An integral solution of moving boundary problems (Q1073694)

An integral method is presented that utilizes Galerkin functions and leads to closed-form solutions for temperature distribution in the liquid and solid phase. Unlike methods using quasi-steady assumptions, this method retains the contribution of the internal heat capacity of solid and liquid, therefore, accommodating problems involving time-dependent temperature along the boundary. The method is applied to classical one- and two-dimensional solidification problems to test its accuracy. The agreement between this method and the existing one-dimensional boundary- layer integral method is excellent. The two-dimensional results for a square geometry are compared to the experimental data obtained for octadecane.