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The nonlinear density thermal/solutal fluctuations in the buoyancy force term cannot be ignored when the temperature/concentration difference between the surface and fluid is large. The purpose of this paper is to investigate the nonlinear density fluctuations across a flowing fluid with heat mass transfer effects on a non-axial rotating plate. Therefore, the impact of nonlinear convection in the flow of Casson fluid over an oscillating plate has been analytically investigated.

The governing equations are modeled with the help of conservation equations of velocity, energy and concentration under the transient-state situation. The dimensional governing equations are non-dimensionalized by utilizing non-dimensional variables. Later, the subsequent non-dimensional problem has been solved analytically using Laplace transform method.

The effects of thermal Grashof number, solute Grashof number, nonlinear convection parameters, Casson fluid parameter, unsteady parameter, Prandtl number as well as Schmidt number on hydrodynamic, thermal and solute characteristics have been quantified. The numeric data for skin friction coefficient, Nusselt number and Sherwood number are presented. It is established the nonlinear convection aspect has a significant influence on heat and mass transport characteristics.

The effect of nonlinear convection in the dynamics of Casson fluid past an oscillating plate which is rotating non-axially is investigated for the first time.

In heat transfer problems, if the temperature difference is not sufficiently so small then the linear Boussinesq approximation is not adequate to describe thermal analysis. Also, nonlinear density variation with respect to temperature/concentration has a significant impact on heat and fluid flow characteristics. Because of this reason, the impact of nonlinear density variation in the buoyancy force term cannot be neglected. Therefore in this paper, the unsteady flow and heat transfer of radiating magneto-micropolar fluid by considering nonlinear Boussinesq approximation is investigated analytically.

The flow is fully developed and time-dependent. Heat and mass flux boundary conditions are also accounted in the analysis. The governing equations of transport phenomena are treated analytically using regular perturbation method. To analyze the tendency of the obtained solutions, a parametric study is performed.

It is established that the velocity field is directly proportional to the nonlinear convection parameter and the same trend is observed with the increase of the value of Grashof number. The micro-rotational velocity profile decreases with increase in the nonlinear convection parameter. Further, the temperature profile increases due to the presence of radiative heat aspect.

The effectiveness of nonlinear Boussinesq approximation in the flow of micropolar fluid past a vertical plate in the presence of thermal radiation and magnetic dipole is investigated for the first time.

The purpose of this paper is to analyze the natural convection of a yield stress fluid in a square enclosure with differentially heated side walls. In particular, the Casson model is considered which is a commonly used model.

The coupled conservation equations of mass, momentum and energy related to the two-dimensional steady-state natural convection within square enclosures are solved numerically by using the Galerkin's weighted residual finite element method with quadrilateral, eight nodes elements.

Results highlight a small degree of the shear-thinning in the Casson fluids. It is shown that the yield stress has a stabilizing effect since the convection can stop for yield stress fluids while this is not the case for Newtonian fluids. The heat transfer rate, velocity and Yc obtained with the Casson model have the smallest values compared to other viscoplastic models. Results highlight a weak dependence of Yc with the Rayleigh number: Yc∼Ra0.07. A supercritical bifurcation at the transition between the convective and the conductive regimes is found.

The originality of the present study concerns the comprehensive and detailed solutions of the natural convection of Casson fluids in square enclosures with differentially heated side walls. It is shown that there exists a major difference between the cases of Casson and Bingham models, and hence using the Bingham model for analyzing the viscoplastic behavior of the fluids which follow the Casson model (such as blood) may not be accurate. Finally, a correlation is proposed for the mean Nusselt number Nu¯.