Fluid flow chronologically is widely recognized due to its various uses in turbines, the framework of spinning magnet stars, gyromagnetic generators, and chemical engineers observing the progression of petroleum through the aquifer, and blood vessels in the respiratory alveolar plate. Tropical cyclones, pools of water, and storms all exhibit rotational movement. The current investigation aims to analyse the micro polar fluid flow between two infinite vertical discs enclosing Hall impact, varying thermal conductivity, heat flux as well as anomalous heat generation. The implication of a chemical change combined with chemical potential improves mass propagation. Suitable similarity conversions are used to convert the defined problems into conventional differential equations (ODEs). Furthermore, by introducing new variables the ODEs are transformed into nonlinear coupled ODEs and then solved numerically by the RK 4th order along with the shooting technique. The velocity profiles decrease as suction parameter increases. The temperature field exhibits a rising behaviour for the increasing values of thermophoresis, Brownian and radiations parameters while the concentration field shows a decreasing behaviour. Shear stress at the upper wall increases when the rotation variable and suction variable are augmented. Heat transmission escalations at the bottom wall when Prandtl number and radiation factor are enhanced. The novelty of the present work is to examine the Buongionro model in the presence of a heat source and chemical reaction inside the Darcian porous rotating channel, which has not been investigated yet. In some limiting cases, a comparison of the on-going study with existing literature is also included to justify the contemplated problem.

On the account of technological development and engineering applications, the enhancement of thermal energy by introducing nanoparticles is a crucial task in the present era. This present work is to investigate the physical characteristics of a chemical reaction, heat and mass transfer effects on hydrodynamic stagnation point flow of Watlers-B nanoliquid configured by a stretching surface. The effect of fluid viscosity, electrical and thermal conductivity is assumed as temperature function. In addition, the impression of thermal conductivity, Brownian and thermophoretic diffusion are incorporated in the revised model. A theoretical framework is employed to simulate the arisen nonlinear (PDEs). With the assistance of transformations techniques, the contemporary (PDEs) are then diminished to nonlinear system of (ODEs). For nonlinear computations, the resulting equations are programmed in the Mathematica 11.0 programing platform. The impression of the model parameters on diverse flow fields is visualized through plotted graphs. Stability and convergence analysis is established for the authentication of the proposed model. Researchers are encouraged to conduct trials to authenticate the innovative consequences provided in this study, which could be obliging in the improved design of mechanical systems comprising the nanofluids that enables heat and mass transfer mechanism.

The second law, thermal, magnetic field, and concentration of viscous fluid across a permeable stretching surface are the focus of this study. The transverse and longitudinal velocities, temperature, and concentration with boundary conditions are computed numerically by applying Runge-Kutta 4th-order method. For this determination the system of governing equations are first converted to the first order ordinary linear equations and then solve by RK4 built-in function in MATHLAB SOFTWARE by taking step size Δ η = 0 . 01 . The existing work is compared with the difference between existing and published work. The iteration procedure was stopped until all of the nodes in the η -direction met the convergence condition 10 −5 . For confirmation of the results, the BVPh2 package is also applied and excellent agreement is found. Both on longitudinal and transverse kinematics, the impact of ferromagnetic and viscoelastic factors are examined. The temperature is studied in relation to the Prandtl number, the magnetism factor, and the heat reference factor. The concentration is also shown, as well as how it varies well with Schmidt number and the magnetic factor. The entropy generation number is calculated using fluid velocity, energy, and volume fraction coefficient. Moreover, the current work is also equated with the available work for limiting cases. The longitudinal and transverse velocities are declined when the viscoelastic and magnetic parameters are increased. The temperature profile enhances as the magnetic parameters and heat source-sink parameters increase, but declines as Prandtl number increases. At the same time, concentration raises as the magnetic parameters rises. From this investigation it is also observed that the concentration falls, as the Sc enhances. The entropy generation number decreases with the increasing values of magnetic parameter. It is perceived that as Pr enhances, the Ns increases near the surface but with increasing η , the situation reverses. For higher values of Sc , the generation number Ns declines at the surface, however, the situation reverses via η rises.

This manuscript studies the impact of heat transfer in the context of their valuable applications. There has been a lot of interest in using non-Newtonian fluids in biological and engineering disciplines. With such a considerable interest in non-Newtonian fluids, we aim to examine the MHD flow of chemically reactive Casson liquid by a permeable stretching surface by considering the heat source and viscous dissipation effects. The impression of current conductivity as a linear function of the temperature field is subjected to temperature-dependent viscosity fluctuation. A mathematical model simulates the arisen nonlinear partial differential equations (PDEs). By using the suitable transformations, the system of PDEs is then transformed to a nonlinear system of ordinary differential equations (ODEs). The impacts of the pertinent parameters on the velocity profile, energy, and concentration distribution have been discussed. The fundamental dimensionless partial differential flow laws are analyzed using an efficient and validated analytical homotopic (HAM) technique. The ongoing investigation has been converged, according to a stability and convergence analysis. The impression of innumerable dominant physical parameters on the momentum boundary layer, thermal boundary layer, and concentration profile has been made realistically by plotted graphics.

We investigate the unsteady magnetohydrodynamic (MED) flow of an Oldroyd-B fluid through a porous space induced by sawtooth pulses. The fluid is assumed to be electrically conducting in the presence of a transverse uniform magnetic field. The porous space is taken into account using modified Darcy's law for the Oldroyd-B fluid. Exact solutions of the governing problem are obtained by using the Laplace transform method. The effects of the magnetic parameter, the permeability of the porous space and the elasticity parameter of the fluid are studied on the flow characteristics.