In the present study, the influence of numerical analysis involves the transfer of heat for moving fin under convection and radiation with fluid properties depending on internal heat generation is considered. The temperature field for the fin is derived based on the defined geometry. This is transformed into a linear model as per the boundary conditions. The dimensionless analysis is performed, and the equations obtained are solved by Runge-Kutta Fehlberg fourth-order method coupled with the shooting method. The effects of the relative parameters are studied and depicted graphically. Finally, the computational observation indicates that there is an enhancement of temperature variation under the influence of thermal conductivity gradient, heat generation, and opposite behavior results. In understanding the thermal characteristics of various effects, it was seen that thermo geometric film, radiation conduction, and Peclet number were very useful for many industrial applications. To validate the numerical scheme, a comparative study has been done with an earlier result on a few nondimensional parameters and was found in good agreement.
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