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The study of the electro-osmotic forces (EOF) in the flow of the boundary layer has been a topic of interest in biomedical engineering and other engineering fields. The purpose of this paper is to develop an innovative mathematical model for electro-osmotic boundary layer flow. This type of fluid flow requires sophisticated mathematical models and numerical simulations.

The effect of EOF on the boundary layer Williamson fluid model containing a gyrotactic microorganism through a non-Darcian flow (Forchheimer model) is investigated. The problem is formulated mathematically by a system of non-linear partial differential equations (PDEs). By using suitable transformations, the PDEs system is transformed into a system of non-linear ordinary differential equations subjected to the appropriate boundary conditions. Those equations are solved numerically using the finite difference method.

The boundary layer velocity is lower in the case of non-Newtonian fluid when it is compared with that for a Newtonian fluid. The electro-osmotic parameter makes an increase in the velocity of the boundary layer. The boundary layer velocity is lower in the case of non-Darcian fluid when it is compared with Darcian fluid and as the Forchheimer parameter increases the behavior of the velocity becomes more closely. Entropy generation decays speedily far away from the wall and an opposite effect occurs on the Bejan number behavior.

The present outcomes are enriched to give valuable information for the research scientists in the field of biomedical engineering and other engineering fields. Also, the proposed outcomes are hopefully beneficial for the experimental investigation of the electroosmotic forces on flows with non-Newtonian models and containing a gyrotactic microorganism.

The purpose of this paper is to present a porous medium model for forced air convection in pin/plate‐fin heat sinks subjected to non‐uniform heating of a hot gas impinging jet. Parametric studies are performed to provide comparisons between inline square pin‐fin and plate‐fin heat sinks in terms of overall and local thermal performance for a fixed pressure drop.

Heat conduction in substrates is coupled with forced convection in the pin/plate‐fin flow channel. The forced convection is considered by employing the non‐Darcy model for fluid flow and the thermal non‐equilibrium model for heat transfer. A series of experiments is performed to validate the model for both the pin‐fin and plate‐fin heat sinks.

The present porous medium model is capable of capturing the presence of lateral heat spreading in the plate‐fins and the absence of lateral heat spreading in the pin‐fins under non‐uniform thermal boundary condition, attributing to the adoption of the orthotropic effective thermal conductivity for the solid phase in the energy equation. The present results show that the inline square pin‐fin heat sink has topological advantage over the plate‐fin heat sink, although the heat spreading through the plate‐fins on reducing the peak temperature on the substrate is pronounced.

This paper reports an original research on theoretical modeling of forced convection in pin/plate‐fin heat sinks subjected to the non‐uniform heating of an impinging jet.

A thoroughly literature review reveals that considerable attention have been given only to the two common cases, i.e. enclosure heated from below and heated from the side. For the inclined layer, on the other hand, the numbers of investigations are relatively small. Therefore, this paper aims to investigate the natural convective heat transfer in an inclined porous cavity using non-Darcian flow model, including the boundary surface and inertia effects.

The flow characteristics have been assumed to be two-dimensional, steady, incompressible flow, whereas the properties of porous media have been considered to be homogeneous and isotropic properties solid matrix. The non-Darcian flow model, including the boundary surface and inertia effects, has been numerically solved using finite difference method.

The initiation of multicellular flow and counter-rotating cell are strongly dependent on the aspect ratio A and the inclination angle θ. The orientation of the porous cavity, for a given Ra*, Fs/Pr* and A, has a significant effect on the heat transfer rate. The results also indicated that A has a dominant effect on the Nusselt number. The Nusselt number is strongly dependent on the Ra*, Fs/Pr*, A and θ. Therefore, operating conditions and geometry of the porous enclosure are required to be properly designed to achieve the desired objective.

The developed model can reveal the non-Darcian effects on the fluid flow and heat transfer in inclined porous media under natural convection case.

The aims of this study is to numerically investigate the thermal phenomena during magnetohydrodynamic (MHD) free convection in an oblique enclosure filled with porous media saturated with Cu–Al₂O₃/water hybrid nanofluid and heated at the left wavy wall. The thermophysical phenomena are explored thoroughly by varying the amplitude (λ) and undulation (n) of the wavy wall and the inclination of the enclosure (γ) along with other pertinent physical parameters. Darcy–Rayleigh number (Ra_m), Darcy number (Da), Hartmann number (Ha) and nanoparticle volumetric fraction (ϕ). The effect of all parameters has been analyzed and represented by using heatlines, isotherms, streamlines, average Nusselt number and local Nusselt number.

The finite volume method is used to work out the transport equations coupled with velocity, pressure and temperature subjected to non-uniform staggered grid structure after grid-sensitivity analysis by an indigenous computing code and the semi-implicit method for pressure linked equations (SIMPLE) algorithm. The solution process is initiated following an iterative approach through the alternate direction implicit sweep technique and the tridiagonal matrix algorithm (TDMA) algorithm. The iterative process is continued until successive minimization of the residuals (<1e-8) for the governing equations.

This study reveals that the increase in the heating surface area does not always favor heat transfer. An increase in the undulation amplitude enhances the heat transfer; however, there is an optimum value of undulation of the wavy wall for this. The heat transfer enhancement because of the wall curvature is revealed at higher Ra_m, lower Da and Ha and lower volume fraction of nanoparticles. In general, this augmentation is optimum for four undulations of the wavy wall with an amplitude of λ = 0.3. The heat transfer enhancement can be more at the cavity inclination   γ = 45°.

The technique of this investigation could be used in other multiphysical areas involving partial porous layers, conducting objects, different heating conditions, wall motion, etc.

This study is to address MHD thermo-fluid phenomena of Cu–Al₂O₃/water-based hybrid nanofluid flow through a non-Darcian porous wavy cavity at different inclinations. The amplitude and number of undulations of the wavy wall, permeability of the porous medium, magnetic field intensity, nanoparticle volumetric fraction and inclinations of the enclosure play a significant role in the heat transfer process. This analysis and the findings of this work can be useful for the design and control of similar thermal systems/devices.

Many researchers have examined the problem of buoyancy-induced free convection in a wavy-porous cavity packed with regular fluids or nanofluids. However, the effect of magnetic fields along with the amplitude (λ) at different undulations (n) of the heated wavy wall of an inclined enclosure is not attended so far to understand the transport mechanisms. Most often, the evolutions of the thermo-fluid phenomena in such complex geometries invoking different multiphysics are very intricate. Numerical implementations for simulations and subsequent post-processing of the results are also challenging.

This paper deals with theory and computation of fluid flow in fractured rock. Non‐Darcian flow behavior was observed in pumping tests at the geothermal research site at Soultz‐sous‐Forêts (France). Examples are examined to demonstrate the influence of fracture roughness and pressure‐gradient dependent permeability on pressure build‐up. A number of test examples based on classical models are investigated, which may be suited as benchmarks for non‐linear flow. This is a prelude of application of the non‐linear flow model to real pumping test data. Frequently, conceptual models based on simplified geometric approaches are used. Here, a realistic fracture network model based on borehole data is applied for the numerical simulations. The obtained data fit of the pumping test shows the capability of fracture network models to explain observed hydraulic behavior of fractured rock systems.

A comparative study is made between different flow models for analysis of natural convection in a differentially heated vertical square cavity filled with a fluid saturated porous medium. The solution is obtained by using a finite element method. The Darcy‐modified Rayleigh number, Ra^*, is varied from 50 to 1000 while the Darcy number, Da, ranges from 5 × 10^–7 to 10^–2. It is generally observed that for small values of Ra^* and Da, all other models converge with the Darcy flow model. However, for large values of Ra^* and Da, the Darcy flow model predicts the highest heat transfer rate, and the Brinkman‐Forchheimer extension yields the lowest heat transfer rate whilst prediction from the Brinkman‐extended model lies in between.

The purpose of this study is to analyze the entropy generation in magnetohydrodynamics stagnation point mixed convection flow of Carreau nanofluid through porous medium.

The system is solved using the homotopy scheme.

Minimizing radiation, magnetic, permeability and temperature difference parameters responds to minimizing entropy production.

To the best of the authors’ knowledge, no such analysis has yet been reported.

Transient conjugated forced convection in the thermal entry region of a thick‐walled annulus, filled with a homogeneous and isotropic porous medium, has been numerically investigated using finite‐difference techniques. Non‐Darcian effects as well as axial conduction of heat have been considered. The flow is assumed to be hydrodynamically fully developed and steady but thermally developing and transient. The thermal transient is initiated by a step change in the prescribed isothermal temperature on the outer surface of the external tube of the annulus while the inner surface of the internal tube is kept adiabatic. A parametric study is carried out to explore the effects of the Darcy number, the inertia term, the Peclet number and the porous medium heat capacity ratio on the transient thermal behavior in a given annulus.

This study aims to numerically investigate the transient forced convection of non‐Newtonian fluid in the entrance region of porous concentric annuli. The hydrodynamic behavior of the flow is assumed to be steady and it is modeled using the non‐Darcian flow and the power law models. The transients in the thermal behaviors result from sudden changes in the boundary temperatures. The effects of different fluid flow and solid matrix parameters on the thermal behavior of the annular are investigated.

A porous cavity flow field generates entropy owing to energy and momentum exchange within the fluid and at solid barriers. The heat transport and viscosity effects on fluid and solid walls irreversibly generate entropy. This numerical study aims to investigate convective heat transfer together with entropy generation in a partially heated wavy porous cavity filled with a hybrid nanofluid.

The governing equations are nondimensionalized and the domain is transformed into a unit square. A second-order finite difference method is used to have numerical solutions to nondimensional unknowns such as stream function and temperature. This numerical computation is conducted to explore a wide range of regulating parameters, e.g. hybrid nano-particle volume fraction (σ = 0.1%, 0.33%, 0.75%, 1%, 2%), Rayleigh–Darcy number (Ra = 10, 10², 10³), dimensionless length of the heat source (ϵ = 0.25, 0.50,1.0) and amplitude of the wave (a = 0.05, 0.10, 0.15) for a number of undulations (N = 1, 3) per unit length.

A thorough analysis is conducted to analyze the effect of multiple factors such as thermal convective forces, heat source, surface corrugation factors, nanofluid volume fraction and other parameters on entropy generation. The flow and temperature fields are studied through streamlines and isotherms. The average Bejan number suggested that entropy generation is entirely dominated by irreversibility due to heat transport at Ra = 10, and the irreversibility due to the viscosity effect is severe at Ra = 10³, but the increment in s augments irreversibility due to the viscosity effect over the heat transport at Ra = 10².

To the best of the authors’ knowledge, this numerical study, for the first time, analyzes the influence of surface corrugation on the entropy generation related to the cooling of a partial heat source by the convection of a hybrid nanofluid.