The Spline Method for the Solution of the Transient Heat Conduction Problem with Nonlinear Initial and Boundary Conditions for a Plate

摘要

There are many cases in the engineering practice when it is necessary to know the transient temperature field in a flat plate. At that, temperature distribution is studied experimentally or by calculation. However, the obtained calculation results do not always provide the required accuracy. This paper obtains the spline-method grade 3 defect 1, which allows simulating the process of the thermal conductivity for the infinitely extended plate at nonlinear initial and boundary conditions of the first kind on the plate sides. For accurate evaluation of the solution of the heat conduction equation with the help of the spline-method, the standard problem is created for a one-dimensional infinite flat plane which has the exact analytical solution. This paper shows the use of spline method for the solution of transient heat conduction problem which gives an error of no more than MO’5 and thus satisfies obtaining of the sufficient accuracy to solve many practical problems.