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.