TITLE:
Simplified Integral Calculations for Radial Fin with Temperature-Dependent Thermal Conductivity
AUTHORS:
Okey Oseloka Onyejekwe
KEYWORDS:
Radiative Radial Fin, Temperature-Dependent Thermal Conductivity, Discretized Problem Domain, Boundary Integral Technique, Generic Elements, Assembly of Element Equations
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.7 No.3,
March
12,
2019
ABSTRACT: Numerical solution of a radiative radial fin with
temperature-dependent thermal conductivity is presented. Calculations are
implemented along the lines of a boundary integral technique coupled with
domain discretization. Localized solutions of the nonlinear governing
differential equation are sought on each element of the problem domain after
enforcing inter-nodal connectivity as well as the boundary conditions for the
dependent variables. A finite element-type assembly of the element equations
and matrix solution yield the scalar profile. Comparison of the numerical
results with those found in literature validates the formulation. The effects
of such problem parameters as radiation-sink
temperature, thermal conductivity, radiation-conduction fin parameter, volumetric
heat generation, on the scalar profile were found to be in conformity with the
physics of the problem. We also observed from this study that the volumetric
heat generation plays a significant role in the overall heat transfer activity
for a fin. For relatively high values of internal heat generation, a situation
arises where a greater percentage of this energy can not escape to the
environment and the fin ends up gaining energy instead of losing it. And the
overall fin performance deteriorates. The same can also be said for the radiation-conduction
parameter , whose increases can only
give physically realistic results below a certain threshold value.