Spline-functions method for solving thermal conductivity problems

Abstract

There are many cases in 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 thermal conductivity for the infinitely extended plate: at temperaturedependent thermophysical material properties and at nonlinear initial and boundary conditions of the first kind on the plate sides. For accuracy evaluation of the solution of the heat conduction equation by using spline-method the standard problems are created for one-dimensional infinite flat plane that have the exact analytical solutions. This paper shows the use of spline method for the solution of transient heat conduction problem gives an error of no more than 1?10?5, which satisfies an obtaining of the sufficient accuracy to solve many practical problems.