Transient response of longitudinal rectangular fins to step change in base temperature and in base heat flow conditions

In this paper, we construct solutions for model describing heat transfer in longitudinal rectangular fins. The imposed boundary conditions are the step change in the base temperature and the step change in base heat flow. Both the thermal conductivity and the heat transfer coefficients are assumed to be power law temperature dependent. We employ the local and nonlocal symmetry techniques to analyze the problem at hand. In one case the reduced equation transforms to the tractable Ermakov–Pinney equation. Nonlocal symmetries are admitted when some arbitrary constants appearing in the governing equations are specified. The exact analytical steady state solutions which satisfy the prescribed boundary conditions are constructed. Since the obtained general exact analytical solutions for the transient state satisfy only the zero initial temperature and adiabatic boundary condition at the fin tip, we sort numerical solutions. The effects of the thermo-geometric fin parameter and the power law exponent on temperature distribution are studied.