A variety of methodologies have been used to explore heat transport enhancement, and the fin approach to inspect heat transfer characteristics is one such effective method. In a broad range of industrial applications, including heat exchangers and microchannel heat sinks, fins are often employed to improve heat transfer. Encouraged by this feature, the present research is concerned with the temperature distribution caused by convective and radiative mechanisms in an internal heat-generating porous longitudinal dovetail fin (DF). The Darcy formulation is considered for analyzing the velocity of the fluid passing through the fin, and the Rosseland approximation determines the radiation heat flux. The heat transfer problem of an inverted trapezoidal (dovetail) fin is governed by a second-order ordinary differential equation (ODE), and to simplify it to a dimensionless form, nondimensional terms are utilized. The generated ODE is numerically solved using the spectral collocation method (SCM) via a local linearization approach. The effect of different physical attributes on the dimensionless thermal field and heat flux is graphically illustrated. As a result, the temperature in the dovetail fin transmits in a decreasing manner for growing values of the porosity parameter. For elevated values of heat generation and the radiation-conduction parameter, the thermal profile of the fin displays increasing behavior, whereas an increment in the convection-conduction parameter downsizes the thermal dispersal. It is found that the SCM technique is very effective and more conveniently handles the nonlinear heat transfer equation. Furthermore, the temperature field results from the SCM-based solution are in very close accordance with the outcomes published in the literature.
The present examination elaborates on the thermal distribution and thermal stress analysis of a hyperbolic- and rectangular-profiled annular fin subjected to radiation, internal heat generation, and convection. The temperature-dependent nonlinear thermal properties governed by the power law are considered. The heat transport and steady-state thermal distribution in the fin are scrutinized using a mathematical model. The modeled equation has been converted into nonlinear ordinary differential equations (ODEs) using relevant non-dimensional terms. The resultant nonlinear coupled ODEs are solved analytically using the DTM-Pade approximant. The behavior of temperature distribution and thermal stress in the presence of various arising parameters is signified using graphical formations. The analytical results achieved from this investigation are compared to existing studies, and they show a good agreement. The thermal distribution in the fin is reduced as a result of elevated convective and radiative parameter values. Improved heat generation parameter values optimize the thermal distribution in the fin.
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