A fractional model of magnetohydrodynamics Oldroyd-B fluid with couple stresses, heat and mass transfer: A comparison among Non-Newtonian fluid models

The present article aims to extend some of the already existing fluid models to a large class of fluids namely, Oldroyd-B couple stress fluid (OBCSF). The main focus of the present work is to combine the existing fluid models in ordered to get a new class of fluid. The unsteady magnetohydrodynamics (MHD) Oldroyd-B fluid (OBF) with couple stresses, porosity, heat and mass transfer is considered in the present analysis. The Oldroyd-B couple stress fluid is assumed to flow in channel. The classical model is fractionalized by considering Atangana-Baleanu (AB) operator in ordered to highlight the memory analysis. To develop closed form solutions the combined (Laplace + Fourier) integrals have been used. The results obtained are portrayed through graphs for all pertinent flow parameters which involved in the present dynamic model. Moreover, the impact of AB time fractional parameter is investigated graphically on flow, temperature and concentration distributions exploiting MATHCAD software. Secondly, for better understanding the present solutions of Oldroyd-B couple stress fluid (OBCSF) are reduced to Odroyd-B fluid (OBF) without couple stresses, Maxwell solutions, Couple stress solutions and Newtonian viscous fluid solutions and the results have been compared for classical and fractional order derivatives. In addition to this a limiting case is carried out by our solutions to already published work which verify our solutions. In addition to this during the analysis we noticed that the flow heat and concentrated get lowered for the escalating numerical values of AB fractional derivatives. Similarly, it is also noticed that the velocity in channel accelerated with the increment of numeric values of pressure, porosity, thermal buoyancy and relaxation time parameter. In the same manner temperature and concertation profiles gets low with the higher values of Prandtl number, Reynold number and fractional operator. Finally, skin friction for momentum equation, Nusselt number for temperature and Sherwood number for concentration have been calculated and given in tabular forms.

Automated summary

The aim of this article is to extend existing fluid models to Oldroyd-B couple stress fluid (OBCSF) and develop closed form solutions involving this new class of fluid. The study considers the unsteady magnetohydrodynamics (MHD) Oldroyd-B fluid (OBF) with couple stresses, porosity, heat and mass transfer flowing in a channel. The effects of Atangana-Baleanu (AB) operator and flow parameters on velocity, temperature and concentration distributions are investigated using MATHCAD software. Additionally, the solutions for OBCSF are compared to classical and fractional order derivatives, as well as other fluid models. Skin friction, Nusselt number and Sherwood number are calculated and presented in tabular forms.