Mathematical modeling of air duct heater using the finite difference method

Abstract

In this research, mathematical modeling of a duct heater has been performed using energy conservation law, Stefan-Boltzman law in thermal radiation, Fourier's law in conduction heat transfer, and Newton's law of cooling in convection heat transfer. The duct was divided to some elements with equal length. Each element has been studied separately and air physical properties in each element have been used based on its temperature. The derived equations have been solved using the fi nite difference method and consequently air temperature, internal and external temperatures of the wall, internal and external convection heat transfer coeffi cients, and the quantity of heat transferred have been calculated in each element and effects of the variation of heat transfer parameters have been surveyed. The results of modelling presented in this paper can be used for the design and optimization of heat exchangers.