Aim of the paper is to investigate the effects of linearly varying VISCOSITY and thermal conductivity on steady free convective flow of a viscous incompressible fluid along an isothermal vertical plate in the presence of HEAT sink. The governing equations of continuity, momentum and energy are transformed into coupled and nonlinear ordinary differential equations using similarity transformation and then solved using Runge-Kutta fourth order method with shooting technique. The velocity and temperature distributions are discussed numerically and presented through graphs. Skin-friction coefficient and Nusselt number at the plate are derived, discussed numerically and their numerical values for various values of physical parameters are presented through Tables.

In this research article, we investigated the weakly non-linear effect of gravity modulation for the temperature dependent viscous fluid in a horizontal porous layer in the presence of internal HEAT source. We use power series expansion in terms of the amplitude of gravity modulation, which is considered to be small for double-diffusive convection in porous media. We graphically show the effect of internal HEAT source, solute Rayleigh number, Lewis number, Vadá sz number, thermo-rheological parameter, the amplitude of gravity modulation, the frequency of modulation on the HEAT and mass transfer using Ginzburg-Landau equation. The effect of gravity modulation is found significant and is more effective for the low values of frequency of modulation.

In the current study, non-Newtonian flow pattern and HEAT transfer in an enclosure containing a tilted square are examined. In order to numerically simulate the problem, the mesoscopic lattice Boltzmann method is utilized. The non-Newtonian Carreau-Yasuda model is employed. It is able to adequately handle the shear-thinning case. The simulation results of flow and HEAT transfer have been successfully verified with the previous studies. Several parameters such as Nusselt number, Drag coefficient, and Carreau number are investigated in details. Considering the temperature-dependent VISCOSITY, it is seen that with increasing the temperature-thinning index, the drag coefficient increases, but the Nusselt number decreases. By rotating the square obstacle, the results display that increasing the angle of inclination from zero to 45 degrees, increases both the drag coefficient and the Nusselt number. Also, the highest rate of HEAT transfer occur at the angle of 45 degrees (diamond); however it has a negative impact on the Drag coefficient.

In this paper the effect of using various models for conductivity and VISCOSITY considering Brownian motion of nanoparticles is investigated. This study is numerically conducted inside a cavity full of Water-Al2O3 nano fluid at the case of mixed convection HEAT transfer. The effect of some parameters such as the nanoparticle volume fraction, Rayleigh, Richardson and Reynolds numbers has been examined. The governing equations with specified boundary conditions has been solved using finite volume method. A computer code has been prepared for this purpose. The results are presented in form of stream functions, isotherms, Nusselt number and the flow power with and without the Brownian motion taken into consideration. The results show that for all the applied models the stream functions and isotherm have approximately same patterns and no considerable difference has been observed. In all the studied models when considering the Brownian motion, the average Nusselt number is higher than not taking this effect into account. The models of Koo-Kleinstreuer and Li-Kleinstreuer give almost same values for the maximum stream function and average Nusselt number. It is also true about the models of Vajjha-Das and Xiao et al.

This article delves into the interpretation of the Lorentz force's impact when employing the Carreau hybrid nanofluid model with infinite shear rate VISCOSITY over a stretching sheet, which incorporates porous medium. This model is highly effective in elucidating various non-Newtonian fluid behaviors, encompassing shear thinning and thickening properties. The governing equations consist of coupled nonlinear PDEs, which are transformed into a set of coupled nonlinear ODEs using similarity transformations. These equations are then numerically solved using a MATLAB built-in solver (bvp4c). Different characteristics of the considered flow of various parameters, such as the magnetic parameter, porous media parameter, Weissenberg number, stretching parameter, ratio parameter, coefficients space, and HEAT source/sinks, on temperature and velocity profiles, which are presented graphically. Additionally, the impacts of these parameters on the skin-friction coefficient and Nusselt number are tabulated. The Key findings suggest that, the higher values of the porous media parameter, magnetic parameter, Weissenberg number, and stretching parameter led to a decrease in velocity by 67.12% and 75.49% on average. Moreover, the velocity profile, Nusselt number, and skin friction coefficient are higher for the Al2O3/KO-based nanofluid compared to the Al2O3+MoS2/KO-based hybrid nanofluid. Also, the boundary layer of the hybrid nanofluid is observed to be hotter than that of the single nanoparticle nanofluid.