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The purpose of this study is to produce a numerical model capable of predicting the mixed convection flows in a rectangular cavity filled with a porous medium and to analyze the effects of several parameters on convective flow in porous media in a differentially heated enclosure.

The authors used the finite volume method.

The authors predicted and analyzed the effects of Richardson number, Darcy number, porosity values and Prandtl number in heat transfer and fluid flow. On other hand, the porosity and Richardson number values lead to reducing the heat transfer rate of mixed convection flow in a porous medium.

A comparison between Darcy–Brinkman–Forchheimer model and Darcy–Brinkman model is discussed and analyzed. The authors finally conclude that the Darcy–Brinkman model overestimates the heat transfer rate.

The purpose of this study is to examine the Darcy–Forchheimer flow of viscous nanoliquid because of a rotating disk. Thermophoretic diffusion and random motion aspects are retained. Heat and mass transfer features are analyzed through convective conditions.

The governing systems are solved numerically by the shooting technique.

Higher porosity parameter and Forchheimer number Fr depict similar trend for both velocity profiles f' and g. Both temperature and concentration profiles show increasing behavior for higher Forchheimer number Fr. An increase in Prandtl number Pr corresponds to lower temperature profile, while opposite trend is noticed for thermal Biot number. Larger concentration Biot number exhibits increasing behavior for both concentration and its associated layer thickness.

To the best of the author’s knowledge, no such consideration has been given in the literature yet.

A numerical simulation of the fully developed forced convection in a circular duct partly filled with a fluid saturated porous medium is presented. The Brinkman‐Forchheimer‐extended Darcy equation is used to describe the fluid flow in the porous region. The energy equation for the porous region accounts for the effect of thermal dispersion. The dependence of the Nusselt number on a number of parameters, such as the Reynolds number, the Darcy number, the Forchheimer coefficient, as well as the thickness of the porous region is investigated. The numerical results obtained in this research are in agreement with published experimental data.

The purpose of this paper is to construct mathematical model for squeezed flow of carbon-water nanofluid between parallel disks considering Darcy–Forchheimer porous medium. Thermal conductivity of carbon nanotubes is estimated through the well-known Xue model. Such research work is not carried out in the past even in the absence of Darcy–Forchheimer porous space. Forchheimer equation is preferred here to account for both low and high velocity inertial effects. Researchers also found that dispersion of carbon nanotubes in water elevates the thermal conductivity of resulting nanofluid by 100 per cent.

Homotopy analysis method (HAM) is used for the convergent series solutions of the governing system.

Nusselt number at the lower disk increases when squeezing parameter Sq enlarges. This illustrates that heat transfer rate at the lower wall can be enhanced by increasing the squeezing velocity of the lower disk. The results demonstrate a decreasing trend in temperature profile for increasing volume fraction of carbon nanotubes. Moreover, improvement in heat transfer rate because of existence of carbon nanotubes is also apparent. A significant enhancement in temperature profile is depicted when inertial permeability coefficient is enhanced. Skin friction coefficients at the lower and upper disks are higher for MWCNTs in comparison to the SWCNTs.

To the best of author’s knowledge, no such consideration has been given in the literature yet.

This paper aims to discuss the salient aspects of the Darcy–Forchheimer flow of viscous liquid in carbon nanotubes (CNTs). CNTs are considered as nanofluid, and water is taken as the continuous phase liquid. The flow features are discussed via curved surface. Water is taken as the base liquid. Flow is generated via nonlinear stretching. Energy expression is modeled subject to heat generation/absorption. Furthermore, convective conditions are considered at the boundary. The Xue model is used in the mathematical modeling which describes the features of nanomaterials. Both types of CNTs are considered, i.e. single-walled CNTs and multi-walled CNTs.

Appropriate transformations are used to convert the flow expressions into dimensionless differential equations. The bvp4c method is used for solution development.

Velocity enhances via higher estimations of nanoparticles volume fraction while decays for higher Forchheimer number, curvature parameter, behavior index and porosity parameter. Furthermore, thermal field is an increasing function of nanoparticle volume fraction, behavior index, Forchheimer number and porosity parameter.

Here, the authors have discussed two-dimensional CNTs-based nanomaterial Darcy–Forchheimer flow of viscous fluid over a curved surface. The authors believe that all the outcomes and numerical techniques are original and have not been published elsewhere.

The purpose of this study is to study flow caused by rotating frame. Effects of Darcy–Forchheimer and porous medium are considered to study velocity field. Concentration field is discussed in presence of activation energy. Darcy–Forchheimer in a rotating frame is examined. Flow because of stretched sheet fills the porous space. Binary chemical reaction is entertained. Resulting system is numerically solved. The plots are arranged for rotational parameter, porosity parameter, coefficients of inertia, Prandtl number and Schmidt number. It is revealed that rotation on velocity has opposite effects when compared with temperature and concentration distributions. Skin friction coefficients and local Nusselt and Sherwood numbers are numerically discussed.

Darcy–Forchheimer in a rotating frame is examined. Flow because of stretched sheet fills the porous space. Binary chemical reaction is entertained. Resulting system is numerically solved. The plots are arranged for rotational parameter, porosity parameter, coefficients of inertia, Prandtl number and Schmidt number. It is revealed that rotation on velocity has opposite effects when compared with temperature and concentration distributions. Skin friction coefficients and local Nusselt and Sherwood numbers are numerically discussed.

The major findings here are as follows: an addition in porosity λ causes decay in velocity f′(η) while there is opposite behavior for temperature θ(η) and concentration ϕ(η) fields. θ and ϕ via β have similar results qualitatively. There is an opposite behavior of Pr on temperature and concentration. Inverse behavior of λ on ϕ and wall mass flux is noted. Concentration ϕ is decreasing function of reaction rate constant σ. Skin friction coefficient has similar qualitative results for λ and β. Temperature gradient −θ^′(0) is decreased by λ and β.

Here, the authors are interested to investigate rotating flow in a porous space. Dissipation and radiation effects are neglected. Effects of activation energy are studied. This work is not done yet in literature.

Aiming at finding the velocity distribution profile and other flow characteristic parameters such as the Poiseuille (Po) number, this study aims to focus on the three-dimensional forced convective flow inside rectangular ducts filled with porous media commonly used in air-based solar thermal collectors to enhance the thermal performance. The most general model for the fluid flow (i.e. the non-linear Darcy–Brinkman–Forchheimer partial differential equation subjected to slip and no-slip boundary conditions) is considered.

The general governing equations are solved analytically based on the perturbation technique and the results are validated against numerical simulation study based on a finite-difference solution over a non-uniform but structured grid.

The analytical velocity distribution profile based on exponential functions for the above-mentioned general case is obtained, and accordingly, expressions for the Po are introduced. It is found that the velocity distribution tends to be uniform by increasing the aspect ratio of the duct. Moreover, a criterion for considering/neglecting the nonlinear drag term in the momentum equation (i.e. the Forchheimer term) is proposed. According to the sensitivity analysis, results show that the nonlinear drag term effects on the Nusselt number are important only in porous media with high Darcy numbers.

A general analytic solution for three-dimensional forced convection flows through rectangular ducts filled with porous media for the general model of Darcy–Brinkman–Forchheimer and the general boundary condition including both no-slip and slip-flow regimes is obtained. An analytic expression to calculate Po number is obtained which can be practical for engineering estimations and a basis for validation of numerical simulations. A criterion for considering/neglecting the nonlinear drag term in the momentum equation is also introduced.

The aim of this works is to characterize the role of Cattaneo?Christov heat flux in two-dimensional flows of second-grade and Walter’s liquid B fluid models.

In this study similarity transformations have been used to transform the system into ordinary ones. Numerical and analytical solutions are computed through homotopic algorithm and shooting technique.

The numerical values of temperature gradient are tabulated, and the temperature gradient reduces rapidly with enhancing values of the Darcy parameter, but this reduction is very slow for Forchheimer parameter.

No such analyses have been reported in the literature.

The objective of the present work was to perform a detailed numerical study of laminar forced convection in a three‐dimensional square duct packed with an isotropic granular material and saturated with a Newtonian fluid. Hydrodynamic and heat transfer results are reported for three different thermal boundary conditions. The flow in the porous medium was modeled using the semi‐empirical Brinkman‐Forchheimer‐extended Darcy model which also included the effects of variable porosity and thermal dispersion. Empirical models for variable porosity and thermal dispersion were determined based on existing three‐dimensional experimental measurements. Parametric studies were then conducted to investigate the effects of particle diameter, Reynolds number, Prandtl number and thermal conductivity ratio. The results showed that channeling phenomena and thermal dispersion effects are reduced considerably in a three‐dimensional duct compared with previously reported results for a two‐dimensional channel. It was found that the Reynolds number affects mainly the velocity gradient in the flow channeling region, while the particle diameter affects the width of the flow channeling region. As the Reynolds number increases or as the particle diameter decreases (i.e., when the inertia and thermal dispersion effects are enhanced), the Nusselt number increases. The effects of varing the Prandtl number on the magnitude of the Nusselt number were found to be more significant than those of the thermal conductivity ratio. Finally, the effects of varing the duct aspect ratio on the friction factor can be neglected for small particle diameter (D_p ≤ 0.01) or for high particle Reynolds number (Re_d ≥ 1000) due to the dominant bulk damping resistance from the porous matrix (Darcy term) or strong inertia effects (Forchheimer term), respectively.

The purpose of this paper is to study the effects of chemical reaction, thermal radiation and Soret and Dufour effects of heat and mass transfer by natural convection flow about a truncated cone in porous media.

The problem is formulated and solved numerically by an accurate implicit finite-difference method.

It is found that the Soret and Dufour effects as well as the thermal radiation and chemical reaction cause significant effects on the heat and mass transfer charateristics.

The problem is relatively original as it considers Soret and Dufour as well as chemical reaction and porous media effects on this type of problem.