Some Exact Solutions of Nonlinear Fin Problem for Steady Heat Transfer in Longitudinal Fin with Different Profiles

M. D. Mhlongo, R. J. Moitsheki
2014 Advances in Mathematical Physics  
One-dimensional steady-state heat transfer in fins of different profiles is studied. The problem considered satisfies the Dirichlet boundary conditions at one end and the Neumann boundary conditions at the other. The thermal conductivity and heat coefficients are assumed to be temperature dependent, which makes the resulting differential equation highly nonlinear. Classical Lie point symmetry methods are employed, and some reductions are performed. Some invariant solutions are constructed. The
more » ... ffects of thermogeometric fin parameter, the exponent on temperature, and the fin efficiency are studied.
doi:10.1155/2014/947160 fatcat:omctr325d5c65aypqubww7oyze