Abstract
In this study, the constitutive relation for the heat flux vector is derived to be the Fourier's law of heat conduction with a variable thermal conductivity and time-fractional order. The Stokes' flow of unsteady incompressible thermoelectric fluid due to a moving plate in the presence of a transverse magnetic field is molded. Stokes' first problem is solved by applying Laplace transform with respect to time variable and evaluating the inverse transform integrals by using a numerical approach. Numerical results for the temperature and the velocity distributions are given and illustrated graphically for given problem. The results indicate that the thermal conductivity and time-fractional order play a major role in the temperature and velocity distributions.
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•We derived the fractional thermoelectric heat transfer equation with variable thermal conductivity.•First Stokes' problem of thermoelectric fluid is solved by applying Laplace transform with respect to time variable.•Both the fractional order of heat transfer and thermal conductivity has the same effect on the thermoelectric fluid flow.