Modified decomposition solution of convex fins of different profile index with all power law dependent thermal properties

Abstract

The present work investigates the non-linear mathematical model of one regular and two irregular convex fins where all thermo physical parameters are power law dependent. The extended length of regular convex fins varies parabolically along its length with a power exponent of ½ and two irregular convex fins with different power exponent ¼ and 9/10 respectively. The energy equations of one regular and two irregular convex fins are three different singular value equation but with a common non-linearity. The three different singular value equations are solved separately by the theory of modified Adomian decomposition method (MADM). The effects of power dependent thermal conductivity parameter, effect of conduction-convection parameter, effect of power exponent of heat transfer co-efficient, effect of power exponent of surface emissivity parameter, and effect of power exponent of heat generation number on the temperature distribution of three different convex fins are analyzed and compared separately.

Keywords

• Power law
• Singularity
• Forward operator
• Inverse operator