Stresses Due to Thermal Trapping in Semi-Absorbing Materials Subjected to Intense Radiation

Abstract

Analytical results are presented for the thermal stresses resulting from “thermal trapping” in semi-absorbing materials subjected to symmetric and assymmetric radiation heating and convective cooling with finite heat transfer coefficient, h. The transient stresses during heat-up in both cases were found to be an inverse function of the heat transfer coefficient, h, and increase monotonically with the optical thickness, μa. In contrast, the steady state stresses were independent of h and exhibited a maximum at μa ≃ 1.3 for symmetric heating and at μa = 2 for assymmetric heating with zero stresses at μa = 0 and ∞. For the symmetrically heated plate, the transition from the transient to the steady-state condition involved a reversal in the sign of thermal stress at any position. For the assymmetrically heated plate the steady state maximum tensile thermal stresses occur at the position of the highest temperature, ie. the front surface.