Numerical modelling of heat transfer processes with supplementary data

Abstract

AbstractMathematical models of heat transfer processes are usually studied using formulation that is unique in the mathematical sense. For example, in solving initial‐boundary value problems in conduction heat transfer, the mathematical model consists of the governing equation and initial and boundary conditions. An extension of such an approach by introducing the supplementary information (or data) concerning the process has been proposed here as a method for verifying the accuracy of the model equations. This means that the mathematical model consists of more equations than unknowns which leads in consequence to a finite set of probable solutions. A criterion for choosing the most probable solution has been proposed. Special attention has been paid to numerical formulation. Computational methods have been derived using the Lagrange multipliers. Theoretical considerations have been illustrated by computing the temperature distribution inside a laboratory combustion chamber.