### Numerical Investigation of Transient Heat Conduction through a Thermal Insulation of Temperature Dependant Thermal Properties

#### Abstract

The two-dimensional transient heat conduction through a thermal insulation of temperature dependent thermal properties is investigated numerically using the FVM. It is assumed that this insulating material is initially at a uniform temperature. Then, it is suddenly subjected at its inner surface with a step change in temperature and subjected at its outer surface with a natural convection boundary condition associated with a periodic change in ambient temperature and heat flux of solar radiation. Two thermal insulation materials were selected. The fully implicit time scheme is selected to represent the time discretization. The arithmetic mean thermal conductivity is chosen to be the value of the approximated thermal conductivity at the interface between adjacent control volumes. A temperature dependent specific heat capacity proposed by a 4th Degree polynomial is fitted. A good agreement is obtained when the predicted results are compared with those obtained from the analytical solution.

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