Search results

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.

This study aims to numerically study the buoyant convective flow of two different nanofluids in a porous annular domain. A uniformly heated inner cylinder, cooled outer cylindrical boundary and adiabatic horizontal surfaces are considered because of many industrial applications of this geometry. The analysis also addresses the comparative study of different porous media models governing fluid flow and heat transport.

The finite difference method has been used in the current simulation work to obtain the numerical solution of coupled partial differential equations. In particular, the alternating direction implicit method is used for solving transient equations, and the successive line over relaxation iterative method is used to solve time-independent equation by choosing an optimum value for relaxation parameter. Simpson’s rule is adopted to estimate average Nusselt number involving numerical integration. Various grid sensitivity checks have been performed to assess the sufficiency of grid size to obtain accurate results. In this analysis, a general porous media model has been considered, and a comparative study between three different models has been investigated.

Numerical simulations are performed for different combinations of the control parameters and interesting results are obtained. It has been found that the an increase in Darcy and Rayleigh numbers enhances the thermal transport rate and strengthens the nanofluid movement in porous annulus. Also, higher flow circulation rate and thermal transport has been detected for Darcy model as compared to non-Darcy models. Thermal mixing could be enhanced by considering a non-Darcy model.

The present results could be effectively used in many practical applications under the limiting conditions of two-dimensionality and axi-symmetry conditions. The only drawback of the current study is it does not include the three-dimensional effects.

The results could be used as a first-hand information for the design of any thermal systems. This will help the design engineer to have fewer trial-and-run cases for the new design.

A pioneering numerical investigation on the buoyant convective flow of two different nanofluids in an annular porous domain has been carried out by using a general Darcy–Brinkman–Forchheimer model to govern fluid flow in porous matrix. The results obtained from current investigation are novel and original, with numerous practical applications of nanofluid saturated porous annular enclosure in the modern industry.

The purpose of this paper is to examine the electro-magnetohydrodynamic behavior of a third-grade non-Newtonian fluid, flowing between a pair of parallel plates in the presence of electric and magnetic fields. The flow medium between the plates is porous. The effects of Joule heating and viscous energy dissipation are studied in the present study.

A semi-analytical/numerical method, the differential transform method, is used to obtain solutions for the system of the nonlinear differential governing equations. This solution technique is efficient and may be adapted to solve a variety of nonlinear problems in simple geometries, as it was confirmed by comparisons between the results using this method and those of a fully numerical scheme.

The results of the computations show that the Darcy–Brinkman–Forchheimer parameter and the third-grade fluid model parameter retards, whereas both parameters have an inverse effect on the temperature profile because the viscous dissipation increases. The presence of the magnetic field also enhances the temperature profile between the two plates but retards the velocity profile because it generates the opposing Lorenz force. A graphical comparison with previously published results is also presented as a special case of this study.

The obtained results are new and presented for the first time in the 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 purpose of this paper is to investigate thermally and hydrodynamically fully developed convection in a duct of rectangular cross-section containing a porous medium and fluid layer.

The Darcy–Brinkman–Forchheimer flow model is adopted. A finite difference method of second-order accuracy with the Southwell-over-relaxation method is deployed to solve the non-dimensional momentum and energy conservation equations under physically robust boundary conditions.

It is found that the presence of porous structure and different immiscible fluids exert a significant impact on controlling the flow. Graphical results for the influence of the governing parameters i.e. Grashof number, Darcy number, porous media inertia parameter, Brinkman number and ratios of viscosities, thermal expansion and thermal conductivity parameters on the velocity and temperature fields are presented. The volumetric flow rate, skin friction and rate of heat transfer at the left and right walls of the duct are also provided in tabular form. The numerical solutions obtained are validated with the published study and excellent agreement is attained.

To the author’s best knowledge this study original in developing the numerical code using FORTRAN to assess the fluid properties for immiscible fluids. The study is relevant to geothermal energy systems, thermal insulation systems, resin flow modeling for liquid composite molding processes and hybrid solar collectors.

The purpose of this paper is to address various works on mixed convection and proposes 10 unified models (Models 1–10) based on various thermal and kinematic conditions of the boundary walls, thermal conditions and/ or kinematics of objects embedded in the cavities and kinematics of external flow field through the ventilation ports. Experimental works on mixed convection have also been addressed.

This review is based on 10 unified models on mixed convection within cavities. Models 1–5 involve mixed convection based on the movement of single or double walls subjected to various temperature boundary conditions. Model 6 elucidates mixed convection due to the movement of single or double walls of cavities containing discrete heaters at the stationary wall(s). Model 7A focuses mixed convection based on the movement of wall(s) for cavities containing stationary solid obstacles (hot or cold or adiabatic) whereas Model 7B elucidates mixed convection based on the rotation of solid cylinders (hot or conductive or adiabatic) within the cavities enclosed by stationary or moving wall(s). Model 8 is based on mixed convection due to the flow of air through ventilation ports of cavities (with or without adiabatic baffles) subjected to hot and adiabatic walls. Models 9 and 10 elucidate mixed convection due to flow of air through ventilation ports of cavities involving discrete heaters and/or solid obstacles (conductive or hot) at various locations within cavities.

Mixed convection plays an important role for various processes based on convection pattern and heat transfer rate. An important dimensionless number, Richardson number (Ri) identifies various convection regimes (forced, mixed and natural convection). Generalized models also depict the role of “aiding” and “opposing” flow and combination of both on mixed convection processes. Aiding flow (interaction of buoyancy and inertial forces in the same direction) may result in the augmentation of the heat transfer rate whereas opposing flow (interaction of buoyancy and inertial forces in the opposite directions) may result in decrease of the heat transfer rate. Works involving fluid media, porous media and nanofluids (with magnetohydrodynamics) have been highlighted. Various numerical and experimental works on mixed convection have been elucidated. Flow and thermal maps associated with the heat transfer rate for a few representative cases of unified models [Models 1–10] have been elucidated involving specific dimensionless numbers.

This review paper will provide guidelines for optimal design/operation involving mixed convection processing applications.

The purpose of this paper is to numerically investigate the heat transfer enhancement in a tube filled partially with porous media under non-uniform porosity distribution and thermal dispersion effects. The optimum porous thickness ratio [R_(r,Nu)] for the heat transfer enhancement under these conditions with and without considering required pumping power is evaluated.

The local thermal non-equilibrium and Darcy–Brinkman–Forchheimer models are used to simulated thermal and flow fields in porous region. The tube wall and flow regime are assumed to be isothermal and laminar, respectively. The impacts of Darcy number (Da = 10^-6 - 10^-1) and inertia parameter (F = 0 − 2) on the Nusselt number and friction factor are studied for non-uniform porosity distribution.

First, the effect of Nusselt number indicates that there are two different behaviors with respect to uniform and non-uniform porosity for partially and fully filled porous pipe. Second, variable porosity in porous region has significant influence on the optimum thickness ratio with considering required pumping power. For negligible inertia term, it depends on the Darcy number, whereas it is 0.9 at F > 1. Third, the plug flow assumption cannot be valid even at lower Darcy number under non-uniform porosity, while this assumption is applicable at Da < 10^-3 for constant porosity distribution in porous region.

According to the best knowledge of authors, the optimum porous thickness ratio for the heat transfer enhancement considering the pressure loss effects under variable porosity has not reported up to now. Also the plug flow assumption in such physics is not discussed.

Investigates numerically the mechanism of enhancing heat transfer by using porous substrate. The numerical investigation is carried out for transient forced convection in the developing region of a parallel‐plate channel partially filled with a porous medium. A porous substrate is inserted in the channel core in order to reduce the boundary layer thickness and hence, enhance heat transfer. Darcy‐Brinkman‐Forchheimer model is used to simulate the physical problem. Results of the current model show that the existence of the porous substrate may improve the Nusselt number at the fully developed region by a factor of four and even higher depending on the value of Darcy number. It is found that the maximum Nusselt number is achieved at an optimum thickness. Also, the study shows that partially filled channels have better thermal performance than the totally filled ones. However, there is an optimum thickness of porous substrate, beyond it the Nusselt number starts to decline.

The purpose of this paper is to develop a numerical framework based on the accurate spectral element method (SEM) to simulate the mixed convective heat transfer within a porous enclosure with three adiabatic thin baffles of different lengths in nine cases and analyze the effects of several parameters.

The authors develop an improved time-splitting method to solve the Darcy–Brinkman–Forchheimer model. No extra assumptions are introduced for the intermediate velocity, and the final velocity field satisfies the incompressible constraint strictly compared with the classical method. The governing equations are split into a pure convection problem, a Stokes problem and a thermal diffusion problem. The least-squares variation is adopted for the Stokes problem, and the Galerkin variation is used for the other two problems, such that the pressure and velocity can be discretized with the same interpolation order, which benefits the numerical accuracy and program design.

Regarding the method, the excellent spectral accuracy, the capability of discretizing complex computational regions and the improved time-splitting methods make SEM an effective tool to accurately predict the non-Darcy convective heat transfer; as for the numerical tests, it is observed that weakened convection and heat transfer are induced by the increasing length of the baffles. The flow and heat transfer in channel 1 is only related to the length of baffle 1 because of the downward-driven right sidewall, and it is more difficult for baffle 3 to form the secondary flow on its tip.

A novel numerical framework for Darcy–Brinkman–Forchheimer model is developed, expanding the application of SEM for simulating non-Darcy convective heat transfer to improve the numerical accuracy. Numerical results and analysis for flow and heat fields could help designers understand the control of heat transfer using adiabatic baffles better.

The microfluidics has a wide range of applications, such as micro heat exchanger, micropumps, micromixers, cooling systems for microelectronic devices, fuel cells and microturbines. However, the enhancement of thermal energy is one of the challenges in these applications. Therefore, the purpose of this paper is to enhance heat transfer in a microchannel flow by utilizing carbon nanotubes (CNTs). MHD Brinkman-Forchheimer flow in a planar microchannel with multiple slips is considered. Aspects of viscous and Joule heating are also deployed. The consequences are presented in two different carbon nanofluids.

The governing equations are modeled with the help of conservation equations of flow and energy under the steady-state situation. The governing equations are non-dimensionalized through dimensionless variables. The dimensionless expressions are treated via Runge-Kutta-Fehlberg-based shooting scheme. Pertinent results of velocity, skin friction coefficient, temperature and Nusselt number for assorted values of physical parameters are comprehensively discussed. Also, a closed-form solution is obtained for momentum equation for a particular case. Numerical results agree perfectly with the analytical results.

It is established that multiple slip effect is favorable for velocity and temperature fields. The velocity field of multi-walled carbon nanotubes (MWCNTs) nanofluid is lower than single-walled carbon nanotubes (SWCNTs)-nanofluid, while thermal field, Nusselt number and drag force are higher in the case of MWCNT-nanofluid than SWCNT-nanofluid. The impact of nanotubes (SWCNTs and MWCNTs) is constructive for thermal boundary layer growth.

This study may provide useful information to improve the thermal management of microelectromechanical systems.

The effects of CNTs in microchannel flow by utilizing viscous dissipation and Joule heating are first time investigated. The results for SWCNTs and MWCNTs have been compared.