In this work, we present the theoretical investigation of the transient rotating electro-osmotic flow of a couple stress fluid in a microchannel, through the Laplace transform technique. The analysis is dependent on the Debye–Hückel linear approximation for electrical potentials. The governing equations of the couple stress fluid are taken to address the flow field in a rotating environment. The mathematical formulation of these governing equations provides a system of ordinary differential equations, which are then solved to achieve analytical solutions for electrostatic potential, axial and transverse velocity distribution, and volumetric flow rate. A comparison was made for the present analytical solution with data available in the literature. There was excellent matching. The characteristics of different influential parameters on axial and transverse velocity distributions, volume, and angle flow rates are pictorially deliberated. The study reveals that the rise in the couple stress parameter accelerates the axial electro-osmotic flow velocity inside the electrical double layer.

Investigation of unsteady hydromagnetic natural convection flow with heat and mass transfer of a viscous, incompressible, electrically conducting, chemically reactive and optically thin radiating fluid past an exponentially accelerated moving vertical plate with arbitrary ramped temperature embedded in a fluid saturated porous medium is carried out. Exact solutions of momentum, energy and concentration equations are obtained in closed form by Laplace transform technique. The expressions for the shear stress, rate of heat transfer and rate of mass transfer at the plate for both ramped temperature and isothermal plates are derived. The numerical values of fluid velocity, fluid temperature and species concentration are displayed graphically whereas those of shear stress, rate of heat transfer and rate of mass transfer at the plate are presented in tabular form for various values of pertinent flow parameters. It is found that, for isothermal plate, the fluid temperature approaches steady state when 1.5 t  . Consequently, the rate of heat transfer at isothermal plate approaches steady state when 1.5 t  .

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Investigation of Soret and Hall effects on unsteady MHD free convection heat and mass transfer flow of a viscous, incompressible, electrically conducting and optically thick radiating fluid past an impulsively moving infinite vertical plate with ramped temperature through a uniform porous medium in a rotating system in the presence of first order chemical reaction is carried out. Exact analytical solution of the governing equations for fluid velocity, fluid temperature and species concentration subject to appropriate initial and boundary conditions is obtained using Laplace transform technique. Expressions for shear stress, rate of heat transfer and rate of mass transfer at the plate are derived for both ramped temperature and isothermal plates. The numerical values of primary and secondary fluid velocities, fluid temperature and species concentration are displayed graphically whereas those of shear stress and rate of mass transfer at the plate are presented in tabular form for various values of pertinent flow parameters.

In this article, the impacts of Hall current and Arrhenius activation energy on three-dimensional hydromagnetic Williamson nanofluid flow past a slendering stretching sheet in the presence of multiple slips, viscous dissipation, Joule heating and binary chemical reaction is analyzed. The presence of nonlinear thermal radiation and nonlinear mixed convection is also taken into consideration. The dimensional governing equations are transformed into non-dimensional ordinary differential equations by using some suitable similarity transformation. The resulting coupled and highly nonlinear boundary value problem is then solved numerically by shooting technique based on Runge-Kutta-Fehlberg method. The behaviors of concentration, temperature and velocity distributions w.r.t. the various controlling parameters are illustrated graphically. However, the numerical values of local skin-friction coefficients, local heat and mass transfer rates are explained and presented in tabular form. Furthermore, a result validation is performed to check the accuracy and correctness of the obtained results by comparing the results with previously published results for some limited case of the present problem and an excellent agreement is found between the results.