A mathematical analysis of non-linear unsteady heat conduction. I - General fundamental idea
Abstract
In this paper, a new analytical method is presented for the boundary value problem of the nonlinear unsteady heat conduction with temperature-dependent thermal properties. Two nonequilibrium integral functions have been introduced: a function of the thermal conductivity and a function of the heat capacity. By setting the integration intervals of these functions such as to satisfy a specified relation, the nonlinear heat conduction equation can be linearized. This method is applicable to the cases such as linear, quadratic, and exponential variations of the thermal conductivity and heat capacity.
- Publication:
-
JSME International Journal Series B
- Pub Date:
- October 1985
- Bibcode:
- 1985JSMEB..28.2341K
- Keywords:
-
- Boundary Value Problems;
- Conductive Heat Transfer;
- Nonlinear Equations;
- Unsteady Flow;
- Entire Functions;
- Numerical Analysis;
- Specific Heat;
- Temperature Dependence;
- Temperature Distribution;
- Thermal Conductivity;
- Fluid Mechanics and Heat Transfer