Numerical investigation of hydrodynamic nanofluid convective flow in a porous enclosure (original) (raw)
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Steady-state natural convection heat transfer in a three-dimensional porous enclosure filled with a nanofluid using the mathematical nanofluid model proposed by Buongiorno is presented. The nanofluid model takes into account two important slip mechanisms in nanofluids like Brownian diffusion and thermophoresis. The study is formulated in terms of the dimensionless vector potential functions, temperature and concentration of nanoparticles. The governing equations were solved by finite difference method on nonuniform mesh and solution of algebraic equations was made on the basis of successive under relaxation method. Effort has been focused on the effects of six types of influential factors such as the Rayleigh and Lewis numbers, the buoyancy-ratio parameter, the Brownian motion parameter, the thermophoresis parameter and the aspect ratio on the fluid flow, heat and mass transfer. Three-dimensional velocity, temperature and nanoparticle volume fraction fields, average Nusselt numbers are presented. It is found that low Rayleigh and Lewis numbers and high thermophoresis parameter reflect essential non-homogeneous distribution of nanoparticles inside the cavity, hence a non-homogeneous model is more appropriate for the description of the system.
This work analyses free convection flow of a nanofluid in an inclined square enclosure consisting of a porous layer and a nanofluid layer using the finite difference methodology. Sinusoidal temperature boundary conditions are imposed on the two opposing vertical walls. Nanofluids with water as base and Ag or Cu or Al 2 O 3 or TiO 2 nanoparticles are considered for the problem. The related parameters of this study are the Darcy number, nanoparticle volume fraction, phase deviation, amplitude ratio, porous layer thickness and the inclination angle of the cavity. A comparison with previously published work is performed and the results are in good agreement. Detailed numerical data for the fluid flow and thermal distributions inside the square enclosure, and the Nusselt numbers are presented. The obtained results show that the heat transfer is considerably affected by the porous layer increment. Several nanoparticles depicted a diversity improvement on the convection heat transfer. Studies about free convective fluid flow and heat transfer in porous media domains have received considerable attention over the past few years and their findings are gaining significant importance. This is due to their ability to resolve a wide range of environmental situations or industrial applications such as, geothermal systems , thermal insulation, filtration processes, ground water pollution, storage of nuclear waste, drying processes, solidification of castings, storage of liquefied gases, biofilm growth, fuel cells. The problem of dealing with the fluid motions in the clear region and the porous medium has been studied for many years. Beavers and Joseph 1 presented the simple situation of the boundary conditions between a porous media and a homogeneous fluid. Poulikakos et al. 2 considered high value of Rayleigh in free convection in a fluid overlaying a porous bed using the Darcy model. Meanwhile, Beckermann et al. 3 studied free convective flow and heat transfer between a fluid layer and a porous layer inside a rectangular cavity. Free convective heat and mass transfer in solidification was studied by Beckermann et al. 4. On the other hand, Chen and Chen 5 investigated convective stability in a superposed fluid and porous layer when heated from below. Heat transfer and fluid flow through fibrous insulation was studied by Le Breton et al. 6. Singh and Thorpe 7 presented a comparative study of different models of free convection in a confined fluid and overlying porous layer. The problem with studying the solute exchange by convective within estuarine sediments had been considered by Webster et al. 8. Goyeau et al. 9 discussed the problem of using one-or two domain formulations for the conservation equations. Meanwhile, Gobin et al. 10 analyzed the specified sub-class of such problems where free convection occupies venue in a closed cavity with a partially-saturated porous medium. Nessrine et al. 11 have applied the non-Darcy model to study the flow and heat transfer characteristics in a pipe saturated porous medium. Sui et al. 12 used analytically the homotopy analysis method to study the convec-tion heat transfer and boundary layer in a power-law fluid through a moving conveyor and inclined plate. Their results indicated that increasing the inclination angle clearly improved the rate of heat transfer. Bhattacharya and Das 13 considered numerically different values of Rayleigh and Nusselt numbers on natural convective flow within a square-shaped cavity. Thermal fluids are very important for heat transfer in many industrial applications. The poor thermal conductivity of classical heat transfer fluids like water and oils is the
Natural Convection of Nanofluid in Cylindrical Enclosure Filled with Porous Media
Journal of Energy and Power Engineering, 2013
A numerical study has been carried out to investigate the effect of aspect ratio on heat transfer by natural convection of nanofluid taking Cu nano particles and the water as based fluid. The flow is laminar, steady state, axisymmetric two-dimensional in a vertical cylindrical channel filled with porous media. Heat is generated uniformly along the center of the channel with its vertical surface remain with cooled constant wall temperature and insulated horizontal top and bottom surfaces. The governing equations which used are continuity, momentum and energy equations using Darcy law and Boussinesq's approximation which are transformed to dimensionless equations. The finite difference approach is used to obtain all the computational results using the MATLAB-7 program. The parameters affected on the system are Rayleigh number ranging within (10 ≤ Ra ≤ 10 3), aspect ratio (1 ≤ As ≤ 5) and the volume fraction (0 ≤ φ ≤ 0.2). The results obtained are presented graphically in the form of streamline and isotherm contour plots and the results show that as φ increase from 0.01 to 0.2 the value of the mean Nusselt number increase 50.4% for Ra = 1,000.
PLOS ONE, 2015
The free convection heat transfer of Cu-water nanofluids in a parallelogrammic enclosure filled with porous media is numerically analyzed. The bottom and top of the enclosure are insulated while the sidewalls are subject to limited temperature difference. The Darcy flow and the Tiwari and Das' nanofluid models are considered. The governing dimensionless partial differential equations are numerically solved using a finite difference code. The results are reported for isotherms and streamlines as well as Nusselt number as a function of the volume fraction of nanoparticles, porosity, types of the porous matrix, inclination angle, aspect ratio and different Rayleigh numbers. It is found that the presence of the nanoparticles inside the enclosure deteriorates the heat transfer rate, which is caused due to the increase of dynamic viscosity by the presence of nanoparticles. Therefore, in applications in which the nanofluids are used for their advantages, such as enhanced dielectric properties or antibacterial properties, more caution for the heat transfer design of the enclosure is necessary. engineering applications. In many cases, the enclosures are filled with a porous medium, which is saturated by a fluid. Convection in porous media has many applications in several sections of industries such as cooling of electronic devices, buildings, solar collectors, geothermal energy, fuel cells, food, etc. .
Study of Laminar Naturel Convection in Partially Porous Cavity in the Presence of Nanofluids
Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 2020
The objective of this work is the mathematical modelling and the numerical simulation of the stationary, laminar, and natural convection, in a confined square cavity (H = L) filled with two fluids (a mixture of nanoparticles of aluminum oxide and Al2O3 water) in one partition and pure water in the other partition. A porous conductive wall of thickness w (w = L/e) and thermal conductivity Keff constitutes the exchange surface between these two partitions. The fluid movement is modeled by the Navier-Stokes equations in the two partitions, while the porous medium is modelled by the Darcy–Brinkman equation. Comsol Multiphysics software is used to solve the system of differential equations that is based on the finite element method. The results are discussed with particular attention to the mean and local Nusselt number (Nu), streamlines and isotherms. A parametric study for Rayleigh number Ra (102 to 106), volume fraction j (0% to 10%), and Darcy number Da (10-7 to 10-2) is performed. T...
Natural Convection in an H-shaped Porous Enclosure Filled with a Nanofluid
Computers, Materials & Continua
This study simulates natural convection flow resulting from heat partitions in an H-shaped enclosure filled with a nanofluid using an incompressible smoothed particle hydrodynamics (ISPH) method. The right area of the H-shaped enclosure is saturated with non-Darcy porous media. The center variable partitions of the H-shaped enclosure walls are kept at a high-temperature T h. The left and right walls of the H-shaped enclosure are positioned at a low temperature T c and the other walls are adiabatic. In ISPH method, the source term in pressure Poisson equation (PPE) is modified. The influences of the controlling parameters on the temperature distributions, the velocity field and average Nusselt number are discussed. The performed simulations proofed that the length of the heated partitions augments the velocity field and temperature distributions in an H-shaped enclosure. Rayleigh number rises the fluid velocity and heat transfer in an H-shaped enclosure. The porous layer on the right side of the H-shaped enclosure at a lower Darcy parameter causes a high resistance force for the fluid flow and heat transfer characteristic inside an H-shaped enclosure. Added nanoparticles reduces the velocity field and enhances the heat transfer inside an H-shaped enclosure.
Journal of Thermal Analysis and Calorimetry, 2019
In the present study, the flow field and heat transfer of a water-copper nanofluid with variable properties in a trapezoidal enclosure saturated with porous media are studied. The governing equations are solved by finite volume method and the SIMPLER algorithm. The nanofluid flow is assumed to be laminar, steady and incompressible. Simulations are performed for sidewall (trapezoid legs) angles of 30°, 45°and 60°with respect to horizontal axis, Reynolds numbers from 10 to 1000, Darcy numbers of 10-2 , 10-3 , 10-4 and volume fractions of 0 to 0.04 of nanoparticles. Numerical results show that the average Nusselt number increases with increasing volume fraction of nanoparticles for all studied Darcy numbers. The convection and motion of the nanofluid decrease by reducing the Darcy number which leads to a reduction in the velocity and local Nusselt number. The average Nusselt number increases by increasing the Darcy number for all aspect ratios. Also, the average Nusselt number increases with increasing Reynolds number for all Darcy numbers, aspect ratios and volume fractions of nanoparticles.
Journal of Theoretical and Applied Mechanics
In this paper, Buongiorno's mathematical model is adopted to simulate both natural convection and mixed convection of a nanofluid in square porous cavities. The model takes into account the Brownian diffusion and thermophoresis effects. Both constant and variable temperatures are prescribed at the side walls while the remaining walls are maintained adiabatic. Moreover, all boundaries are assumed to be impermeable to the base fluid and the nanoparticles. The governing equations are transformed to a form of dimensionless equations and then solved numerically using the finite-volume method. Thereafter, effects of the Brownian diffusion parameter, the thermophoresis number, and the buoyancy ratio on the flow strength and the average Nusselt number as well as distributions of isocontours of the stream function, temperature, and nanoparticles fraction are presented and discussed.
3rd National Conference on Nanostructures, Nanoscience, and Nanoengineering, 2019
In the present paper, conjugate heat transfer (convection + conduction) of cu-water nanofluid inside square porous enclosures is investigated. The enclosure has two vertical isothermal walls with finite thickness and two adiabatic walls. In the porous medium, Darcy's law is assumed to hold, the fluid and the porous matrix are in local thermal equilibrium. With these assumptions, the continuity, Darcy, and energy equations for steady and two-dimensional flow in an isotropic and homogeneous porous medium are solved by FORTRAN code using the finite-volume method. Computations are undertaken for Cu nanoparticle in a base fluid of water. The influences of the thickness of the vertical solid walls are analyzed for different Rayleigh number. Increasing the Rayleigh number or decreasing the thickness of walls enhances the average Nusselt number.
International Journal of Heat and Technology, 2021
The involvement of non-linear convection effects in a natural convective fluid flow and heat transfer along with the effects of magnetic field in a porous cavity is studied numerically. Cu-water filled cavity of higher temperature at the left wall and lower temperature at the right wall. The governing equations are organized to achieve the required flow by using two-dimensional equations of energy, continuity and momentum. Vorticity-stream function based dimensionless equations are solved using the finite difference techniques. The results are discussed for various dimensionless parameters such as the Darcy number, non-linear convection parameter, Hartmann number, Rayleigh number and solid volume fraction of the nanoparticles. An augment in streamline velocity and convection heat transfer are observed by increasing the Rayleigh number, non-linear convection parameter and Darcy number. The non-linear convection parameter has a lesser effect on the lower Rayleigh numbers. Diminished s...