Transient temperature distributions in simple conducting bodies steadily heated through a laminar boundary layer

An analysis is made of the transient heat-conduction effects in three simple semi-infinite bodies: the flat insulated plate, the conical shell, and the slender solid cone. The bodies are assumed to have constant initial temperatures and, at zero time, to begin to move at a constant speed and zero angle of attack through a homogeneous atmosphere. The heat input is taken as that through a laminar boundary layer. Radiation heat transfer and transverse temperature gradients are assumed to be zero. The appropriate heat-conduction equations are solved by an iteration method, the zeroeth-order terms describing the situation in the limit of small time. The method is presented and the solutions are calculated to three orders which are sufficient to give reasonably accurate results when the forward edge has attained one-half the total temperature rise (nose half-rise time). Flight Mach number and air properties occur as parameters in the result. Approximate expressions for the extent of the conduction region and nose half-rise times as functions of the parameters of the problem are presented. (author)