On the convergence of the heat balance integral method
نویسندگان
چکیده
Convergence properties are established for the piecewise linear heat balance integral solution of a benchmark moving boundary problem, thus generalising earlier results [Numer. Heat Transfer 8 (1985) 373]. A convergence rate of O(n ) is identified with minor effects at large values of the Stefan number b (slow interface movement). The correct O(n ) behaviour for incident heat flux is recovered for b ! 0 (pure heat conduction) as previously found [Numer. Heat Transfer 8 (1985) 373–382]. Numerical illustrations support the theoretical findings. 2005 Elsevier Inc. All rights reserved.
منابع مشابه
Numerical Solution of a Free Boundary Problem from Heat Transfer by the Second Kind Chebyshev Wavelets
In this paper we reduce a free boundary problem from heat transfer to a weakly Singular Volterra integral equation of the first kind. Since the first kind integral equation is ill posed, and an appropriate method for such ill posed problems is based on wavelets, then we apply the Chebyshev wavelets to solve the integral equation. Numerical implementation of the method is illustrated by two ben...
متن کاملConvergence of product integration method applied for numerical solution of linear weakly singular Volterra systems
We develop and apply the product integration method to a large class of linear weakly singular Volterra systems. We show that under certain sufficient conditions this method converges. Numerical implementation of the method is illustrated by a benchmark problem originated from heat conduction.
متن کاملEfficient quadrature rules for a class of cordial Volterra integral equations: A comparative study
A natural algorithm with an optimal order of convergence is proposed for numerical solution of a class of cordial weakly singular Volterra integral equations. The equations of this class appear in heat conduction problems with mixed boundary conditions. The algorithm is based on a representation of the solution and compound Gaussian quadrature rules with graded meshes. A comparative stud...
متن کاملThermodynamic analysis of a magnetohydrodyamic oldroyd 8-constant fluid in a vertical channel with heat source and slippage
Thermodynamic analysis of a steady state flow and heat transfer of an Oldroyd 8-constant fluid with effect of heat source, velocity slip and buoyancy force under tranverse a magnetic field is is carried out in this paper. The model for momentum and energy balance is tackled numerically using Method of Weighted Residual (MWR). Partition method is used to minimize the associated residuals. The re...
متن کاملBoundary temperature reconstruction in an inverse heat conduction problem using boundary integral equation method
In this paper, we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain. This problem consists of determining the temperature on the interior boundary curve from the Cauchy data (boundary temperature and heat flux) on the exterior boundary curve. To this end, the boundary integral equation method is used. Since the resulting system of linea...
متن کامل