TEMPERATURES, THERMAL STRESS, AND SHOCK IN HEAT-GENERATING PLATES OF CONSTANT CONDUCTIVITY AND OF CONDUCTIVITY THAT VARIES LINEARLY WITH TEMPERATURE

摘要

Working formulas are presented for the steady-state temperatures and thermal stress in heat-generating infinite plates of constant conductivity, and of conductivity that decreases linearly with temperature as the temperature increases, for the case in which the heat is generated uniformly throughout the plate thickness and both faces of the plate are equally cooled. In addition to exact formulas for the variable-conductivity plates, simpler approximate formulas are derived, and criteria for their applicability are indicated.nIt is shown that, of all planes in the plate, the plate surfaces are always under the greatest tension, and the midplane is under the greatest compression.nA criterion is indicated for determining the surface cooling conditions under which the thermal shocks at the surface and midplane will be smaller than, equal to, or greater than the steady-state thermal stresses at those planes. The shocks exceed the steady-state stresses only when the initial surface-cooling conditions of the transient state are more severe than the surface cooling conditions of the steady state. The criterion is expressed for heat-generating plates by a simple relation between a steady-state heat-transfer parameter of the heat-generating plate and the Biot number of the transient state.