A semi-analytical method for solving the non-linear differential equation of a completely wet trapezoidal fin

Abstract

The assessment of shrinking/stretching on a completely wet trapezoidal fin exhibiting in- ternal generation of heat is performed mathematically. The controlling equations are turned dimensionless by incorporating non-dimensional variables into the formulation. The approx- imate analytical approach (ASM) is utilized to attain the fin’s temperature explicitly in a dimensionless manner. The physical components in the temperature are depicted graphically to interpret their implications. The dimensionless fin efficiency is also evaluated. Additionally, the dimensionless fin efficiency is assessed. The analytical outcomes confirm an excellent fit in contrast to the numerical result. Furthermore, an effective result for this kind of fin challenge is verified by the employed technique. This methodology is capable of being extended to address exponential fin systems in physical science and inspect the fin’s temperature characteristics.