Summary: We consider numerically a laminar flow of water on an ice layer subjected to slip condition. The paper describes a parametric mathematical model to simulate the coupled heat and mass transfer occurring in moving boundary problems associated with a quasi steady state steady flow process. The discretization technique of elliptic governing differential equations of mass, momentum and energy is based on the control-volume finite difference approach and enthalpy method. The results illustrate the distribution of heat transfer coefficient, ice melting thickness, slip velocity on solid moving boundary and boundary layer thickness for some values of slip velocity coefficient.