Solution Of Nonlinear Heat Conduction Problem Research Articles

On the integral transform method in nonlinear heat-conduction problems for bodies of complicated shape

Using the construction procedure of numerical-analytic methods and the boundary element technique, we extend the integral transform method to the solution of nonlinear heat-conduction problems for bodies of nonstandard shape.

Solution of nonlinear heat-conduction problems for a semitransparent body

We solve the nonlinear heat-transfer problem in a semitransparent optically thick body by the finite-differences method in combination with the small-parameter method.

Solution of nonlinear heat-conduction problems in a medium with phase transitions

A new method is proposed for solving one-dimensional nonlinear heat-conduction problems in a medium having any number of phase transitions (nonlinear Stefan problems). The method consists of a direct calculation of the isotherms and reduces to the Cauchy problem for a system of ordinary differential equations.

Generalization of the nonlinear-resistance method to an arbitrary thermal-conductivity-temperature relationship for steady-state heat-conduction problems

The method previously proposed by the author for solution of nonlinear heat-conduction problems is extended to the case in which there is an arbitrary relationship between the thermal conductivity and the temperature. The possibility of using the method to solve nonsteadystate problems is considered.

On an approximate method of solution of nonlinear heat-conduction problems

An approximate method is presented for the solution of problems of transient heat conduction in solids with thermal conductivity and specific heat linearly dependent on temperature.

The solution of non-linear heat-conduction problems on the Pilot Ace

A method, suitable for use on an automatic computer, is developed for the solution of the heat-conduction equation. The treatment of latent heat is discussed and the method applied to a simple case. An Ace programme is briefly described, and the results obtained for a typical experimental case are given in graphical form.