Magnetohydrodynamics free convection flow of Carbon nanotubes viscous nanofluids over an infinite plate with Newtonian heating and fractional derivative

Abstract

The problem of hydromagnetic (MHD) free convection flow of viscous nanofluids over a moving infinite vertical plate with carbon nanotubes (CNTs) and Newtonian heating on the boundary is considered. The Caputo time‐fractional derivative is introduced to classical constitutive equations by using the generalized constitutive shear stress equation and generalized Fourier law. Analytical solution for the temperature distribution and semi‐analytical solution for the velocity profile are found by means of Laplace transform. The solution of temperature distribution is presented in terms of Wright and Gauss complementary error functions. The inverse Laplace transform of velocity profile is approximated by Stehfest algorithm, and for validation, Tzou algorithm is used. Finally, for illustration, three special cases are considered, and the influence of physical parameters on some fundamental motions are graphically underlined and discussed. The fractional derivative and volume faction parameter has a good influence on temperature distribution and velocity field.