Temperature-dependent variable viscosity and thermal conductivity effects on non-Newtonian fluids flow in a porous medium

Purpose The purpose of this paper is to consider the simultaneous flow of Casson Williamson non Newtonian fluids in a vertical porous medium under the influence of variable thermos-physical parameters. Design/methodology/approach The model equations are a set of partial differential equations (PDEs). These PDEs were transformed into a non-dimensionless form using suitable non-dimensional quantities. The transformed equations were solved numerically using an iterative method called spectral relaxation techniques. The spectral relaxation technique is an iterative method that uses the Gauss-Seidel approach in discretizing and linearizing the set of equations. Findings It was found out in the study that a considerable number of variable viscosity parameter leads to decrease in the velocity and temperature profiles. Increase in the variable thermal conductivity parameter degenerates the velocity as well as temperature profiles. Hence, the variable thermo-physical parameters greatly influence the non-Newtonian fluids flow. Originality/value This study considered the simultaneous flow of Casson-Williamson non-Newtonian fluids by considering the fluid thermal properties to vary within the fluid layers. To the best of the author’s knowledge, such study has not been considered in literature.

Assessing the robustness and scalability of the accelerated pseudo-transient method towards exascale computing

The development of highly efficient, robust and scalable numerical algorithms lags behind the rapid increase in massive parallelism of modern hardware. We address this challenge with the accelerated pseudo-transient iterative method and present here a physically motivated derivation. We analytically determine optimal iteration parameters for a variety of basic physical processes and confirm the validity of theoretical predictions with numerical experiments. We provide an efficient numerical implementation of pseudo-transient solvers on graphical processing units (GPUs) using the Julia language. We achieve a parallel efficiency over 96 % on 2197 GPUs in distributed memory parallelisation weak scaling benchmarks. 2197 GPUs allow for unprecedented terascale solutions of 3D variable viscosity Stokes flow on 49953 grid cells involving over 1.2 trillion degrees of freedom. We verify the robustness of the method by handling contrasts up to 9 orders of magnitude in material parameters such as viscosity, and arbitrary distribution of viscous inclusions for different flow configurations. Moreover, we show that this method is well suited to tackle strongly nonlinear problems such as shear-banding in a visco-elasto-plastic medium. A GPU-based implementation can outperform CPU-based direct-iterative solvers in terms of wall-time even at relatively low resolution. We additionally motivate the accessibility of the method by its conciseness, flexibility, physically motivated derivation and ease of implementation. This solution strategy has thus a great potential for future high-performance computing applications, and for paving the road to exascale in the geosciences and beyond.

EMHD hybrid squeezing nanofluid flow with variable features and irreversibility analysis

This study discusses the entropy generation analysis of electro-magneto hydrodynamics (EMHD) hybrid nanofluid copper oxide-aluminum oxide/ethylene glycol (CuO-Al2O3/C2H6O2) flow amidst two rotating disks in a porous media having variable thermophysical features. The addition of the surface catalyzed to the homogeneous-heterogeneous reactions shorten the reaction time that may be taken as a novel aspect of the undertaken EMHD hybrid nanofluid squeezing flow. The inimitability of the assumed model is supplemented by considering the simultaneous effects of the variable thermal conductivity and viscosity. To simplify the governing flow model, suitable conversions are used to accurately translate the obtained partial differential equations to ordinary differential equations. The flow and energy transfer characteristics are computed and sketched graphically by using the Keller box scheme. The outcomes reveal that the drag force in radial and tangential directions depict the opposing trend for variable viscosity parameter. Furthermore, the normal magnetic and transverse electric fields play an essential role in the alignment of the nanoparticles throughout the flow field. The validation of the envisaged model is also a part of this study.

Heat Transfer and Flow Characteristics of Pseudoplastic Nanomaterial Liquid Flowing over the Slender Cylinder with Variable Characteristics

The present article investigates heat transfer and pseudoplastic nanomaterial liquid flow over a vertical thin cylinder. The Buongiorno model is used for this analysis. The problem gains more significance when temperature-dependent variable viscosity is taken into account. Using suitable similarity variables, nonlinear flow equations are first converted into ordinary differential equations. The generating structure is solved by the MATLAB BVP4C algorithm. Newly developed physical parameters are focused. It is observed that the heat transfer rate and the skin friction coefficient is increased remarkably because of mixing nano-particles in the base fluid by considering γb=1, 2, 3, 4 and λ=1, 1.5, 2, 2.5,3. It is found that the temperature field increases by inclining the values of thermophoresis and Brownian motion parameters. It is also evaluated that the velocity field decreases by increasing the values of the curvature parameter, Weissenberg number and buoyancy ratio characteristics.

Numerical Study of Variable Viscosity and Thermal Conductivity on Natural Convection Flow along a Vertical Flat Plate with Pressure Work and Heat Conduction

A heated vertical flat plate in the presence of heat generation is an extremely significant technological issue, and many academics have studied this sort of problem. A vertical plate submerged in a fluid with varying viscosity will be used in this research to investigate the effects of variable viscosity and thermal conductivity on heat generation free convection flow. The boundary layer equations in this section are two-dimensional, laminar, and unstable. The fundamental governing equations are turned into non-dimensional governing equations by using the necessary variables. Using the Crank-Nicolson implicit finite-difference technique, these equations are solved numerically. Viscosity and thermal conductivity are temperature-dependent properties of a viscous, incompressible fluid. Variations in the study's numerous parameters will reveal and compare the velocities, temperatures, local skin friction, and local heat transfer co-efficient profiles. There will be a comparison between the current numerical data and previously reported data findings. Besides that, we'll compare our current work numbers to those of past released publications. Graphs and tables will be used to display the findings for a variety of key physical characteristics.

A novel approach for EMHD Williamson nanofluid over nonlinear sheet with double stratification and Ohmic dissipation

The current article highlights the non-Newtonian Williamson nanofluid with electro-magnetohydrodynamic (EMHD) flow over a nonlinear expanding sheet. Thermal and solutal stratification effects are considered due to the higher temperature difference and the impact of variable viscosity along with Ohmic dissipation is also incorporated. Transformation is applied for the conversion of physical partial differential equations (PDEs) into non-dimensional higher order nonlinear ordinary differential equations (ODEs). A well-known analytical approach known as the homotopy analysis method (HAM) is effectively applied to solve the differential equations. Different non-dimensional emerging parameters such as Weissenberg and Hartman number, Brownian motion and stratification parameters, stretching index, viscosity parameter, and Lewis number are used to check their impacts on velocity, concentration, and temperature profiles. To acquire the optimal solution through HAM, [Formula: see text] -curves are drawn. In the tabulated form, the numerical values for the non-dimensional Nusselt number and skin friction are arranged.