Spline Based Numerical Method for Heat Conduction Nonlinear Problems Solution

Numerical Solution of a Nonlinear Inverse Heat Conduction Problem

The inverse heat conduction problem also frequently referred as the sideways heat equation, in short SHE, is considered as a mathematical model for a real application, where it is desirable for someone to determine the temperature on the surface of a body. Since the surface itself is inaccessible for measurements, one is restricted to use temperature data from the interior measurements. From a ...

A Numerical Method for the Solution of Two- Dimensional Inverse Heat Conduction Problems

A numerical method for the solution of inverse heat conduction problems in two-dimensional rectangular domains is established and its performance is demonstrated by computational results. The present method extends Beck's' method to two spatial dimensions and also utilizes future times in order to stabilize the ill-posedness of the underlying problems. The approach relies on a line approximatio...

Solving an Inverse Heat Conduction Problem by Spline Method

In this paper, a numerical solution of an inverse non-dimensional heat conduction problem by spline method will be considered. The given heat conduction equation, the boundary condition, and the initial condition are presented in a dimensionless form. A set of temperature measurements at a single sensor location inside the heat conduction body is required. The result show that the proposed meth...

Bivariate Spline Method for Numerical Solution

We use the bivariate spline method to solve the steady state Navier-Stokes equations numerically. The bivariate spline we use in this paper is the space of splines of smoothness r and degree 3r over triangulated quadrangu-lations. The stream function formulation for the steady state Navier-Stokes equations is employed. Galerkin's method is applied to the resulting nonlinear fourth order equatio...

Numerical solution of transient heat conduction problems using improved meshless local Petrov-Galerkin method