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.
Highlights
The heat transfer and thermal conductivity of the wall boundary layers of buildings ensure the temperature potentials inside and outside the wall boundaries of buildings
We investigate how quickly the external wall boundary adopts the temperature of the air boundary layer under a constant temperature of the internal wall boundary
Our objective is to determine by continual approaches function u(0, t) which shows in time the change of temperature of the external wall boundary layer x = 0, taking into account that the air flow parallel to the wall modifies in time the α(t) heat transfer factor of the wall-air boundary layer according to exponential equation presented in formula (1)
Summary
The heat transfer and thermal conductivity of the wall boundary layers of buildings ensure the temperature potentials inside and outside the wall boundaries of buildings. We investigate how quickly the external wall boundary adopts the temperature of the air boundary layer under a constant temperature of the internal wall boundary Our objective is to determine by continual approaches function u(0, t) which shows in time the change of temperature of the external wall boundary layer x = 0, taking into account that the air flow parallel to the wall modifies in time the α(t) heat transfer factor of the wall-air boundary layer according to exponential equation presented in formula (1). The speed of the change in temperature perpendicularly impacting the wall is proportional to the difference in the temperature of the wall surface and the air and the proportion factor is heat transfer coefficient α0 obtained by formula (1)
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