Hydrodynamic analysis of nanofluids flow over 45° inclined porous square cylinder using Darcy–Brinkman–Forchheimer model

Effects of Prandtl number on the forced convection heat transfer from a porous square cylinder

Numerical modeling of flow around and through a porous cylinder with diamond cross section

Flow around porous square cylinders with a periodic and scalable structure

Unsteady convection heat transfer for a porous square cylinder varying cylinder-to-channel height ratio

PurposeThis study aims to investigate lattice Boltzmann (LB) simulation of the fluid flow and heat transfer characteristics of a heated porous elliptic cylinder in uniform flow based on the two-domain scheme. In the present research, the effect of axis ratio (1 ≤ AR ≤ 2), Reynolds number (5 ≤ Re ≤ 40) and Darcy number (10−4 ≤ Da ≤ 10−2) are studied.Design/methodology/approachTo perform the LB simulation based on the two-domain scheme, the nonequilibrium extrapolation method is modified to model the heat transfer interfacial conditions required at the curved interface.FindingsThe results show that the axis ratio as well as Reynolds and Darcy numbers significantly affect the fluid flow and heat transfer characteristics of the porous elliptic cylinder. It is shown that for AR > 1, the phenomenon of detached recirculating zone occurs at much higher Darcy numbers compared with the case of the porous circular cylinder (AR = 1). The results show that the location of maximum temperature within the cylinder moves downstream when the Reynolds number, Darcy number and axis ratio increase. It is also concluded that the average Nusselt number of a porous elliptic cylinder is always lower than that of a porous circular cylinder.Originality/valueThe LB simulation of forced convection from a porous cylinder in uniform flow with a curved interface based on the two-domain scheme has not been studied yet.

Incompressible, two-dimensional flow around a porous square cylinder placed in an infinite stream is simulated using the d2q9i model of the lattice Boltzmann method. The Reynolds number (based on the height of the cylinder) is kept at 100. The porosity ϕ of the cylinder is varied from 0.25 to 0.9 and permeability through the Darcy number Da from 0.0001 to 0.1. The velocity data at a point downstream of the cylinder are collected at each time step. Discrete Fourier transform analysis of this data is carried out to extract the dominant frequencies of the unsteady flow field behind the cylinder. Strouhal numbers (St) calculated using these dominant frequencies are compared with those of corresponding solid cylinder to bring out the effect of the porous medium on the wake structure and the vortex shedding. At Re=100, as the nondimensional permeability Da is increased from the solid cylinder limit, more flow results through the porous cylinder. The reduction in the value of the dominant frequency with increasing porous medium permeability Da and porosity ϕ indicates a substantial reduction in the vortex shedding. Corresponding static pressure plots and St values corroborate this observation at Re=100 and 200.

This article investigates the laminar flow of power-law fluids through two porous square cylinders in a side-by-side configuration. The effects of power-law index (n), Darcy number (Da), and gap ratio (g/W) are examined within ranges of g/W = 0.5–5, n = 0.4–0.8, and Da = 10−6–10−2, respectively. Two flow conditions are considered: first, for a creeping flow (unseparated flow) at Re = 1 where Darcy's law is applicable; second, for a viscous dominant flow at Re = 100, where Darcy–Forchheimer-extended model is exercised. Flow patterns behind the porous cylinders are analyzed using streamlines, velocity profiles, pressure distribution curves, and vorticity structural parameters (Г). In low permeability levels, the flow exhibits an irregular nonperiodic vortex shedding characterized by a single large vortex street far off the downstream for g/W = 0.5. However, synchronized wake patterns were observed in either antiphase or in-phase modes for higher gap ratios. Leading-edge separation with two-side recirculation induces quasi-periodicity in the flow for all g/W. It was found that increasing the permeability can prevent the leading edge separation. Additionally, a transition from antiphase to in-phase mode occurs when the permeability is altered while maintaining constant flow-time. The presence of a jet-like flow between cylinders significantly impacts unsteady wake patterns. The impact of g/W, power-law index, and permeability on drag is also examined. A jump in some flow parameters was observed at higher Re for the midrange Darcy number, but no such increase was noted for the high shear-thinning behavior. These findings provide a potential approach for improving the design of fluidic systems involving porous cylinders.

PurposeThe purpose of this study is to explore numerically the conjugate natural convection of a nanofluid (Al2O3/water) within a non-Darcy’s porous square cavity containing two opposing solid blocks influenced by a horizontal external magnetic field.Design/methodology/approachThe configuration studied involves a square cavity filled with a porous medium saturated by Al2O3/water nanofluid. The vertical walls are isothermal with hot and cold wall temperatures, while the horizontal walls are adiabatic. Two baffles, with high thermal conductivity relative to the fluid, are positioned midway on the vertical hot and cold walls. A constant horizontal magnetic field is applied, influencing natural convection, heat transfer and fluid motion within the cavity. The Koo–Kleinstreuer–Li (KKL) model, which provides a more accurate representation of the viscosity and thermal conductivity at the nanoscale, was used to include the effect of Brownian motion on the nanofluid’s properties. Conservation equations are modelled via the Darcy–Brinkman–Forchheimer formulation and solved numerically with the finite volume method implemented in a FORTRAN program. Velocity-pressure coupling is achieved using the SIMPLER algorithm. The study investigates the influence of various parameters such as Rayleigh and Darcy numbers, nanoparticle volume fraction and magnetic field strength.FindingsThe results indicate that increasing Rayleigh number (Ra), Darcy number (Da) and nanofluid volume fraction (f) enhances flow dynamics, promoting convection and significantly improving heat transfer, particularly nanoparticle-facilitated. Conversely, Hartman number Ha diminishes heat transfer by restraining fluid motion through the Lorentz force. Later, a novel correlation of the average Nusselt number (Nu) ¯ versus Ra, Da, f and Ha has been established to simplify future predictions of the heat transfer rate for similar configurations.Research limitations/implicationsThis study has several limitations. It relies on steady-state conditions, potentially overlooking transient behaviours that could arise in real applications. The assumption of a uniform magnetic field and homogeneity in nanofluid properties may not accurately represent actual conditions. Additionally, while the Darcy–Brinkman–Forchheimer model is effective, it may not fully capture scenarios where inertial effects are significant. The investigation covers a range of Rayleigh and Darcy numbers as well as nanoparticle volume fractions but does not consider factors such as temperature-dependent fluid properties and non-Newtonian behaviour, which could further influence heat transfer and fluid dynamics.Practical implicationsThe implications of this research are considerable for the design of thermal systems using nanofluids in porous media, especially in applications involving magnetic fields. The derived correlation for the average Nusselt number serves as a valuable predictive tool for engineering applications. Future work should address these limitations by incorporating transient analyses and exploring a wider array of operational parameters to deepen the understanding of nanofluid behaviour in magnetically influenced settings.Social implicationsThe findings of this study have significant social implications, particularly in enhancing energy efficiency in thermal management systems. Improved heat transfer in applications such as HVAC, refrigeration and renewable energy systems can lead to reduced energy consumption and lower utility costs for consumers. Furthermore, the application of nanofluids in environmentally friendly technologies aligns with global sustainability goals, potentially reducing carbon footprints and promoting cleaner energy solutions. By advancing the understanding of nanofluid behaviour in porous media, this research contributes to the development of innovative, sustainable technologies that can improve energy accessibility and environmental quality for communities.Originality/valueThis study presents a novel numerical analysis of the natural convection of Al2O3/water nanofluid in a non-Darcy porous cavity influenced by a horizontal magnetic field, with the consideration of conjugated opposing baffles on hot and cold walls. It investigates the effects of Ra, Da and Ha numbers and nanoparticle volume fraction on flow and heat transfer using the Darcy–Brinkman–Forchheimer model. A new correlation between the average Nusselt number and key parameters is introduced, providing an advanced predictive tool for engineering applications. The findings have direct relevance to advanced thermal management systems, including electronic cooling, energy storage and industrial heat exchangers, where optimizing heat transfer efficiency is critical.

Application of flow past bluff bodies like (cylinders, spheres etc) has been spread to other engineering fields (e.g., ship hydrodynamics, pipelines, heat exchangers in nuclear reactors, cooling systems, skyscrapers etc.) and no more a topic of interest only to aerodynamicists. Porous cylinders with sufficient mechanical properties and strength as of solid cylinders will be preferred due to their better fluid flow and heat transfer properties. In this work, an attempt using computational fluid dynamics (CFD) approach was made to compare the fluid flow and heat transfer properties of the porous square cylinder and square solid cylinder for different low Reynolds numbers. An Unsteady Reynolds Averaged Navier-Stokes (URANS) Equations were solved for the two chosen cylinders where turbulence is introduced into the equations through Shear Stress Transport (SST) k-w model. Heat transfer to the flowing fluid from the cylinders is estimated using the Nusselt number. Brinkman model in conjunction with Forchheimer term has been used to develop the flow through the porous media. The study carried out on 3-Dimensional space using commercial software Ansys. Dependence on grid and mesh has been studied by increasing the number of elements by √2 to verify and validate the methodology followed. The study has been done for different low Reynolds numbers, namely, Re = 170, 185, 200 and 250. The results are encouraging the preference of porous square cylinder than solid square cylinder for few applications.

This study experimentally investigates the bleeding flow characteristics downstream of isotropic porous square cylinders as a function of permeability and pore configuration across a broad range of Darcy numbers ( $2.4 \times 10^{-5} \lt \textit{Da} \lt 2.9 \times 10^{-3}$ ). The porous cylinders, constructed with a simple cubic lattice design, were fabricated using a high-resolution three-dimensional printing technique. This novel design method, based on a periodic and scalable lattice structure, allows fine control over the number of lattice pores along the cylinder width, $D$ , and the corresponding permeability, independently of porosity. Permeability was carefully determined by measuring the pressure drop and superficial velocity for each porous structure considered in this study. High-resolution particle image velocimetry measurements were conducted in an open-loop wind tunnel to characterize the downstream flow structures. The results reveal that bleeding flow characteristics near the cylinder trailing edge are strongly influenced by both permeability and pore configuration. These structural behaviours are further explored using an analogy to multiple plane turbulent jets. This approach identifies three distinct flow regions downstream of porous square cylinders, determined by the structural pattern of the bleeding flow. Additionally, an analytical framework is developed to model the longitudinal extent of the merging region by integrating the momentum equation, incorporating the Darcy–Brinkman–Forchheimer model, with a boundary layer assumption. The analytical model is validated against experimental data, demonstrating its capability to predict the key dynamics of bleeding flow evolution. Our results provide new insights into the fluid dynamics of porous bluff bodies, establishing pore configuration and permeability as dominant parameters governing downstream flow structures.

The laminar mixed convection flow across the porous square cylinder with the heated cylinder bottom at the axis in the channel has been carried out numerically in this paper using a semi-implicit projection finite element method. The governing equations with the Brinkman–Forcheimer-extended Darcy model for the region of square porous cylinder were solved. The parameter studies including Grashof number, Darcy number, and channel-to-cylinder height ratio on heat transfer performance have been explored in detail. The results indicate that the heat transfer is augmented as the Darcy number and channel-to-cylinder height ratio increase. The buoyancy effect on the local Nusselt number is clearer for B/H=0.1 than for B/H=0.3 and B/H=0.5.

Interception efficiency in two-dimensional flow past confined porous cylinders

The aim of this numerical work is to study the improvement of the heat and mass transfers during the evaporation of a liquid film with neglected thickness in a heated channel with a built-in porous square cylinder. The cylinder has a constant porosity and permeability. The calculations have been completed for a Reynolds number ranging from 20 to 100, Darcy number Da ≤ 10-6, and a blockage ration of H/h = 1/4. To achieve this, we solved the classic equation of forced convection and the Darcy-Brinkman-Forchheimer model. Results are presented to show the influence of the porous cylinder on the mass transfer. There is an improvement in the mass transfer with the presence of the porous cylinder. This improvement is greater with an increase in air inlet velocity and heat flux density. It is also greater with a decrease in temperature and relative humidity of the air at the inlet. At Da = 10-6, the flow does not penetrate through the porous cylinder; the flow pattern is similar to that of a solid square cylinder.With an increase of the Darcy number, the flow starts to pass through and around the cylinder. Finally, a correlation has been proposed for the Sherwood number as a function of the Reynolds and Biot numbers.

We numerically investigate the effects of an inserted square porous cylinder in a horizontal channel on flow structure and heat and mass transfer. Channel walls have a thin liquid water film and are heated with a constant heat flux density. Several blockage ratio (β) and gap distances (γ) between cylinder and channel wall are considered for study of geometric effects on heat and mass transfer. We perform a comparison between two configurations (with and without porous square cylinder) to highlight the effect of the addition. To achieve this, we solve the classical equations of forced convection and the Darcy−Brinkman−Forchheimer model. Our investigation finds an improvement in heat and mass transfer with the presence of porous cylinder. This improvement is greater with a decrease in Darcy number (Da) and when the obstacle is placed in the middle of the channel. The Sherwood number, which characterizes mass transport, is correlated by a relationship with Reynolds number and ratio blockage. We provide some design guidelines related to Da, β, and γ that can be used in an engineering environment.

A two‐dimensional numerical simulation using the commercial computational fluid dynamics package ANSYS Fluent 15.0 is performed to investigate the effect of a transverse magnetic field on the wake dynamics around a heated porous circular cylinder. The study is conducted considering a Newtonian, incompressible, and electrically conductive fluid with constant properties for the low Reynolds number laminar regime. In the range of Reynolds number (Re = 10–40), recirculating vortices are observed to penetrate (or detach) into (from) the porous cylinder surface depending on the Darcy number, Da (10−6 to 10−2). The effect of the magnetic field parameter (Hartmann number) Ha (0–10) on the detachment and penetration characteristics of a porous cylinder is reported for the first time. A steady separated flow behind the cylinder turns into an attached flow at a critical magnetic field strength. Accordingly, the critical Hartmann number (Hacr) is estimated for the complete suppression of the flow separation behind the porous cylinder. Hacr is found to decrease with an increase in Da and a decrease in Re. The wake behind the cylinder is also found to be detached from the cylinder surface at a particular value of the magnetic field strength termed as the detachment Hartmann number (Had). Had also decreased with an increase in Da and decrease of Re. In addition, the effect of Ha on the separation angle, recirculation length, detachment length, and drag coefficient is also discussed. Furthermore, the effect of the magnetic field on the forced convective heat transfer characteristics is also studied considering various fluids (Prandtl number, Pr = 0.02, 0.71, and 7) past the circular permeable cylinder. At a particular Pr, the heat transfer rate is almost invariant for low permeability, whereas it increases significantly at higher permeability with an applied magnetic field. The rate of heat transfer increases with the Prandtl number for all Hartmann and Darcy numbers. Finally, a correlation is developed to predict the average heat transfer as a function of Re, Pr, Da, and Ha.