Purpose The purpose of this paper is to consider the problem of thermal destratification facing engineers and scientists during the motion of fluids which consist of rigid and randomly oriented particles suspended in a viscous medium under the influence of Lorentz force. This paper provides an insight into the non-linear transfer of thermal radiation within the boundary layer. Design/methodology/approach Similarity transformation and parameterization of the non-linear partial differential equation are carried out. The approximate analytical solution of the governing equation which models the free convective flow of strong and weak concentration of micro-elements in a micropolar fluid over a vertical surface is presented. Findings It is observed that the velocity and temperature distribution are decreasing properties of thermal stratification parameter St. Maximum local skin friction coefficients are ascertained at an epilimnion level (St=0) when the magnitude of thermal radiation is small. Thermal stratification parameter has no significant effect on the temperature distribution in the flow near a free stream. Originality/value The relationship between stratification of temperature and the transfer of thermal energy during the problem of thermal destratification facing engineers and scientist during the motion of fluids which consist of rigid and randomly oriented particles suspended in a viscous medium under the influence of Lorentz force is unravelled in this paper.

This communication presents analysis of gravity-driven flow of a thixotropic fluid containing both nanoparticles and gyrotactic microorganisms along a vertical surface. To further describe the transport phenomenon, special cases of active and passive controls of nanoparticles are investigated. The governing partial differential equations of momentum, energy, nanoparticles concentration, and density of gyrotactic microorganisms equations are converted and parameterized into system of ordinary differential equations and the series solutions are obtained through Optimal Homotopy Analysis Method (OHAM). The related important parameters are tested and shown on the velocity, temperature, concentration and density of motile microorganisms profiles. It is observed that for both cases of active and passive control of nanoparticles, incremental values of thermophoretic parameters corresponds to decrease in the velocity distributions and augment the temperature distributions.

The dynamics of steady, two-dimensional magnetohydrodynamics (MHD) free convective flow of micropolar fluid along a vertical porous surface embedded in a thermally stratified medium is investigated. The ratio of pressure drop caused by liquid-solid interactions to that of pressure drop caused by viscous resistance are equal; hence, the non-Darcy effect is properly accounted for in the momentum equation. The temperature at the wall and at the free stream which best accounts for thermal stratification are adopted. Similarity transformations are used to convert the nonlinear partial differential equation to a system of coupled non-linear ordinary differential equation and also to parameterize the governing equations. The approximate analytical solution of the corresponding BVP are obtained using Homotopy Analysis Method (HAM). The effects of stratification parameter, thermal radiation and other pertinent parameters on velocity, angular velocity and temperature profiles are shown graphically. It is observed that increase in the stratification parameter leads to decrease in both velocity and temperature distribution and also makes the microrotation distribution to increase near the plate and decrease away from the plate. The influence of both thermal stratification and exponential space dependent internal heat source on velocity, micro-rotation and temperature profiles are presented. The comparison of the solutions obtained using analytical techniques (HAM) and MATLAB package (bvp4c) is shown and a good agreement is observed.

The study considers the effect of thermophoresis particle deposition on the flow properties of second grade fluid with variable viscosity, variable thermal conductivity and variable concentration diffusivity subjected to a convective boundary condition. To further describe the transport phenomenon, the special case of assisting and opposing flows is explored. Using similarity transformations, the governing equations of the fluid model are transformed and parameterized into a system of nonlinear ordinary differential equations. The approximate analytic solution of a dimensionless system is obtained through the Optimal Homotopy Analysis Method (OHAM). It is observed that velocity and temperature distributions are decreasing functions of the second grade parameter for both assisting and opposing flows. When the thermophoretic parameter is increased, the concentration distributions at the first and fourth orders of chemical reaction decrease. For both opposing and assisting flows, velocity distributions are enhanced due to larger temperature-dependent viscous parameters.

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