Finite Element Method for Analysis of Conjugate Heat Transfer between Solid and Unsteady Viscous Flow

Abstract

A fractional four-step finite element method for analyzing conjugate heat transfer between solid and unsteady viscous flow is presented. The second-order semi-implicit Crank-Nicolson scheme is used for time integration and the resulting nonlinear equations are linearized without losing the overall time accuracy. The streamline upwind Petrov-Galerkin method (SUPG) is applied for the weighted formulation of the Navier-Stokes equations. The method uses a three-node triangular element with equal-order interpolation functions for all the variables of the velocity components, the pressure and the temperature. The main advantage of the method presented is to consistently couple heat transfer along the fluid-solid interface. Four test cases, which are the lid-driven cavity flow, natural convection in a square cavity, transient flow over a heated circular cylinder and forced convection cooling across rectangular blocks, are selected to evaluate the efficiency of the method presented

The Effect of Water Evaporation in Automotive Windshield Defrosting

“…Thus, the initial heat loss to the ambient is primarily due to convection from the solid-ice layer. The congugate heat transfer between solid-ice layer and air can be computed numerically [29,30], or using empirical formulae. In still air, this heat loss from the top of the ice-layer to the ambient is from natural convection.…”