**ABSTRACT
**

The present works focusses on numerical and analytical investigations of the thermal stability of a radiative-convective moving porous fin with temperature-dependent thermal conductivity and internal heat generation are presented using differential transformation and finite difference methods. The results of the two methods are compared and very good agreements are established. It is depicted that the results of differential transform and finite difference methods are very good agreement with the results of the exact analytical method. However, this only happen in the range of thermal stability of the fin for the linear problem. As the value of the thermo-geometric parameter increases to a level of thermal instability, the results of the exact analytical method become inaccurate. Further investigations reveal that increase in the internal heat generation leads to increase in the range of value for the thermal stability of the fin. This shows that internal heat generation can be used to control the thermal instability in the fin. However, this must be done with the caution and proper selection of the operating parameters. It was established that the numerical and the approximate analytical methods are used for deeper understanding to predict the anomalies in the fin which are not possible in the exact analytical method. Therefore, the operational parameters of the fin must be carefully selected to ensure that the fin retains its primary purpose of removing heat from the primary surface.

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