The increasing global demand for energy necessitates devoted attention to the formulation and exploration of mechanisms of thermal heat exchangers to explore and save heat energy. Thus, innovative thermal transport fluids require to boost thermal conductivity and heat flow features to upsurge convection heat rate, and nanofluids have been effectively employed as standard heat transfer fluids. With such intention, herein, we formulated and developed the constitutive flow laws by utilizing the Rossland diffusion approximation and Stephen’s law along with the MHD (...) effect. The mathematical formulation is based on boundary layer theory pioneered by Prandtl. Governing nonlinear partial differential flow equations are changed to ODEs via the implementation of the similarity variables. A well-known computational algorithm BVPh2 has been utilized for the solution of the nonlinear system of ODEs. The consequence of innumerable physical parameters on flow field, thermal distribution, and solutal field, such as magnetic field, Lewis number, velocity parameter, Prandtl number, drag force, Nusselt number, and Sherwood number, is plotted via graphs. Finally, numerical consequences are compared with the homotopic solution as a limiting case, and an exceptional agreement is found. (shrink)

This study presents a modified simplest equation method to investigate some real and exact solutions of conformable time fractional Benjamin-Bona-Mahony equation and Chan-Hilliard equation. We use traveling wave transformation to obtain the results in the form of series solution. Some calculations are performed through Mathematica software to analyze the accuracy of this approach. Graphical representations are reported for more significant results at different fractional-order which demonstrates that this approach is very simple, adequate, and legitimate.