Fractional order study of magnetohydrodynamical time-dependent flow of Prandtl fluid

Abstract

Although the thermal and flow analysis of complex mechanisms of electrochemistry, dispersion and viscoelasticity is significantly addressed in the literature but none of the studies are made through the concept of fractional differential operators with computationally stable numerical solutions. The current work is a first attempt for the fractional classification and computational analysis of the Prandtl fluid. The physical model is formulated to examine the thermal, flow and concentration transference for a naturally convective, time-dependent, incompressible, and stagnation point flow of Prandtl fluid over an infinite plate under the impacts of magnetic, chemical reaction, Soret and Dufour. The mathematical expression of the model is expressed in terms of partial differential equation coupled with Caputo's fractional temporal differential operator. The computational code based on finite difference scheme is formulated to simulate the model. The detailed analysis of the flow pattern, thermal management and concentration of the diffusive species are made computationally. It is noted that involvement of the fractional parameter is useful to control the flow motion, heat transport and concentration of the diffusive species according to the required physical system. The temperature of the system increases 64 % against the variation of radiation parameter when fractional order parameter α=0.4 then the integer order. The study will be a useful addition to non-Newtonian computational mechanics and numerical treatment of such complex models.