Legendre wavelet residual approach for moving boundary problem with variable thermal physical properties

Abstract The main aim of the current article is to describe an uni-dimensional moving boundary problem with conduction and convection effect when thermal conductivity and specific heat varying linearly with temperature and time. The Mathematical model has nonlinearity due to presence of variable thermal conductivity and specific heat. A Legendre wavelet residual approach is introduced to get the solution of the problem with high accuracy. The surface heat flux is taken as an exponent function of time while latent heat is presented as an exponent function of position. Galerkin technique is used to obtain the numerical solution in case of constant physical properties while collocation technique is used for variable thermal physical properties. When it is considered that thermal physical properties are constant then obtained numerical solution was compared with exact solution and found in good acceptance. The effect of convection and variable thermal conductivity with time and temperature on the location of the moving layer thickness is analyzed. Further the effect of Peclet number and other physical parameters on the location of moving layer thickness are discussed in detail.