cos an x t cos0, « JC2