Numerical Investigation of the Heat Transfer Dynamics of a Rough Semispherical Extended Surface Using the Keller‐Box and Chebyshev Collocation Methods

ABSTRACT We consider heat transfer by natural convection with radiation effects on a rough, wet, semispherical fin. The wetness on the fin surface with varying roughness, compounded with the internal heat generation and their influence on the fin's thermal profile and heat transfer rate, is investigated. The governing equation of the model is nondimensionalized, and the resulting nonlinear differential equation is numerically solved by the Keller‐box method and validated using the Chebyshev collocation method subject to quasilinearization. The robustness of these numerical methods is tabulated, and the impact of the critical dimensionless parameters on the thermal profile of the extended surface and the heat transfer rate along it is analyzed graphically and quantitatively. Fin efficiency is also computed, and the influence of the pertinent parameters on it is inferred. The study reveals that the fin's thermal profile is enhanced with a surge in the generation number, temperature‐dependent heat generation parameter, surface roughness, ambient temperature, and exponent of the convective heat transfer, while there is a significant drop in the heat transfer rate with a surge in these parameters. The wetness, convection, and radiation parameters assist the heat transfer rate throughout the fin and degrade its thermal profile.