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The problem of hydromagnetic fully developed laminar mixed convection flow in a vertical channel and asymmetric wall heating conditions in the presence of electrical conductivity effect is considered through proper choice of dimensionless variables. The governing with symmetric equations are developed and three types of thermal boundary conditions are presented. These boundary conditions are isothermal-isothermal, isoflux-isothermal, and isothermal-isoflux for the left-right walls of the channel respectively. The velocity fleld and the temperattire fleld are obtained by perturbation series method which employs a perturbation parameter proportional to the Brinkman number. In addition, closed form expressions for reversal flow conditions at both the left-right channel walls are derived. Selected set of graphical results illustrating the effects of the various parameters involved in the problem including magnetic dissipation, heat generation or absorption, and the electrical conductivity on the velocity and temperature proflles as well as flow reversal situation are presented. The solutions obtained are also compared with that of results obtained byflnite difference method.

Present study explains about unsteady Casson nanoliquid film flow over a surface moving with velocity $$U_w=\lambda x/t$$ U w = λ x / t . The governing momentum equation is reduced to ODE by using corresponding similarity transformation, which is then tackled by employing numerical technique. The problem is analysed for both two-dimensional film flow and axisymmetric film flow. The exact solution is derived which satisfies the governing equation. It is noted that solution exists only for a specified scale of the moving surface parameter $$\lambda$$ λ . ie., $$\lambda \ge -1/2$$ λ ≥ - 1 / 2 for two-dimensional flow and $$\lambda \le -1/4$$ λ ≤ - 1 / 4 for axisymmetric flow. The velocity increases first and reaches the maximum velocity and then decreases to the boundary condition. Streamlines are also analysed for both axisymmetric and two-dimensional flow patterns by considering the stretching ($$\lambda >0$$ λ > 0 ) and shrinking wall conditions ($$\lambda <0$$ λ < 0 ). Study has been made for large values of wall moving parameter $$\lambda$$ λ . The aim of this investigation is to analyse the Casson nanoliquid film flow which finds applications in industries like coating of sheet or wire, laboratories, painting, many more.

The purpose of the study is to scrutinize the entropy generation analysis on magnetohydrodynamic heat transfer flow from Casson single-walled carbon nanotube on a wedge with Joule heating and viscous dissipation. Kerosene oil is considered as base fluid because of its exclusive features, advanced thermal conductivity, application, and unique behavior. Using similarity variables, the regulating equations are modified into nonlinear coupled, ordinary differential equations, which are then tackled using homotopy analysis method. Impacts of emerging parameters on entropy generation, temperature, velocity, and Bejan number distributions are discussed and shown graphically. The Nusselt number and skin-friction coefficient values are shown in a table. The results reveal that velocity enhances due to increasing magnetic and Casson parameters. It was inspected that entropy production enhances due to increasing wedge angle and magnetic parameter and decays with Casson parameter. Also, it is examined that the Bejan number upsurges due to larger Casson and wedge angle

The study examines the entropy generation in the Williamson nanofluid flowing in a vertical porous channel exposed to nonlinear thermal radiation and heat source or sink. Constant temperature and fixed nanoparticle concentration are maintained at the boundaries of the channel. Governing equations are derived by applying the conservation laws incorporating the brownian motion and thermophoretic force impacts of nanofluids utilizing Buongiorno’s model. These equations are non dimensionalised by choosing suitable dimensionless variables. The governing simultaneous equations are tackled by implementing adomian decomposition technique for velocity, tempearture, dimensionless shear stress heat transfer rate. The findings of the study are analysed through graphs. The major findings of the study are porous parameter reduces velocity because of resistance to the flow and enhances temperature. Thermal radiation parameter reduces both velocity and temperature fields. Williamson parameter enhances the velocity field and reduces the temperature to a very small extent. These results are also corresponds with skin friction and Nusselt number graphs. Entropy generation in the considered flow system can be minimized by increasing Williamson number.