On the thermal analysis of magnetohydrodynamic Jeffery fluid via modern non integer order derivative

Abstract The uniqueness of thermal radiation effects on materials has an adhesive role in engineering. This article emphasizes the effects of thermal radiation of Jeffery fluid with magnetic field by employing Caputo-Fabrizio fractional derivative. Analytical solutions for the velocity field and temperature distribution are based on integral transforms (Fourier Sine and Laplace transform) with their inversion. The general solutions have been established in terms of elementary functions and product of convolution theorem satisfying initial and boundary conditions. This analysis is one of the infrequent contributions to elucidate the rheology of Jeffery fluid for free convective problem on oscillating plate. In order to bring physical insights, four models have been prepared for comparison i-e (i) Jeffery fluid with magnetic field (ii) Jeffery fluid without magnetic field (iii) Second grade fluid with magnetic field and (iv) Second grade fluid without magnetic field for several rheological parameters for instance, viscosity ν , thermal radiation Rd , thermal conductivity k , Jeffrey fluid parameter λ , Hartmann number H a , magnetic field M , Prandtl number P r , Grashof number on fluid flow. At the end, our results suggested that Ordinary Jeffery fluid with magnetic field oscillates more rapidly to remaining models of fluid but fractionalized Jeffery fluid with magnetic field has reciprocal behavior of fluid flow.

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