Biconvective transport of magnetized couple stress fluid over a radiative paraboloid of revolution

In the present study, the physical features of the bioconvective MHD flow of a couple stress fluid over an upper horizontal surface (i.e. surface shaped like a submarine or any ( uhsp) aerodynamical automobile) is analysed by considering radiation and viscous dissipation effects. In the fluid-saturated domain flow is induced due to the reaction of catalytic surface, double diffusion and stretching fluid layers. In fact, couple stress fluid is electrically conducted because non-uniform magnetic field is imposed. With the assistance of appropriate similarity transformations governing equations of the study are reduced to set of ordinary differential equations. Thereafter, built-in MATLAB solver bvp4c is implemented to solve the system numerically. By means of graphs and tables variations of the velocity, temperature, concentration, friction factor, local heat and mass transfer rates are observed thoroughly by varying the flow controlling parameters. From this analysis, main observations are, for rising values of couple stress and magnetic parameter velocity is decline, whereas temperature rises for the same parameters and increase in the thermal boundary layer is noted for the Brinkman number, whereas reverse trend is noted in the concentration boundary layer. Finally, comparison is done and a good correlation is identified between the present analysis and perversely recorded analysis.

Influence of Boundary Roughness on Magnetohydrodynamic Kelvin-Helmholtz Instability in Couple-stress Fluid

The Kelvin-Helmholtz instability (KHI) occurs at the interface amongst two fluids, which are in relative motion with a common boundary. The growth rate of waves occurs whenever the relative velocity is greater as compared with the critical relative velocity. In the present paper, the influence of boundary roughness on KHI under the impact magnetic field in a couple-stress fluid layer bounded by a rigid surface at the lower side and upper side by a fluid saturated porous layer. Using suitable surface and boundary conditions, we have derived the dispersion relation and results are depicted graphically. As observed in presence of sharp interface, magnetic field exhibits stabilizing effect however, destabilizing effect is shown by the buoyancy force on KHI. Also, noted that the growth rate of interface reduces, as there is a rise in roughness parameter value.

Analysis of newly developed fractal-fractional derivative with power law kernel for MHD couple stress fluid in channel embedded in a porous medium

Fractal-fractional derivative is a new class of fractional derivative with power Law kernel which has many applications in real world problems. This operator is used for the first time in such kind of fluid flow. The big advantage of this operator is that one can formulate models describing much better the systems with memory effects. Furthermore, in real world there are many problems where it is necessary to know that how much information the system carries. To explain the memory in a system fractal-fractional derivatives with power law kernel is analyzed in the present work. Keeping these motivation in mind in the present paper new concept of fractal-fractional derivative for the modeling of couple stress fluid (CSF) with the combined effect of heat and mass transfer have been used. The magnetohydrodynamics (MHD) flow of CSF is taken in channel with porous media in the presence of external pressure. The constant motion of the left plate generates the CSF motion while the right plate is kept stationary. The non-dimensional fractal-fractional model of couple stress fluid in Riemann–Liouville sense with power law is solved numerically by using the implicit finite difference method. The obtained solutions for the present problem have been shown through graphs. The effects of various parameters are shown through graphs on velocity, temperature and concentration fields. The velocity, temperature and concentration profiles of the MHD CSF in channel with porous media decreases for the greater values of both fractional parameter $$\alpha$$ α and fractal parameter $$\beta$$ β respectively. From the graphical results it can be noticed that the fractal-fractional solutions are more general as compared to classical and fractional solutions of CSF motion in channel. Furthermore, the fractal-fractional model of CSF explains good memory effect on the dynamics of couple stress fluid in channel as compared to fractional model of CSF. Finally, the skin friction, Nusselt number and Sherwood number are evaluated and presented in tabular form.

Effect of Couple Stress Fluid in an Irregular Couette Flow Channel: An Analytical Approach

The work embodied in this paper presents the combined effects of Soret, chemical reaction, and Dufour on Couette flow in an irregular channel for dusty viscoelastic couple stress fluid. The behavior of the boundary layer is studied with the help of Brinkman-Forchheimer's extended Darcy model as a momentum equation for the unsteady, incompressible dusty viscoelastic fluid. The heat transfers are considered due to the radiation absorption parameter and Dufour effect, the mass transfer influenced by the chemical reaction, and the Soret effect. The boundary conditions of the problem and leading equations of the physical problem are solved by a similarity transformation, and the consequent ordinary linear differential equations are solved by the perturbation method. The obtained results are shown graphically. The computational results show a good agreement between our values and a particular case of the earlier work.

Study of Slip Effects in Reverse Roll Coating Process Using Non-Isothermal Couple Stress Fluid

The non-isothermal couple stress fluid inside a reverse roll coating geometry is considered. The slip condition is considered at the surfaces of the rolls. To develop the flow equations, the mathematical modelling is performed using conservation of momentum, mass, and energy. The LAT (lubrication approximation theory) is employed to simplify the equations. The closed form solution for velocity, temperature, and pressure gradient is obtained. While the pressure and flow rate are obtained numerically. The impact of involved parameters on important physical quantities such as temperature, pressure, and pressure gradient are elaborated through graphs and in tabular form. The pressure and pressure gradient decreases for variation of the couple stress parameter and velocity ratio parameter K. While the variation of the slip parameter increases the pressure and pressure gradient inside the flow geometry. Additionally, flow rate decreases for the variation of the slip parameter as fluid starts moving rapidly along the roller surface. The most important physical quantity which is responsible for maintaining the quality of the coating and thickness is flow rate. For variation of both the couple stress parameter and the slip parameter, the flow rate decreases compared to the Newtonian case, consequently the coating thickness decreases for the variation of the discussed parameter.