The Heat-Balance Integral and Its Application to Problems Involving a Change of Phase

Abstract

An approximate mathematical technique utilizing the “heat-balance integral” is presented for solving for the location of the melt line in heat-conduction problems involving a change of phase. Analytical expressions are derived when (a) boundary temperature is fixed; (b) heat flux at boundary is given; (c) heat flux is generated aerodynamically or by radiation; (d) heat flux at boundary is given and melt is completely removed; (e) heat flux at boundary is given, and at time t₀ melt begins to vaporize. Comparisons with known solutions have been made when available, and ultimately all the solutions are presented in graphical form.