Transient Surface Heating of Large Solids Subject to Surface Heat Loss

Attention is focused on two classes of problems for the heating of semi-infinite solids subject to surface heat loss governed by Newton's Law of Cooling. A solution in the form of a definite integral is obtained for time independent sources having circular symmetry and for sources having symmetry about a line on the surface. These transient solutions generalize and extend a number of special case results previously described in the literature. For a uniform strip source, a steady state solution in the form of tabulated functions is obtained which is valid for all values of the space coordinates. Extensive graphs are included depicting the behavior of the dimensionless temperature as a function of the various dimensionless parameters for several of the most commonly used source functions. (Author)