Some exact solutions of the fin problem with a power law temperature-dependent thermal conductivity

Application of Differential Transform Method to Thermoelastic Problem for Annular Disks of Variable Thickness with Temperature-Dependent Parameters

“…Moreover, because of the nonlinearity due to the temperature-dependent internal heat generation, the difference in the temperature and thermal stress distributions between different values ofc becomes more pronounced for a smaller value of B. Figure 5 depicts the temperature distributions for various values of n ∈ {0, 1, 2} with a fixed B value, as seen in [13][14][15]32], along with the related thermal stress distributions. Figure 5a indicates that the temperature decrease along the radius is more moderate for higher values of the HTC's exponent n. This result is consistent with that obtained by Liaw and Yeh [1].…”

“…With regard to the heat conduction problems with a temperature-dependent HTC, Kumakura et al [9] introduced a Runge-Kutta numerical solution, Takeyama et al [10] and Unal [11] developed an implicit form solution, and Abbasbandy and Shivanian [12] recently derived an exact implicit form solution. In addition, several analytical solutions were also derived by different approaches such as the Adomian decomposition method (ADM) [13], the Homotopy-perturbation method [14], and the classical Lie symmetry technique [15]. Moreover, heat conduction problems with temperature-dependent internal heat generation were analyzed by Zhu and Satvravaha [3], Unal [16], Gamayunov and Klinger [17], Moitsheki and Rowjee [18], and Aziz and Bouaziz [19].…”

Existence, uniqueness and construction of the solution of the energy transfer problem in a rigid and non-convex blackbody with temperature-dependent thermal conductivity

“…Since the thermal conductivity is assumed to be dependent of the temperature, this differential equation is nonlinear [3,16]. Phenomena involving temperature-dependent thermal conductivity have been increasingly studied, due to the necessity of providing more accurate simulations for the temperature distributions [2,4,6,8,10,[17][18][19][20][21][22][23].…”

Conservation laws and associated Lie point symmetries admitted by the transient heat conduction problem for heat transfer in straight fins

“…Lie symmetry analysis of a nonlinear fin equation in which the thermal conductivity is an arbitrary function of the temperature and the heat transfer coefficient is an arbitrary function of a spatial variable was performed, for example, by [7][8][9][10][11]. Recently, the study of fins in boiling liquids has been increasing enormously and it has been found that the heat transfer coefficient may not only be given by a constant but also depends on the temperature distribution between the heated surface and its adjacent fluid [12], see also [13]. Thus, the resulting equations becomes highly nonlinear even in the simplest one-dimensional analysis [14].…”