This research investigates the numerical study of heat transfer between a fluid phase and the solid surface of a rectangular and convex parabolic fin, considering radiation and natural convection. This work helps to understand the design of advanced thermal devices employing fin systems under LTNE conditions. A mathematical model consisting of equations of solid and fluid phases is assumed to be distinct and coupled through local convective heat transfer. The governing equations of the mathematical model are non-linear ordinary differential equations reduced to dimensionless forms by applying suitable non-dimensional variables. The resultant set of equations, along with the boundary conditions are resolved using Runge-Kutta Fehlberg's (RKF 45) method, and the obtained solution is validated with pre-existing results. The primacy of crucial aspects of the temperature profile and average Nusselt number is demonstrated through graphs. From the graphs, it is found that both solid and fluid phase temperature is more in the rectangular profile when compared to the convex parabolic profile. Further, the rate of heat transfer is analysed for both the profiles using Response surface methodology (RSM). The response surface methodology is performed on derived rate of heat transfer as a response function for input factors for different parameters. Additionally, the accuracy of the model for rectangular and convex parabolic fin are found to be 97.47% and 96.36%, respectively.
Manjunatha et al. (Wed,) studied this question.