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This paper aims at the transient heat transfer analysis on extended surfaceswith temperature-dependent thermal conductivity, constant internal heatgeneration, and five different geometries. The governing equations developed inthis work consider the effects of the function that describes the shapesstudied. To ensure a more effective thermal analysis, we investigated theimpact of the fin's surface area and its arc length on the convection term, andthe influence of the overall function of the fin profile affecting thevolumetric rate of stored thermal energy. The imposed boundary conditions areadiabatic type on the tip of the fin and prescribed base temperature. A hybridmathematical method, known as the Generalized Integral Transform Technique(GITT), was used to solve the cases presented here. The results obtained withGITT were firstly validated with FEM results, presenting excellent agreementbetween them, proving been a method suitable for handling non-linear problems.Physical effects on the temperature distribution and efficiency due to thethermo-geometric parameter (M), internal heat generation (Q), and variablethermal conductivity were investigated.The analysis shows that increasing M ordecreasing Q results in a longer transient period, regardless of the geometryassessed. Besides, the efficiency if the increasing linear shape is higher thanthose of the rectangular fin for any parameter choice. Moreover, depending onthe thermo-geometric value, the rectangular fin becomes more efficient amongthe remaining shapes. However, for higher values, those differences becomeundistinguished from each other, demonstrating a significant impact of thevarying cross-sectional area and the fin surface area on the overall thermalanalysis.

Transient heat transfer analysis of fins with variable surface area and  temperature-dependent thermal conductivity using an integral transform  technique