Narrow Results

This paper proposes a study of the computational efficiency of a lattice Boltzmann model (LBM) solver to simulate the behavior of a generalized Newtonian fluid. We present recent progress concerning a 4-1 planar contraction considering a power-law and a Carreau-law model. First we compare the power-law model for a Poiseuille flow with the analytical solution, and show that our model is second-order accurate in space. Then we compare the results obtained with LBM for both laws to those obtained using a commercial finite element solver for the 4-1 plane sharp corner contraction.

A transient flow model for power-law fluid in fractal porous media is derived by combining transient flow theory with the fractal properties of tortuous capillaries. Pressure changes of transient flow for power-law fluid in fractal porous media are related to pore fractal dimension, tortuosity fractal dimension and the power-law index. Additionally, the starting pressure gradient model of power-law fluid in fractal porous media is established. Good agreement between the predictions of the present model and that of the traditional empirical model is obtained, the sensitive parameters that influence the starting pressure gradient are specified and their effects on the starting pressure gradient are discussed.

Interaction between nonuniform heat source/sink, magnetic field and thermal radiation with heat flux through the flow of non-Newtonian power-law fluid due to a linearly stretching sheet was studied numerically using an implicit finite difference method (FDM). The heat flux is assumed to depend on both the thermal conductivity and the thermal radiation. Besides, the effects of all governing parameters, such as the magnetic parameter, thermal conductivity parameter, the power-law index parameter, Prandtl number, the space-dependent heat source/sink parameter, the temperature-dependent heat source/sink parameter, and the radiation parameter, on the profiles of velocities and temperature are studied and discussed. In particular, thermal radiation was found to play a key role in the heat transfer characteristics and in the formation of thermal boundary layer. Generally, our numerical results reveal that both the velocity and temperature distributions are marginally influenced by both the magnetic parameter and power-law index. A good agreement is observed between our results via finite difference method and the previously published numerical results for some special case.

The vortex in the branching microchannel enhances the mixing and heat transfer performance. To investigate the vortex intensity quantitatively, a lattice Boltzmann model for incompressible power-law fluid is developed by setting the range of lattice viscosity (0.001 $\le \nu \le$ 1). The validation of the current model is carried out by modeling the vortex in a T-shaped branching channel and the Poiseuille flow of power-law fluids. Then the vortex intensity in the $\psi$-shaped microchannel is numerically studied in terms of Reynolds number, branching angle and power-law index. The result indicates that both the recirculation length and height increase with the increase of the Reynolds number. The branching angle has a negative impact on the recirculation length, and it has little effect on the recirculation height. The influence of the power-law index on recirculation length and height depends on the Reynolds number.

The flow of non-Newtonian liquids and their heat transfer characteristic gained more importance due to their technological, industrial and in many engineering applications. Inspired by these applications, the magnetohydrodynamic (MHD) flow of non-Newtonian liquid characterized by a power-law model is scrutinized. Further, viscous dissipation, Marangoni convection and thermal radiation are taken into the account. In addition, the production of entropy is investigated as a function of temperature, velocity and concentration. For different flow parameters, the total entropy production (EP) rate is examined. The appropriate similarity transformations are used to reduce the modeled equations reduced into ordinary differential equations (ODEs). The Runge–Kutta–Fehlberg 45-order procedure is then used to solve these reduced equations numerically using the shooting technique. Results reveal that the escalating values of radiation parameter escalate the heat transference, but the contrary trend is portrayed for escalating values of power-law index. The augmented values of thermal Marangoni number decline the heat transference. The gain in values of radiation parameter progresses the entropy generation.

Lubrication theory has attained attention lately due to its practical applications, such as the formation of thin films, adhesives, and lubrication of components of machines. Jeffrey’s nanofluid flow over the stagnation region past a power-law lubricated surface is presented in this study. Buongiorno’s model is employed to scrutinize the effects of thermophoresis and Brownian motion phenomena with constant wall and prescribed surface temperature (PST) and effects of heat source/sink, chemical reaction, and Joule heating. Due to the continuity of shear stress of fluid-lubricant and velocity at the interface, interfacial conditions are generated. By similarity conversions, ordinary differential equations are obtained and their solutions are computed numerically. For power-law index equaling $\frac{1}{2}$, local similarity solutions are calculated by adopting a finite difference scheme, viz. bvp4c in MATLAB. The energy profiles for constant and prescribed temperatures are monitored. The effects of pertinent parameters on the flow, thermal, and mass distributions are scrutinized and illustrated in graphs. Flow field decreases significantly by raising slip parameter as the aptitude of power-law lubricant to improve the velocity of the bulk fluid. The numerical comparison of wall stress and Nusselt number is also presented. The slip and Jeffrey’s material parameters raise the numerical outcomes of the wall shear stress. In addition, increment in Prandtl number enhances the numerical value of the Nusselt number; however, it reduces for relaxation-to-retardation times ratio.

In this paper, we study bioconvection radiative flow of power-law nanofluid. Nanofluid characteristics are incorporated by utilizing the Buongiorno model. The influence of motile gyrotactic microorganism is retained. Magnetohydrodynamics and time-dependent aspects are under consideration. Related governing expressions are transformed into dimensionless partial differential system. The resulting nonlinear system is tackled through finite difference technique. Outcomes of emerging variables like Prandtl number, Hartmann number, Buoyancy ratio parameter, Grashof number, Peclet number, bioconvection Rayleigh number, Peclet number, radiation and Schmidt number are graphically discussed. Velocity is controlled by higher Hartman number while it boosts against higher Grashof and bioconvection Rayleigh numbers, buoyancy ratio and stretching parameters. Higher radiation, Brownian and thermophoresis parameters lead to intensification in temperature profile while it reduces for higher Prandtl number. Bioconvection profile reduces against higher Peclet and Lewis numbers.

Present analysis deals with the impact of nonlinear convection on MHD non-Newtonian fluid flow considering exponentially stretched sheet through porous media. Additionally, the effects of radiation, Joule heating and energy dissipation have been taken into account. The considered flow situation of nonlinear PDEs is transmuted to nonlinear ODEs using similarity analysis. The numerical computations are derived using a fourth-order Runge–Kutta scheme with a shooting technique. Meaningful observations are discussed for velocity and energy profiles. Further, the impact of pertinent parameters considering pseudoplastic fluids $(n=0.6)$ and dilatant fluids $(n=1.3)$ is briefed through graphs. It is noted that the escalation in the values of the power-law index declines the velocity and energy profile. Higher values of the nonlinear parameter decline the energy profile.

In this paper, we discuss the forced convective heat transfer of power-law fluid flow through porous annular sector duct by applying the Brinkman-extended Darcy flow model. A strongly implicit procedure (SIP) is utilized to solve the algebraic momentum and energy equations which was discretized by using the finite volume method (FVM). The effects of permeability factor and power-law index corresponding to the Brinkman-extended Darcy flow model and power-law fluid, respectively, on flow and heat transfer rate are carried out numerically and graphically against different values of parameters corresponding to geometrical configuration. In the pseudo-plastic fluids, a maximum decrease of more than $100\%$ has been observed in $f\mathrm{\text{Re}}$, whereas maximum decrease in dilatant fluid is around $30\%$, when we increase the values of k. A decrease of 16.02% in Nu has been carried out in pseudo-plastic fluid, whereas unforeseen decrease in Nu has been observed in both Newtonian and dilatant fluids comparably pseudo-plastic fluid for particular values of k.

During the development of deep-water oil and gas resources, severe engineering problems or even marine geological hazards might be induced by the complex geological characteristics of deep-water weakly consolidated (DWC) formation. To solve these problems, the power-law cementing fluid was used to solidify the DWC formation during the well-cementing operation. However, the transportation process of cementing fluid in DWC formation is still unclear. To guide the solidification operation of DWC formation, a mathematical model for predicting the penetration distance of cementing fluid in DWC formation was proposed based on the generalized Darcy’s law and fractal theory. All the parameters in this model have clear physical meaning and no empirical parameter is involved. The numerical and experimental validation results show that the proposed model calculated penetration distance agrees well with both simulated and experimental results. The model capacity relates to the penetration pressure, the viscosity of cementing fluid, the permeability of formation, the effective radius of the flow path and the fractal dimension of formation. The maximum error of this model is less than 20%, which indicates that the mathematical model is reliable.

The study characterizes power-law fluid through charged fibrous porous media with spatial fractional-derivative and fractal geometry. Seepage flow of power-law fluid across fractal fibrous porous media in the presence of electric double layers (EDLs) is investigated based on the capillary bundle model. The acquired velocity distribution equation in a narrow capillary is then transformed into the form of series with appropriate Taylor approximation. After that, an analytical formula for dimensionless permeability is derived based on the generalized Darcy’s law. The effects of diverse parameters, including the fractal dimension of pore area, porosity, fractional order and Zeta potential on dimensionless permeability, are discussed. It can be seen from the results that lower fractional order has an amplification effect on dimensionless permeability with the change in Zeta potential. The results provide some theoretical guidance for revealing the seepage mechanism of a power-law fluid in charged porous media.

Many scholars have studied the interporosity flow function (IFF) and shape factor. However, the existing research does not consider the complex microstructure of dual media and the influence of fluid types on interporosity flow. In this paper, the anisotropic IFF and shape factor model of power-law fluid in smooth and rough fracture dual media are established by using the rough capillary bundle model and considering the influence of the microstructure of dual media and the type of fluid. The relationship between IFF, shape factor, and relative roughness in dual media is studied. It is found that the relative roughness is inversely proportional to the IFF and inversely proportional to the shape factor. In addition, the model is compared with the existing research and experimental data to verify the rationality of the model.

Interaction between two spheres with an interstitial fluid is essential in Discrete Element modeling for simulating the behaviors of "wet" particulate materials. In this paper the interaction between two spheres with an interstitial Power-law fluid was approximately resolved as normal and tangential interactive models respectively, for which the governing equations were simplified on the basis of Reynolds approximation. These equations were then solved analytically together with the boundary conditions to obtain the pressure distributions for each individual model, and eventually solutions of the viscous squeeze force and the tangential viscous resistance were obtained, which provide a set of solu-tions for implementing into DEM code or other purposes.