Thermal Performance Optimization of Extended Surfaces under Natural Convection in Non-Newtonian Fluids

“Extended surfaces (fins) are widely employed in thermal systems to enhance heat dissipation, particularly under natural convection conditions where heat transfer rates are inherently limited. While extensive studies exist on fins operating in Newtonian fluids, the thermal behavior of fins interacting with non-Newtonian fluids—commonly encountered in industrial applications such as polymer processing, food engineering, biofluids, and slurry flows—has received comparatively less attention. In view of this, the present article theoretically investigates the problem of an optimum profiled fin dissipating heat by natural convection to a quiescent non-Newtonian fluid”. “This analysis is carried out by modelling the non-Newtonian behavior of the surrounding fluid using a power-law model, characterized by the flow behavior index (n), which accounts for shear-thinning and shear-thickening fluids. The governing energy equation for the fin is formulated by incorporating variable heat transfer coefficients arising due to natural convection in non-Newtonian fluids. Appropriate boundary conditions, including the insulated fin tip and prescribed base temperature, are applied to obtain physically realistic solutions. Using these conditions, generalized analytical expressions for the temperature distribution along the fin and the corresponding heat transfer rates are derived”. “A non-dimensional formulation is adopted to identify the key controlling parameters, particularly the fin parameter (M), which represents the combined effects of fin geometry, material properties, and convection strength. The influence of both the flow behaviour index (n) and the fin parameter (M) on thermal performance is systematically examined. The resulting temperature profiles, local heat transfer coefficients, and average heat transfer coefficients are presented and analyzed through graphical representations”. “The results reveal that the flow behaviour index (n) has a pronounced effect on the thermal behaviour of the fin. Variations in (n) significantly alter the convection characteristics, leading to noticeable changes in both local and average heat transfer coefficients. In addition, the fin parameter (M) strongly influences the rate of heat dissipation, indicating that optimal fin design must carefully account for both fluid rheology and fin geometry. One of the notable findings of this study is that, for a wide range of fin parameters, the local heat transfer coefficient does not vary monotonically along the fin length. Instead, it exhibits non-monotonic behaviour, highlighting the complex interaction between natural convection and non-Newtonian fluid properties”. “The theoretical results presented in this article provide valuable insights into the design and optimization of fins operating in non-Newtonian environments. The generalized solutions developed can serve as a useful reference for engineers and researchers involved in the thermal design of heat exchangers, electronic cooling systems, and industrial equipment where non-Newtonian fluids are present”.