Low Darcy Number Research Articles

Exploring enhanced heat transfer in wavy porous enclosures: Optimization and analysis of ternary nanofluid integration under varied boundary conditions with MHD mixed convection

This study explores the application of Al2O3-ZnO-Fe3O4/Water ternary nanofluids for enhanced thermal management in engineering applications, addressing the MHD Darcy–Forchheimer problem with an emphasis on optimizing cooling processes in a 2D-wavy cavity under various moving boundary conditions. Aimed at surpassing the limitations of conventional cooling fluids, the research employs the finite volume method within the OpenFOAM® framework to investigate the impact of nanofluid integration on heat transfer efficiency and entropy generation, utilizing partial heating and eight distinct boundary scenarios. By comparing the performance of ternary nanofluids against that of hybrid and mono nanofluids, we identify optimal conditions that significantly enhance cooling effectiveness, as evidenced by a 37% improvement in heat exchange efficiency over water. The findings demonstrate the superior performance of Al2O3-ZnO-Fe3O4/Water nanofluids in achieving higher average Nusselt numbers at low Darcy numbers, despite an increase in entropy. Optimal conditions were identified for the most favorable scenario involving the movement of cavity lids, based on the Nusselt number, specifically in Case 7 (ul1+ and ul2−). Decreasing the number of waves in the cavity enhances heat transfer and reduces irreversibility. Finally, the study shows that the influence of lid motion on skin friction significantly varies with Richardson numbers, and the use of nanofluids over pure water notably reduces skin friction.

Optimizing heat transport in a permeable cavity with an isothermal solid block: Influence of nanoparticles volume fraction and wall velocity ratio

Abstract This study examines the influence of wall velocity ratio on mixed convective heat transport in a permeable cavity containing an isothermal solid block at its center. The analysis considers the characteristics of various flow variables, i.e., Darcy number, wall velocity ratio, Richardson number, and volume fraction of suspended nanoparticles, on heat transport and material flow characteristics. The principal equations are solved implementing the semi-implicit method for pressure linked equations algorithm, and the outcomes are compared with existing literature. The study shows that rising estimations of Darcy number, velocity ratio, Richardson number, and nanoparticles volume fraction lead to improved heat transfer rates. For example, at high Richardson number (100) and solid volume fraction (0.05), increasing the velocity ratio from 0.5 to 1.5 results in a 6% (5%) upsurge in heat transport rate. Conversely, at smaller Richardson number (0.01), the heat transport rate upsurges by 29% (28%). Similarly, at high Darcy numbers and low wall velocity ratios, a 3% (4%) escalate in heat transport rate is observed with an increase in nanoparticles concentration from 0 to 0.05, while a 9% (8%) increase in thermal performance is achieved at low Darcy numbers. The study emphasizes the importance of optimizing the combination of nanoparticles volume fraction, Darcy number, velocity ratio, and Richardson number to maximize thermal performance in the porous cavity.

Rayleigh–Bénard Convection in a Gas-Saturated Porous Medium at Low Darcy Numbers

Abstract Natural convection heat transfer is measured in a horizontal enclosure filled with a gas-saturated porous medium composed of glass spheres. The height-to-pore scale ratio (H/d) is in the range of 25–150, yielding a low Darcy number (5.87×10−8≤Da≤1.94×10−6), which satisfies the porous medium assumption more rigorously. The maximum values attained for the modified Rayleigh numbers (Ra* up to 6150) and fluid Rayleigh numbers (Raf up to 2.5×1011) at these low Darcy numbers enable access to both the Darcy and Forchheimer flow regimes. The heat transfer relationship just beyond the onset of convection is in good accordance with theory and previous experiments, varying linearly with the modified Rayleigh number. For higher modified Rayleigh numbers, the data diverge as a function of the Darcy number, depending on both Da and the modified Rayleigh number. Transition points between the Darcy and Forchheimer regimes are estimated. At the highest fluid Rayleigh numbers, the data with the largest pore scales show some evidence of moving toward a regime similar to that of Rayleigh–Bénard convection, where boundary layer and plume length scales are small enough that the details of the porous medium cease to matter. It is argued that even in this regime, the boundary layer length scales are not diminished enough to make the contribution of Brinkman drag significant.

Effects of anisotropic permeability on EMHD nanofluid flow and heat transfer in porous microchannel with wavy rough walls

This theoretical study thoroughly examines the complexities of fluid flow and heat transfer within microfluidic devices by employing anisotropic porous media with wavy walls. The effect of anisotropic permeability and electromagnetohydrodynamics (EMHD) on nanofluid transport is examined in a wavy microchannel under a constant pressure gradient. The nonlinear coupled governing equations for electric double-layer potential, velocity, temperature, and nanoparticle volume fraction are solved numerically using shooting techniques with the Runge–Kutta method. The numerical results are validated with the asymptotic analytical solutions. We explore the impact of parameters like the Hartmann number, Darcy number, and joule heating on nanofluidic flow. The interplay between anisotropic permeability ratio and angle significantly influences flow, temperature profiles, and nanoparticle volume fraction. Reduction in nanoparticle concentration is attributed to constrained entry into the porous medium due to elevated anisotropic permeability. Frictional heating, influenced by the Forchheimer inertial effect, enhances temperature and induces slug flow at low Darcy numbers. The Nusselt number peaks at low Darcy numbers with an anisotropic angle of φ=π/2, experiencing a minimum when φ=0. These findings deepen our understanding of the role of anisotropic permeability in shaping fluid flow and heat transfer in microfluidic systems influenced by EMHD effects.

Second Law Investigation in a Non-Newtonian Liquid Flow in a Porous Channel with Circular Obstacle

The problem of non-Newtonian fluid flow has taken considerable interest and has been the subject of several work in latest years due to its various requests in different fields of engineering, in particular the interest in the problems of heat transfer in non-Newtonian liquids, such as lubrication, hot rolling, cooling problem and drag reduction. Here, mixed convection heat transport and its related entropy production in a porous channel with circular obstacle saturated via non-Newtonian power law liquid has been scrutinized. The influences on entropy production of the power law index, the Reynolds number, the Rayleigh number and the Darcy number are investigated. Being a novelty of this work, an optimization study of the thermodynamic irreversibility as a function of the channel inclination angle and the power law index is undertaken. The governing equations of the problem are solved employing the COMSOL software. Outcomes illustrate that the governing parameters strongly affect the entropy production. The thermal entropy generation is maximal at low value of power law index and high value of Reynolds number. The effect of Reynolds number become insignificant at relatively high power law index. At fixed Reynolds number value, a rise in the power index (n) leads to a reduce in the thermal entropy. This decrease is tiny, at low value of Reynolds number (Re) and turn into increasingly considerable as Re rises. The streamlines show the existence of two recirculation zones just after the circular obstacle, whose existence depends on both Re and power law index. Results show that the greatest variation relating to the inclination angle is for power law index equal to 0.4. Results indicate also that, at low Darcy number and relatively high power law index, the intrinsic effect of the modified Darcy number on Darcy viscous irreversibility become pronounced giving a sharp increase in the total entropy production.

Mathematical Entropy Analysis of Natural Convection of MWCNT—Fe3O4/Water Hybrid Nanofluid with Parallel Magnetic Field via Galerkin Finite Element Process

Heat transfer in a symmetrical cavity with two semi-cylinders was explored in this study. Several parameters, such as (103≤Ra≤106), (10−5≤Da≤10−2), (0.02≤ϕ≤0.08), (0.2≤ε≤0.8), and (0≤Ha≤100) were selected and evaluated in this research. The outcome of the magnetic field and the temperature gradient on the nanofluid flow is considered. The geometric model is therefore described using a symmetry technique. The flow issue for the governing equations has been solved using the Galerkin finite element method (G-FEM), and these solutions are presented in dimensionless form. The equations for energy, motion, and continuity were solved using the application of the COMSOL Multiphysics® software computer package. According to the results, there is a difference in the occurrence of the magnetic parameter and an increase in heat transmission when the right wall is recessed inward. The heat transmission is also significantly reduced when the right wall is exposed to the outside. The number of Nusselt grows directly proportional to the number of nanofluids in the environment. In contrast, all porous media with low Darcy and Hartmann numbers, high porosity, and low volume fraction have high Nusselt numbers. It is found that double streamlines for the hot side and single cooling for Darcy, Rayleigh, and Hartmann numbers. A cold isotherm at various physical parameters is needed in the top cavity. Rayleigh’s number and a solid volume fraction raise Darcy’s number, increasing heat transmission inside the cavity and thermal entropy determines entropy components.

The Thermal Performance Analysis of an Al2O3-Water Nanofluid Flow in a Composite Microchannel

Partial filling of porous medium insert in a channel alleviates the tremendous pressure drop associated with a porous medium saturated channel, and enhances heat transfer at an optimum fraction of porous medium filling. This study pioneered an investigation into the viscous dissipative forced convective heat transfer in a parallel-plate channel, partially occupied with a porous medium at the core, under local thermal non-equilibrium condition. Solving the thermal energy equation along the Darcy-Brinkman equation, new exact temperature fields and Nusselt number are presented under symmetrical isoflux thermal boundary condition. Noteworthy is the heat flux bifurcation at the interface between the clear fluid and porous medium driven by viscous dissipation, in cases where the combined hydrodynamic resistance to fluid flow and thermal resistance to fluid conduction is considerable in low Darcy number porous medium insert. However, viscous dissipation does not affect the qualitative variation of the Nusselt number with the fraction of porous medium filling. By using Al2O3-Water nanofluid as the working fluid in a uniformly heated microchannel, partially filled with an optimum volume fraction of porous medium, the heat transfer coefficient improves as compared to utilizing water. The accompanied viscous dissipation however has a more adverse impact on the heat transfer coefficient of nanofluids with an increasing Reynolds number.

Prediction of pore-scale-property dependent natural convection in porous media at high Rayleigh numbers

Natural convection in porous media has received increasing attention in recent years due to its significance in engineering applications. This process is traditionally analyzed by the solution of the classical Darcy-Oberbeck-Boussinesq (DOB) equations. According to the DOB equations, natural convection in porous media is exclusively dependent on the Rayleigh-Darcy number, Ra, while the Sherwood number, Sh, has a linear relationship with Ra at high Rayleigh numbers. However, these predictions conflict with experimental observations. In this study, we have performed a pore-scale resolved direct numerical simulation (DNS) study of natural convection in periodic porous media composed of two-dimensional square and circular obstacles. Based on our analysis, a new correlation of Sh for large Rayleigh numbers (Ra≥1000), low Darcy numbers Da, and high Schmidt numbers Sc (Da/Sc≤2×10−8) has been proposed, expressed as Sh=aRa1−0.2φ2+1, where a=0.011±0.002 is a pore-scale geometric parameter. The new correlation has been validated over a wide range of Rayleigh numbers, porosity values, and pore-scale geometries. Our DNS results also show that, with a decrease of porosity, it becomes more difficult for mega-plumes with low wavenumbers to enter the boundary layer. Low wavenumber motions decay much faster with a decrease of Da than the pore-scale motions near the wall. The volume-averaged dissipation rate nondimensionalized using the pore size εˆi has the scaling law εˆi∼Da in the internal region and εˆi∼Da1/2 in the near-wall region. We expect that these characteristics obtained from DNS also apply to natural convection in porous media with much lower Darcy numbers.

Dynamic heat transfer in a tall annulus: Effects of the porous matrix for low Darcy numbers

This work focuses on the transient natural convection in vertical annuli partially filled with a porous medium, characterized by a low value of Darcy number. The generalized porous medium model has been implemented and solved by using a validated and stable version of a fully explicit fractional step algorithm. Sensitivity analyses are performed here by changing both the geometrical features of the cavity and the porous domain, both the properties of the porous medium. The results are compared with those obtained for the same cavity in absence of the porous insert, in order to investigate how it influences the transient evolution of the Nusselt number.

Two-phase modelling of the nanofluid mixed convection in a porous open cavity

The aim of the current work is to study the mixed convection of Fe3O4-water magnetic nanofluid in a heated porous open cavity. Buongiorno's two-phase model is utilised to consider the Brownian and thermophoresis of nanoparticles in the carrier fluid. Using the Darcy-Brinkman and Boussinesq approximations, the governing equations are solved by the finite volume technique, numerically. Numerical computations are performed for various Richardson numbers (Ri = 0.01, 0.1, 1 and 10), Reynolds numbers (Re = 10, 100, 300 and 600), volume fraction of nanoparticle (φ = 0 and 0.06), porosity (ε = 0.5, 0.8 and 1) and Darcy numbers (0.0002 ≤ Da ≤ 500,000). The nanofluid flow and heat transfer rate are discussed in detail by contour plots of streamlines and isotherms of nanoparticles. Numerical results indicate that increasing Reynolds number increases the average Nusselt number. However, in low Darcy numbers, porosity has no significant effect on the Nusselt number.

Analysis of Brinkman-Forchheimer extended Darcy's model in a fluid saturated anisotropic porous channel

<p style='text-indent:20px;'>We present asymptotic analysis of Couette flow through a channel packed with porous medium. We assume that the porous medium is anisotropic and the permeability varies along all the directions so that it appears as a positive semidefinite matrix in the momentum equation. We developed existence and uniqueness results corresponding to the anisotropic Brinkman-Forchheimer extended Darcy's equation in case of fully developed flow using the Browder-Minty theorem. Complemented with the existence and uniqueness analysis, we present an asymptotic solution by taking Darcy number as the perturbed parameter. For a high Darcy number, the corresponding problem is dealt with regular perturbation expansion. For low Darcy number, the problem of interest is a singular perturbation. We use matched asymptotic expansion to treat this case. More generally, we obtained an approximate solution for the nonlinear problem, which is uniformly valid irrespective of the porous medium parameter values. The analysis presented serves a dual purpose by providing the existence and uniqueness of the anisotropic nonlinear Brinkman-Forchheimer extended Darcy's equation and provide an approximate solution that shows good agreement with the numerical solution.</p>

Local thermal non-equilibrium conjugate forced convection and entropy generation in an aircraft cabin with air channel partially filled porous insulation

PurposeThe purpose of this study is to numerically investigate heat transfer and entropy generation between airframe and cabin-cargo departments in an aircraft. The conjugate forced convection and entropy generation in a cylindrical cavity within air channel partly filled with porous insulation material as simplified geometry for airframe and cabin-cargo departments are considered under local thermal non-equilibrium condition.Design/methodology/approachThe non-dimensional governing equations for fluid and porous media discretized by finite volume method are solved using the SIMPLE algorithm with pressure and velocity correction.FindingsThe effects of the following parameters on the problem are investigated; Reynolds number, Darcy number, the size of inlet and exit cross-section, thermal conductivity ratio for solid and fluid phases, angle between the vertical symmetry axis and the end of channel wall exit and the gap between adiabatic channel wall and horizontal adiabatic wall separating cabin and cargo sections.Originality/valueThis paper can provide a basic perspective and framework for thermal design between the fuselage and cabin-cargo sections. The minimum total entropy generation number is calculated for various Reynolds numbers and thermal conductivity ratios. It is observed that the channel wall temperature increases for high Reynolds number, low Darcy number, narrower exit cross-section and wider the gap between channel wall and horizontal.

Effects of an annular porous layer on vortex-induced vibrations of an elastically-mounted circular cylinder

A numerical study is conducted on vortex-induced vibrations (VIVs) of an elastically supported circular cylinder wrapped by a porous layer at a Reynolds number of Re=150. The cylinder is allowed to vibrate only in the transverse direction. The mass ratio and damping ratio of the system are kept constant at mr=2 and ζ = 0.01, respectively. The effects of Darcy number (10−6≤Da≤50), the dimensionless thickness of the porous layer (ep=0,0.25,0.5,1) and reduced velocity (3≤ur≤20) on the vortex shedding pattern, displacement amplitude, displacement frequency as well as lift and drag coefficients are investigated. Results show that increasing Darcy number causes the displacement amplitude of the cylinder to decrease. Moreover, values of Da smaller than 10−4 resemble the wake structures of the bare cylinder. In these low Darcy numbers (also for the bare cylinder) the 2S* mode is observed only at ur=5. However, at higher values of Darcy number the region of 2S* mode is extended to higher values of reduced velocity. Also, except for the limiting cases of very high or very small values of Darcy number (10−6 or 50), the sudden decrease in the displacement amplitude at the end of the traditional lock-in regime is eliminated from the response of the system.

THE EFFECTIVE VISCOSITY OF A SUSPENSION OF POROUS PARTICLES BASED ON THE DARCY-STOKES COUPLING MODEL

Particle suspensions exist widely in nature and engineering applications, and their viscous characteristics have an important influence on their flow behavior. Based on the Darcy-Stokes coupling model, the analytical formulas of effective viscosity of dilute suspensions containing porous particles are derived in this paper. Firstly, an auxiliary problem is solved, that is, the disturbance caused by porous media spheres in the flow field with linear distribution under the condition of low Reynolds number. The fluid flows in the free-flow domain and porous medium are governed by the Stokes equation and Darcy’ law, respectively. The mass conservation law, the balance of normal forces, and the Beavers-Joseph(-Saffman) interface condition are used at the fluid–porous interface. An analytical solution for the present coupled free-flow and porous-medium system is derived by using the undetermined coefficient method. Then the additional heat dissipation rate caused by the porous media particle is calculated. Intrinsic viscosity of the porous media suspension under the condition of low concentration is determined as a function of the Darcy number and the Beavers-Joseph coefficient, which is based on the additional heat dissipation rate under the condition of low concentration. It is found that the intrinsic viscosity increases with increasing the Beavers–Joseph coefficient, and the larger the Beavers–Joseph coefficient is, the slower the increase of the intrinsic viscosity. When Darcy number is in the range of \begin{document}${10^{ - 6}}$\end{document} to \begin{document}${10^{ - 4}}$\end{document} , the intrinsic viscosity is close to 2.5, which was consistent with the classical Einstein viscosity formula. When Darcy number is in the range of \begin{document}${10^{ - 4}}$\end{document} to \begin{document}${10^{ - 1}}$\end{document} , the intrinsic viscosity decreases rapidly, so the effective viscosity coefficient of porous media suspension is closer to the viscosity of the based fluid. At last, the present effective viscosity formula is compared with that obtained by the Darcy-Brinkman equation coupling with the shear stress jump condition. It can be found that the effective viscosities obtained two different models agree well with each other in the low Darcy number regime when the sum of the Beavers-Joseph coefficient and the shear stress jump coefficient is unity.

Numerical Investigation of Simultaneous Effects of Nanofluid Flow and Porous Baffle on Thermal Energy Transfer and Flow Features in a Circular Channel

Abstract In the present work, the forced-convection heat transfer features of different nanofluids in a circular channel with porous baffles are numerically investigated. Nanofluid flow in the porous area is simulated by the simultaneous use of Darcy-Brinkman-Forchheimer and two-phase mixture models. The flow is considered to be laminar, two-dimensional, steady, axially symmetric, and incompressible. The simulations are conducted in fluent software and by using the finite volume method and SIMPLE algorithm. The influences of various parameters, including Reynolds number, volume fractions of nanoparticles, Darcy number, porous region height, and various nanofluid types on the nanofluid flows and their thermal energy transfer features, are investigated. Results show that porous blocks significantly change the flow characteristics and thermal energy transfer features. For instance, at low Darcy numbers, the permeability of the porous region decreases, and the porous baffles have greater resistance against the nanofluid flow. As a result, the vortex area becomes stronger and taller, and streamlines near obstacles are tighter. However, in high Darcy numbers, due to the high permeability of the porous medium, the flow will be the same as the flow in the channel without barriers, and the porous baffles will not have much influence on the flow. For example, at Darcy number Da = 10−4 the vortex area almost disappears. The growth of conductivity ratio increases the local Nu in the vicinity of the barriers. Properties of the porous medium and nanofluid flow affect the thermal energy transfer rate, and it can be improved by making appropriate changes to these features.

Impacts of Amplitude and Local Thermal Non-Equilibrium Design on Natural Convection within NanoflUid Superposed Wavy Porous Layers.

A numerical study is presented for the thermo-free convection inside a cavity with vertical corrugated walls consisting of a solid part of fixed thickness, a part of porous media filled with a nanofluid, and a third part filled with a nanofluid. Alumina nanoparticle water-based nanofluid is used as a working fluid. The cavity’s wavy vertical surfaces are subjected to various temperature values, hot to the left and cold to the right. In order to generate a free-convective flow, the horizontal walls are kept adiabatic. For the porous medium, the Local Thermal Non-Equilibrium (LTNE) model is used. The method of solving the problem’s governing equations is the Galerkin weighted residual finite elements method. The results report the impact of the active parameters on the thermo-free convective flow and heat transfer features. The obtained results show that the high Darcy number and the porous media’s low modified thermal conductivity ratio have important roles for the local thermal non-equilibrium effects. The heat transfer rates through the nanofluid and solid phases are found to be better for high values of the undulation amplitude, the Darcy number, and the volume fraction of the nanofluid, while a limit in the increase of heat transfer rate through the solid phase with the modified thermal ratio is found, particularly for high values of porosity. Furthermore, as the porosity rises, the nanofluid and solid phases’ heat transfer rates decline for low Darcy numbers and increase for high Darcy numbers.

Study of mixed convection in two layers of saturated porous medium and nanofluid with rotating circular cylinder

In this study, a numerical investigation of mixed convective heat transfer in a square enclosure partitioned in two layers with a rotating circular cylinder at the middle of the cavity has been carried out. The experiments are performed with Al2O3–water nanofluid (upper layer) and superposed porous medium (lower layer). The upper and lower horizontal walls are assumed to be insulated, while the left and right walls are kept at high and low temperature respectively. Galerkin finite element method has been used to solve the dimensionless governing equations. This study is focused to investigate the effect of Darcy number (10−2≤ Da ≤10−5), Rayleigh number (103≤ Ra≤106), dimensionless angular rotational velocity (−6000≤ W ≤ 6000), solid volume fraction (0≤ ɸ ≤0.06), and the radius of the inner circular cylinder (R = 0.1, 0.2 and 0.3) on the heat transfer, fluid flow, and the physical characteristics thermal of the thermal fields. The results show that the intensity of the flow, steep temperature gradient, and the average Nusselt number (Nu) increase with increasing the value of Darcy number, Rayleigh number, and solid volume fractions at any cylinder radius. Moreover, the recirculation and isotherm distribution lines of the fluid at low Darcy numbers are high when the cylinder rotates counter-clockwise compering with clockwise. The findings also revealed that when W = 0, the maximum Nu is at R = 0.1 and decreases as the cylinder radius increases. Moreover, at high Darcy number, the highest local Nusselt number is found at the porous layer region in case of clockwise rotation while at the nanofluid layer region in case of anti-clockwise rotation.

Heat transfer characteristics of a circular cylinder covered by a porous layer undergoing vortex-induced vibration

In this study, heat transfer characteristics of an elastically-mounted circular cylinder wrapped by a porous layer are studied numerically. The vibration of the cylinder is modeled as a forced mass-spring-damping system and it is assumed that the cylinder can move only in the transverse direction. The effects of Darcy number (10−6≤Da≤10−2), the dimensionless thickness of the porous layer (ep=0.25,0.5,1) and reduced velocity (3≤ur≤20) on the cylinder displacement, vortex shedding pattern, and Nusselt number are investigated. The Reynolds number, damping ratio, and mass ratio are taken as Re=150,ζ = 0.01 and mr=2, respectively. Results show that increasing Darcy number decreases the displacement amplitude of the cylinder. It is concluded that by increasing the reduced velocity from ur=3 to ur=9, the Nusselt number and the displacement amplitude of the cylinder increase and reach a maximum value at some optimum reduced velocity which depends on the value of Darcy number. Beyond which those quantities are reduced. It is observed that for all values of reduced velocity, the temperature distribution inside the porous layer is not affected by the position of the cylinder and the temperature variations are approximately equal at crest and rest points. Also, at low Darcy numbers, the temperature distributions are uniform in the peripheral direction due to small flow penetration into the porous material Moreover, at Da=10−2,10−3 and 10−4 the Nusselt number is increased by 7%, 9% and 10% for the reduced velocities of ur=7,ur=3 and ur=6, respectively.

Elastohydrodynamics of a deformable porous packing in a channel competing under shear and pressure gradient

Elastohydrodynamics of a deformable porous medium sandwiched between two parallel plates is investigated under the influence of an externally applied pressure gradient as well as an induced shear due to the movement of the upper plate. Biphasic mixture theory is used to describe the macroscopic governing equations for the fluid velocity and the solid displacement, assuming the deformable porous medium as a continuum space. The corresponding reduced mathematical model is a coupled system of elliptic partial differential equations. It is assumed that the fluid at the lower plate experiences slip due to the surface roughness of the plate. The exact solution for unidirectional fluid velocity and solid deformation resembling plain Poiseuille–Couette flow are presented for steady and unsteady states. Asymptotic analysis of the biphasic mixture in the case of low and high Darcy numbers is performed to validate the obtained solution using Prandtl’s matching technique. It is observed that the Womersley number dictates whether the fluid is trapped inside the channel or escapes the channel. The competition between the shear and the pressure gradient is analyzed, and a critical criterion is established that dictates the dominant factor. A mathematical analysis of the current problem is invaluable in understanding the mechanical behavior of biomass under pressure-driven flow in applications such as tissue engineering or shear driven flow inside endothelial glycocalyx layers, which are discussed in brief. In this context, our analysis on the extent of tissue deformation in response to frequency variations is expected to give useful insights to identify the right diagnosis.

Natural convection in a partially heated porous cavity to Casson fluid

Abstract In the present study, the phenomenon of natural convection in a square porous cavity containing Casson fluid is investigated, numerically. The non-Newtonian model of Casson fluid is utilized to obtain the governing equations of a flow problem. The thermal control inside the cavity is managed by partially heating the bottom wall and symmetric cooling of the side walls while the top wall is taken to be adiabatic. The penalty finite element method is used to solve the non-linear coupled equations of the flow problem. The effect of different lengths of heated zone e, Rayleigh number Ra and Darcy number Da has been examined on flow velocity and temperature distribution inside the cavity. The impact of effective viscosity of the fluid by varying Casson fluid parameter γ on the flow of fluid and heat transport has also been investigated. The results are demonstrated by plotting streamlines, isotherms and average Nusselt number over wide ranges of governing parameters. The obtained results show that with an increase in Casson fluid parameter γ and Darcy number Da, heat transfer and flow circulation increases. It is also observed that the conduction dominant heat transfer takes place for low Darcy number over a wide range of the Rayleigh number (102 ≤ Ra ≤ 106).