Heat transfer; longitudinal ﬁn; temperature-dependent heat transfer coefﬁcient and thermal conductivity; symmetry analysis; numerical solutions.
Transient heat transfer through a longitudinal ﬁn of various proﬁles is studied. The thermal conductivity and heat transfer coefficients are assumed to be temperature dependent. The resulting partial differential equation is highly nonlinear. Classical Lie point symmetry methods are employed and some reductions are performed. Since the governing boundary value problem is not invariant under any Lie point symmetry, we solve the original partial differential equation numerically. The effects of realistic ﬁn parameters such as the thermogeometric ﬁn parameter and the exponent of the heat transfer coefﬁcient on the temperature distribution are studied.