Calculation of the temperature of boundary layer beside wall with time-dependent heat transfer coefficient

Abstract

This paper proposes to investigate the changes in the temperature of external wall boundary layers of buildings when the heat transfer coefficient reaches its stationary state in time exponentially. We seek the solution to the one-dimensional parabolic partial differential equation describing the heat transfer process under special boundary conditions. The search for the solution originates from the solution of a Volterra integral equation of the second kind. The kernel of the Volterra integral equation is slightly singular therefore its solution is calculated numerically by one of the most efficient collocation methods. Using the Euler approach an iterative calculation algorithm is obtained, to be implemented through a programme written in the Maple computer algebra system. Changes in the temperature of the external boundary of brick walls and walls insulated with polystyrene foam are calculated. The conclusion is reached that the external temperature of the insulated wall matches the air temperature sooner than that of the brick wall.