Natural convection flow of second grade fluid with thermal radiation and damped thermal flux between vertical channels

What is it about?

In this article the natural convection flow of second grade fluid with thermal radiation is considered. The thermal balance equation is fractionalized by means of generalized Fourier’s law. Analytical solution for temperature field and semi analytical for velocity field has been obtained by Laplace transform. Later on, to find the inverse Laplace transform of velocity field, Stehfest’s algorithm has been used. Finally, some graphs have been sketched to discuss the influence of parameters. It is found that the thermal histories strongly influence the thermal transport for small values of time t. Also, the thermal transport can be enhanced if the thermal fractional parameter decreases or increasing. Velocity field is influenced by the damping of the by the temperature gradient introduced by the fractional derivative.

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Why is it important?

Unsteady natural convection flow of an incompressible second grade fluid with radiation effect inside vertical channels of width d has been focused here. Fractional generalized Fourier’s law has been used. Analytical solution for temperature field and semi analytical for velocity field has been obtained by Laplace transform. Later on, to find the inverse Laplace transform of velocity field, Stehfest’s algorithm has been used. Finally, some graphs have been sketched to discuss the influence of parameters.

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