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Linear and weakly nonlinear stability analyses of thermosolutal convection in a couple‐stress fluid with effects of helical force and rotation are performed. The governing nondimensional equations are solved using the normal modes. We have shown the effect of the helical force parameter, solutal Rayleigh number, Couple stress parameter, Lewis number, Taylor number, and Prandtl number on stationary and oscillatory convection regions and presented graphically. Solutal Rayleigh number, Couple stress parameter, Lewis number, and Taylor number have a stabilizing effect on the system whereas the helical force parameter has a destabilizing effect on the system. To study heat transport by convection we have derived the Ginzburg–Landau equation. [ABSTRACT FROM AUTHOR]

In recent years, a great deal of interest has been generated in modern micro‐ and nanotechnologies for micro/nano‐electronic devices. These technologies are increasingly utilizing sophisticated fluid media to enhance performance. Among the new trends is the simultaneous adoption of nanofluids and biological micro‐organisms. Motivated by bio‐nanofluid vertical channel oxygenators in medical engineering, in the current work, a mathematical model is developed to examine the flow of mixed convective couple‐stress nanofluids in a vertical channel with a transverse magnetic field, fluid viscosity that changes with temperature, and thermal conductivity. The non‐Newtonian model follows Brownian motion and heat spread by nanoparticles in a fluid under coupled stress. Highly linked, nonlinear regulating equations are translated into nondimensional equations using relevant variables. The governing equations are then turned into a form with no dimensions. The Keller‐box technique, a second‐order finite difference method for solving second‐order equations, is used to solve them numerically. On the other hand, the effects of different non‐Newtonian flow parameters, such as the couple stress fluid parameter, the magnetic parameter, the variable fluid viscosity, the variable thermal conductivity parameters, the Brinkman number, the nanofluid and buoyancy parameters, and the rate of chemical reaction parameter, are carefully studied. The velocity, temperature, and concentration fields are calculated over a wide range of possible values for the relevant parameters. [ABSTRACT FROM AUTHOR]

This study provides the exact solutions of couple stress fluid (CSF) in a channel. The CSF is bounded by two plates in which the lower plate is moving with constant velocity Uo and the upper plate is fixed. The influence of the external pressure gradient is considered on the CSF fluid. To transform the classical CSF model, we have introduced three approaches to fractional derivatives, (a) Caputo (b) Caputo–Fabrizio (CF), and (c) Atangana–Baleanu (AB) fractional definitions. Exact solutions have been obtained using the Laplace and finite Fourier sine transforms jointly. Furthermore, the effect of different fractional derivatives is compared, and the results are shown in graphs. Moreover, parameters that affect the CSF motion are discussed in the graphs using the computational software MATHCAD. The most important outcome of the given study is the comparison of Caputo, CF, and AB fractional models with the classical CSF model. From the comparison, it can be noticed that AB fractional model discusses the dynamics of the CSF with a good memory effect as compared to Caputo and CF fractional operators. The CSF model can be reduced to Newtonian fluid as a limiting case and also investigated solutions in the absence of external pressure. Finally, Skin friction is evaluated for lower and upper plates, and the obtained results presented in tabular form. [ABSTRACT FROM AUTHOR]

The present level of literature on the subject matter indicates that nothing is known on the heat transfer across the couple stress rheological fluid flowing over a vertical avenue with Robin (mixed) wall conditions. The obtained conservation equations of the model are solved through DTM (differential transform method) and RPM (regular perturbation method). The nondimensional parameters obtained are a couple stress parameter, Brinkman number, mixed convection parameter, and Biot number. The computations reveal that flow acceleration and thermal enhancement is induced with increasing mixed convection parameter and Brinkman number for symmetric and asymmetric conditions. Increasing couple stress parameters dwindle the velocity and temperature for symmetric and asymmetric cases. The large values of the mixed convection parameter and Brinkman number increase the Nusselt values at the left wall and reduces at the right wall. The mass flow rate is augmented with the mixed convection parameter and Brinkman number but it is reduced with the couple stress parameter. The DTM, RKSM, and RPM solutions are in good agreement. [ABSTRACT FROM AUTHOR]

This paper deals with the effect of three‐dimensional magnetohydrodynamic flow for a couple of stress fluids on an exponentially stretching sheet. The magnetic field is implemented normally to the surface. To observe the transfer of heat phenomenon, the Cattaneo–Christov flux model of heat is employed. Using similarity transformation, the substantial differential equations are reformed into ordinary differential equations. Eventually, the effects of different physical parameters are studied graphically. The drawback in Fourier heat flux model is removed by adding a new paramter known as thermal relaxation time by Cattaneo. This perimeter allows heat transportation by way of propagation of waves thermally at a defined speed. After this, the Cattaneo law is further modified by Christov–Christov to replace the ordinary derivative along Oldroyd's upper‐convective derivative. [ABSTRACT FROM AUTHOR]

The present work aims to examine the effects of viscous dissipation and unsteadiness parameters on nonlinear convective laminar boundary layer flow of micropolar‐couple stress nanofluid past a permeable stretching sheet with non‐Fourier heat flux model in the presence of suction/injection variable. The unsteadiness in the flow, temperature, and concentration profile is caused by the time‐dependence of the stretching velocity, surface temperature, and surface concentration of the boundary layer flow. Similarity transformation is applied to transform the time‐ dependent boundary layer flow equations into the corresponding highly nonlinear coupled ordinary differential equations with appropriate boundary conditions. The robust numerical technique called Galerkin finite element method is used to solve the obtained dimensionless governing equations of the flow. The effects of Eckert number, unsteadiness parameter, suction/injection parameter, mixed convection parameter, material parameter, Schmidt number, and couple stress parameter on linear velocity, angular velocity, temperature, concentration, local skin friction coefficient, local wall couple stress, local Nusselt number, and local Sherwood number is analyzed with the help of graphical and tabular form. Under special conditions, the present result is compared with the existing literature and revealed good agreement. Our result shows that as unsteadiness parameter boost, both heat and mass transfer rate rises. The present study has a significant application in material processing technology. [ABSTRACT FROM AUTHOR]