An improved lumped analysis for transient heat conduction by using the polynomial approximation method

In this study, unsteady state one-dimensional heat conduction is analyzed using a polynomial approximation method. As a classical lumped model is only applicable for use with Biot numbers of less than 0.1, and additionally, it cannot be used for high-temperature gradients within the region, an improved lumped model is implemented for a typical long slab, long cylinder and sphere. It has been shown that in comparison to a finite difference solution, the improved model is able to calculate average temperature as a function of time for higher value of Biot numbers. The comparison also shows that the presented model has better accuracy when compared with others recently developed models. The simplified relations obtained in this study can be used for engineering calculations in many conditions.