Temperature field of an infinite plate in the case of a variable heat-exchange coefficient

Kozlov, Vladimir

doi:10.1007/bf00835367

Cited by 2 publications

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“…Early studies using approximate methods include those of Ivanov et al [10][11][12], which transformed the governing equation into a nonlinear equation using the change of variables and omitted the nonlinear term from the derived equation by restricting the research object to thin bodies. Kozlov [13] reduced the original problem to finding a solution to an infinite number of simultaneous ordinary differential equations, approximating it by a finite number. In addition, the application of the Laplace-Carson integral transform [7], finite integral transform methods with time-dependent eigenvalues [14,15], and Lie point symmetry analysis [16] were reported.…”

Section: Introductionmentioning

confidence: 99%

An Analytical Solution for Transient Heat Conduction in a Composite Slab with Time-Dependent Heat Transfer Coefficient

Chiba

2018

Mathematical Problems in Engineering

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An analytical solution is derived for one-dimensional transient heat conduction in a composite slab consisting of layers, whose heat transfer coefficient on an external boundary is an arbitrary function of time. The composite slab, which has thermal contact resistance at − 1 interfaces, as well as an arbitrary initial temperature distribution and internal heat generation, convectively exchanges heat at the external boundaries with two different time-varying surroundings. To obtain the analytical solution, the shifting function method is first used, which yields new partial differential equations under conventional types of external boundary conditions. The solution for the derived differential equations is then obtained by means of an orthogonal expansion technique. Numerical calculations are performed for two composite slabs, whose heat transfer coefficient on the heated surface is either an exponential or a trigonometric function of time. The numerical results demonstrate the effects of temporal variations in the heat transfer coefficient on the transient temperature field of composite slabs.

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