Multi-layered Porous Foam Effects on Heat Transfer and Entropy Generation of Nanofluid Mixed Convection Inside a Two-Sided Lid-Driven Enclosure with Internal Heating

Transport in Porous Media - Mixed convection of Cu-water nanofluid inside a two-sided lid-driven enclosure with an internal heater, filled with multi-layered porous foams is studied numerically and...     

Forced Convection Heat Transfer of Nanofluids in a Porous Channel

This article is concerned with the effects of flow and migration of nanoparticles on heat transfer in a straight channel occupied with a porous medium. Investigation of force convective heat transfer of nanofluids in a porous channel has not been considered completely in the literature and this challenge is generally considered to be an open research topic that may require more study. The fully developed flow and steady Darcy?CBrinkman?CForchheimer equation is employed in porous channel. The thermal equilibrium model is assumed between nanofluid and solid phases. It is assumed that the nanoparticles are distributed non-uniformly inside the channel. As a result the volume fraction distribution equation is also coupled with governing equations. The effects of parameters such as Lewis number, Schmidt number, Brownian diffusion, and thermophoresis on the heat transfer are completely studied. The results show that the local Nusselt number is decreased when the Lewis number is increased. It is observed that as the Schmidt number is increased, the wall temperature gradient is decreased and as a consequence the local Nusselt number is decreased. The effects of Lewis number, Schmidt number, and modified diffusivity ratio on the volume fraction distribution are also studied and discussed.     

Oscillating Convection of Nanofluid in Porous Medium

In this paper, oscillatory convection in a horizontal layer of nanofluid in porous medium is studied. For porous medium, Darcy model is applied. A linear stability theory and normal mode analysis method is used to find the solution confined between two free boundaries. The onset criterion for oscillatory convection is derived analytically and graphically. Regimes of oscillatory and non-oscillatory convection for various parameters are derived. The effects of Lewis number, concentration Rayleigh number, Prandtl?CDarcy number (Vadasz Number) and modified diffusivity ratio on the oscillatory convection are investigated graphically. We examine the validity of ??PES?? and concluded that ??PES?? is not valid for the problem.     

Nonlinear Two-Dimensional Convection in a Nanofluid Saturated Porous Medium

In this article, we study the linear and nonlinear thermal instability in a horizontal porous medium saturated by a nanofluid. For this, the momentum equation with Brinkman model has been used. Also, it incorporates the effect of Brownian motion along with thermophoresis. The linear stability is based on normal mode technique, and for nonlinear analysis, the truncated Fourier series involving only two terms has been used. The expression of Rayleigh number for linear theory has been derived, and the effects of various parameters on Rayleigh number have been presented graphically. Weak nonlinear theory is used to find the concentration and the thermal Nusselt numbers. The behavior of the concentration and thermal Nusselt numbers is investigated and depicted graphically, by solving the finite amplitude equations using a numerical method.     

Natural Convection in a Nanofluid Saturated Rotating Porous Layer: A Nonlinear Study

The present paper deals with linear and nonlinear analysis of thermal instability in a rotating porous layer saturated by a nanofluid. Momentum equation with Brinkman term, involving the Coriolis term and incorporating the effect of Brownian motion along with thermophoresis has been considered. Linear stability analysis is done using normal mode technique, while for nonlinear analysis, a minimal representation of the truncated Fourier series, involving only two terms, has been used. Stationary and oscillatory modes of convection have been studied. A weak nonlinear analysis is used to obtain the concentration and thermal Nusselt numbers. The behavior of the concentration and thermal Nusselt numbers is investigated by solving the finite amplitude equations using a numerical method. Obtained results have been presented graphically and discussed in details.     

Optimization of Forced Convection Heat Transfer in a Composite Porous Medium Channel

The optimization of heat transfer for forced convection in a composite porous channel was studied. We investigated the question where should one place, in the core or in the sheath, the material with high permeability and high-thermal conductivity and where should one place the material with low permeability and low-thermal conductivity, to maximize heat transfer from the walls. We also investigated the optimal heat transfer situation when one has the freedom to vary the relative volumes of the core and the sheath.     

Analysis of Laminar Flow and Forced Convection Heat Transfer in a Porous Medium

The flow of an incompressible Newtonian fluid confined in a planar geometry with different wall temperatures filled with a homogenous and isotropic porous medium is analyzed in terms of determining the unsteady state and steady state velocities, the temperature and the entropy generation rate as function of the pressure drop, the Darcy number, and the Brinkman number. The one-dimensional approximate equation in the rectangular Cartesian coordinates governing the flow of a Newtonian fluid through porous medium is derived by accounting for the order of magnitude of terms as well as accompanying approximations to the full-blown three-dimensional equations by using scaling arguments. The one-dimensional approximate energy and the entropy equations with the viscous dissipation consisting of the velocity gradient and the square of velocity are derived by following the same procedure used in the derivation of velocity expressions. The one-dimensional approximate equations for the velocity, the temperature, and the entropy generation rate are analytically solved to determine the velocity, the temperature, and the entropy distributions in the saturated porous medium as functions of the effective process parameters. It is found that the pressure drop, the Darcy number, and the Brinkman number affect the temperature distribution in the similar way, and besides the above parameters, the irreversibility distribution ratio also affects the entropy generation rate in the similar way.     

The Onset of Double-Diffusive Nanofluid Convection in a Layer of a Saturated Porous Medium

The onset of convection in a horizontal layer of a porous medium saturated by a nanofluid is studied analytically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. For the porous medium, the Brinkman model is employed. Three cases of free–free, rigid–rigid, and rigid–free boundaries are considered. The analysis reveals that for a typical nanofluid (with large Lewis number), the prime effect of the nanofluids is via a buoyancy effect coupled with the conservation of nanoparticles, whereas the contribution of nanoparticles to the thermal energy equation is a second-order effect. It is found that the critical thermal Rayleigh number can be reduced or increased by a substantial amount, depending on whether the basic nanoparticle distribution is top-heavy or bottom-heavy, by the presence of the nanoparticles. Oscillatory instability is possible in the case of a bottom-heavy nanoparticle distribution.     

A Two-Equation Analysis of Convection Heat Transfer in Porous Media

This paper presents a two-equation analysis on the convection heat transfer in porous media based on the modeling developed by Carbonell and Whitaker (1984). The porous system under consideration is bounded by two parallel walls and heated uniformly from one side surface. The Darcy flow is imposed and the fully developed heat transfer is assumed. General solutions, which take into account the additional convective and conductive terms, are obtained for the temperature fields and the Nusselt number. The detailed studies are presented for the porous systems characterized by consolidated and unconsolidated circular unit cells. The results show that, for the consolidated unit cell case, a prediction without the additional convective term overestimates the heat transfer, while for the unconsolidated unit cell case, this effect is negligible. The additional conductive terms are also examined and found to act conventionally as part of the conductive terms.     

Metal Foam Heat Exchangers for Heat Transfer Augmentation from a Cylinder in Cross-Flow

A numerical study has been conducted to examine the heat transfer from a metal foam-wrapped solid cylinder in cross-flow. Effects of the key parameters including the free stream velocity and characteristics of metal foam such as porosity, permeability, and form drag coefficient on heat and fluid flow are examined. Being a determining factor in pressure drop and heat transfer increment, the porous layer thickness is changed systematically to observe that there is an optimum layer thickness beyond which the heat transfer does not improve while the pressure drop continues to increase. This has been verified by the application of Bejan’s Intersection of Asymptotes method. Results have been compared to those of a finned-tube heat exchanger to observe much higher heat transfer rate with reasonable excess pressure drop leading to a higher area goodness factor for metal foam-wrapped cylinder.     

Measurement and Correlation of Pressure Drop Characteristics for Air Flow Through Sintered Metal Porous Media

Sintered metal porous media are currently used to replace conventional orifices as restrictors in air-bearing systems. The flow properties in porous media are generally approximated by Darcy and Forchheimer regimes in different flow regions. In this study, an ISO expanded expression is proven defective when it is used to represent flow properties through porous media under slight pressure drops ( ${<}10$  kPa). A modified Forchheimer equation is therefore developed to correlate the pressure drop with flow rate, including compressibility and inertial effects. Experimental and theoretical investigations on pressure drop characteristics are conducted with a series of metal-sintered porous media. Permeability is first determined in a strict Darcy region with $Re<0.1$ , followed by the inertial coefficient with $Re>0.1$ , rather than determining these two simultaneously. The theoretical mass flow rate in terms of the modified Forchheimer equation provides close approximations to the experimental data.     

Natural Convection Heat Transfer in 2D and 3D Trapezoidal Enclosures Filled with Nanofluid

The purpose of the present study is to investigate the heat transfer performance due to free convection of nanofluids with variable properties inside 2D and 3D channels with trapezoidal cross sections. The governing equations are solved numerically using the finite volume method and the SIMPLER algorithm. In this study, the effect of the nanoparticle volume fraction, Rayleigh number, side wall angles of the trapezoidal section, and axial slope of the 3D channel are examined. The presented results include the average Nusselt number, flow circulation streamlines, and isothermal contours. The heat transfer rate (i.e., Nusselt number) is seen to increase in both 2D and 3D channels with an increase in the Rayleigh number. In 2D trapezoidal enclosures, the Nusselt number decreases with an increase in the nanoparticle volume fraction from zero to 2% and increases if the nanoparticle volume fraction is greater than 2%. In 3D channels, an increase in the axial slope of the channel leads to an increase in the Nusselt number.     

Fully Developed Forced Convection Heat Transfer in a Porous Channel with Asymmetric Heat Flux Boundary Conditions

An analytical study is performed on steady, laminar, and fully developed forced convection heat transfer in a parallel plate channel with asymmetric uniform heat flux boundary conditions. The channel is filled with a saturated porous medium, and the lower and upper walls are subjected to different uniform heat fluxes. The dimensionless form of the Darcy–Brinkman momentum equation is solved to determine the dimensionless velocity profile, while the dimensionless energy equation is solved to obtain temperature profile for a hydrodynamically and thermally fully developed flow in the channel. Nusselt numbers for the lower and upper walls and an overall Nusselt number are defined. Analytical expressions for determination of the Nusselt numbers and critical heat flux ratio, at which singularities are observed for individual Nusselt numbers, are obtained. Based on the values of critical heat flux ratio and Darcy number, a diagram is provided to determine the direction of heat transfer between the lower or upper walls while the fluid is flowing in the channel.     

Thermodynamically Consistent Limiting Forced Convection Heat Transfer in a Asymmetrically Heated Porous Channel: An Analytical Study

Fluid transport and the associated heat transfer through porous media is of immense importance because of its numerous practical applications. In view of the widespread applications of porous media flow, the present study attempts to investigate the forced convective heat transfer in the limiting condition for the flow through porous channel. There could be many areas, where heat transfer through porous channel attain some limiting conditions, thus, the analysis of limiting convective heat transfer is far reaching. The primary aim of the present study is focused on the limiting forced convection analysis considering the flow of Newtonian fluid between two asymmetrically heated parallel plates filled with saturated porous media. Utilizing a few assumptions, which are usually employed in the literature, an analytical methodology is executed to obtain the closed-form expression of the temperature profile, and in the following the expression of the limiting Nusselt numbers. The parametric variations of the temperature profile and the Nusselt numbers in different cases have been shown highlighting the influential role of different performance indexing parameters, like Darcy number, porosity of the media, and Brinkman number of forced convective heat transfer in porous channel. In doing so, the underlying physics of the transport characteristics of heat has been delineated in a comprehensive way. Moreover, a discussion has been made regarding an important feature like the onset of point of singularity as appeared on the variation of the Nusselt number from the consideration of energy balance in the flow field, and in view of second law of thermodynamics.     

Onset of Convection with Internal Heating in a Porous Medium Saturated by a Nanofluid

Linear stability analysis was applied to the onset of convection due to internal heating in a porous medium saturated by a nanofluid. A model in which the effects of thermophoresis and Brownian motion are taken into account is employed. We utilized more realistic boundary conditions than in the previous work on this subject; now the nanofluid particle fraction is allowed to adapt to the temperature profile induced by the internal heating, subject to the requirement that there is zero perturbation flux across a boundary. The results show that the presence of the nanofluid particles leads to increased instability of the system. We identified two combinations of dimensionless parameters that are the major controllers of convection instability in the layer.     

Natural Convection in a Nanofluid Saturated Rotating Porous Layer with Thermal Non-Equilibrium Model

In the present article, we study the effect of local thermal non-equilibrium on the linear and non-linear thermal instability in a nanofluid saturated rotating porous layer. The Darcy Model has been used for the porous medium, while the nanofluid layer incorporates the effect of Brownian motion along with thermophoresis. A three-temperature model is been used for the effect of local thermal non-equilibrium among the particle, fluid, and solid–matrix phases. The linear stability analysis is based on normal mode technique, while for nonlinear analysis a minimal representation of the truncated Fourier series analysis involving only two terms has been used.     

Numerical Study of Natural Convection Heat Transfer in an Inclined Porous Cavity with Time-Periodic Boundary Conditions

Kalabin et al. (Numer. Heat Transfer A 47, 621-631, 2005) studied the unsteady natural convection for the sinusoidal oscillating wall temperature on one side wall and constant average temperature on the opposing side wall. The present article is on the unsteady natural convective heat transfer in an inclined porous cavity with similar temperature boundary conditions as those of Kalabin et al. The inclined angle of the cavity is varied from 0° to 80°. The flow field is modeled with the Brinkman-extended Darcy model. The combined effects of inclination angle of the enclosure and oscillation frequency of wall temperature are studied for Ra* = 10³, Da = 10⁻³, , and Pr=1. Some results are also obtained with the Darcy–Brinkman–Forchheimer model and Darcy’s law and are compared with the present Brinkman-extended Darcy model. The maximal heat transfer rate is attained at the oscillating frequency f = 46.7π and the inclined angle .     

Forced Convection Heat Transfer on a Flat Plate Embedded in Porous Media for Power-Law Fluids

The effect of the presence of an isotropic solid matrix on the forced convection heat transfer rate from a flat plate to power-law non- Newtonian fluid-saturated porous medium, has been investigated. Numerical results are presented for the distribution of velocity and temperature profiles within the boundary layer. The effects of the flow index, first-order and second-order resistance on the velocity, and temperature profiles are discussed. The missing wall values of the velocity and thermal functions are tabulated.     

The Effect of Double Dispersion on Natural Convection Heat and Mass Transfer in a Non-Newtonian Fluid Saturated Non-Darcy Porous Medium

The effect of power law index parameter of the non-Newtonian fluid on free convection heat and mass transfer from a vertical wall is analyzed by considering double dispersion in a non-Darcy porous medium with constant wall temperature and concentration conditions. The Ostwald–de Waele power law model is used to characterize the non-Newtonian fluid behavior. In this case a similarity solution is possible. The variation of heat and mass transfer coefficients with the governing parameters such as power law index, thermal and solutal dispersion parameters, inertia parameter, buoyancy ratio, and the Lewis number is discussed for a wide range of values of these parameters.