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A variety of engineering applications demand efficient and adaptable fin structures for the intensification of heat exchange. The semi-spherical fin structures are useful in the field of refrigeration, chemical processing systems, aerospace etc. In this regard, the present article numerically investigates the transient thermal behaviour of a fully wetsemi-spherical fin.The study incorporates the Darcy model as the fin is made up of porous material. Further, the fin is exposed to convective-radiative heat exchange and is subject to uniform motion. The heat balance equation has been reduced to get a nonlinear partial differential equation (PDE) which is computed by employing the finite difference method (FDM). The dimensionless terms are grouped together and their influence on the temperature distribution in a semi-spherical fin is studied. Also, the instantaneous heat transfer rate and the transient fin efficiency have been modelled and their variations with relevant parameters have been graphically depicted. And these are found be strong functions of Peclet number, wet porous nature and dimensionless time. As a main outcome the semi-spherical fin efficiency is positively influenced by the Peclet number. Along with the fundamental point of interest the results presented benefit the fin designing purposes.

The thermal behaviour of fully wet porous trapezoidal profiled longitudinal fin structures in the presence of natural convection and radiation has been scrutinized in the present analysis. The rectangular and trapezoidal profiles have been comparatively analysed. The Darcy's law has been incorporated to study the solid-fluid interactions. Further, the internal heat generation has been assumed to be a linear function of temperature. The obtained non-linear second order ordinary differential equation has been reduced and evaluated numerically. The impact of fully wet condition, porous nature, internal heat generation and other relevant parameters on the thermal profile and efficiency of trapezoidal and rectangular fin profiles has been interpreted graphically and discussed. It has been derived that the rectangular fin profile is more efficient than the trapezoidal profile.

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A massive number of engineering disciplines are concerned with the enhancement of heat exchange. In this regard, the present article focuses on thermal analysis of natural convection and radiation of a fractional ordered moving fin problem exposed to the magnetic field and also for the first time Adomian decomposition sumudu transform method (ADSTM) has been introduced to solve the energy balance equation comprising the Peclet number. The governing equations along with the corresponding boundary conditions were solved with the aid of ADSTM. The accuracy of the present work has been validated through comparison with the numerical results. ADSTM results are in good agreement with the existing numerical results. The effect of various parameters on the dimensionless temperature profile for different fractional values of α is discussed in graphical records. Here we found that the temperature distribution along the tip of the fin has a hike of 1.53%, as the Peclet number raises by 400% and also as the value of the Hartman number increases by 400%, there is a hike of 15.09% in a thermal gradient along the fin tip.