Magnetic field influence on CuO–H2O nanofluid convective flow in a permeable cavity considering various shapes for nanoparticles

In this paper, CuO–H₂O nanofluid forced convection in a lid driven porous cavity is investigated under the impact of magnetic field. Shape effect of nanoparticles and Brownian motion impact on nanofluid properties are taken into consideration. Vorticity stream function formulation is utilized. The solutions of final equations are obtained by CVFEM. Graphs are shown for different values of Darcy number (Da), CuO–H₂O volume fraction (?), Reynolds (Ra) and Hartmann (Ha) numbers. Outputs indicate that selecting Platelet shaped nanoparticles results the highest heat transfer rate. Nusselt number augments with rise of Darcy and Reynolds number while it decreases with augment of Lorentz forces.     

MHD conjugate heat transfer and entropy generation analysis of MWCNT/water nanofluid in a partially heated divided medium

The aim of this article is to conduct the lattice Boltzmann simulation of the magnetohydrodynamic (MHD) natural conjugate heat transfer in an apportioned cavity loaded with a multiwalled carbon nanotube/water nanofluid. The divided cavity is, to some extent, heated and cooled at the upright walls, whereas the horizontal walls are adiabatic. The nanofluid properties are evaluated on the basis of experimental correlations. The parameters ranges in the study are as follows: nanoparticles' volume fraction (%): 0 ≤ ? ≤ 0.5, temperature (°C): T = 27, Rayleigh number (Ra): 10³ ≤ Ra ≤ 10⁵, Hartmann number (Ha): 0 ≤ Ha ≤ 90, and the magnetic field inclination angle (γ): 0 ≤ γ ≤ π/2. The current outcomes are observed to be in great concurrence with the numerical results introduced in the literature. The impacts of the aforesaid parameters on local and average heat transfer, entropy generation, and Bejan number (Be) are explored and discussed. Indeed, the transfer of heat increases linearly with ? for a low Ra. As Ra increases, the average Nusselt number decreases for a high value of ?. The increase of nanoparticles' volume fraction leads to a reduction in the entropy generation and an increase in the Bejan number for a high Ra, but at low Ra, these functions remain constant. As the Ha increases, the transfer of heat and the entropy generation decreases, whereas there is an increase in Be. The transfer of heat, total entropy generation, and the Be depends strongly on the direction of the magnetic field. The increase of heater and cooler size has a great influence on the transfer of heat, entropy generation, and Be.     

MHD natural convection in a laterally and volumetrically heated square cavity

A numerical study is presented of unsteady two-dimensional natural convection of an electrically conducting fluid in a laterally and volumetrically heated square cavity under the influence of a magnetic field. The flow is characterized by the external Rayleigh number, Ra_E, determined from the temperature difference of the side walls, the internal Rayleigh number, Ra_I, determined from the volumetric heat rate, and the Hartmann number, Ha, determined from the strength of the imposed magnetic field. Starting from given values of Ra_E and Ha, for which the flow has a steady unicellular pattern, and gradually increasing the ratio S = Ra_I/Ra_E, oscillatory convective flow may occur. The initial steady unicellular flow for S = 0 may undergo transition to steady or unsteady multicellular flow up to a threshold value, Ra_I,cr, of the internal Rayleigh number depending on Ha. Oscillatory multicellular flow fields were observed for S values up to 100 for the range 10⁵-10⁶ of Ra_E studied. The increase of the ratio S results usually in a transition from steady to unsteady flow but there have also been cases where the increase of S results in an inverse transition from unsteady to steady flow. Moreover, the usual damping effect of increasing Hartmann number is not found to be straightforward connected with the resulting flow patterns in the present flow configuration.     

Natural Convection Heat Transfer in an Enclosure Filled with an Ethylene Glycol—Copper Nanofluid Under Magnetic Fields

This article presents the results of a numerical study on natural convection in a square enclosure filled with ethylene glycol–copper nanofluid in the presence of magnetic fields. Two opposite horizontal walls of the enclosure are insulated and the two vertical walls are kept constant at different temperatures. A uniform horizontal magnetic field is externally imposed. The governing equations (mass, momentum, and energy) are formulated and solved numerically with a finite element using COMSOL Multiphysics. The effects of pertinent parameters such as Rayleigh number (10³ ≤ Ra ≤ 10⁷), Hartmann number (0 ≤ Ha ≤ 120), and solid volume fraction (0 ≤ φ ≤ 0.06) on the flow and the heat transfer performance of the enclosure are examined when the Prandtl number is assumed to be Pr = 151.     

Effect of a magnetic field on natural convection in an open cavity subjugated to water/alumina nanofluid using Lattice Boltzmann method

In this paper, the effect of a magnetic field on natural convection in an open enclosure which subjugated to water/alumina nanofluid using Lattice Boltzmann method has been investigated. The cavity is filled with water and nanoparticles of Al₂O₃ at the presence of a magnetic field. Calculations were performed for Rayleigh numbers (Ra = 10⁴–10⁶), volume fractions of nanoparticles (φ = 0,0.02,0.04 and .0.06) and Hartmann number (0 ≤ Ha ≤ 90) with interval 30 while the magnetic field is considered horizontally. Results show that the heat transfer decreases by the increment of Hartmann number for various Rayleigh numbers and volume fractions. The magnetic field augments the effect of nanoparticles at Rayleigh number of Ra = 10⁶ regularly. Just as the most effect of nanoparticles for Ra = 10⁴ is observed at Ha = 30, so the most influence of nanoparticles occurs at Ha = 60 for Ra = 10⁵.     

Magnetohydrodynamic mixed convection in a horizontal channel with an open cavity

The development of magnetic field effect on mixed convective flow in a horizontal channel with a bottom heated open enclosure has been numerically studied. The enclosure considered has rectangular horizontal lower surface and vertical side surfaces. The lower surface is at a uniform temperature T_h while other sides of the cavity along with the channel walls are adiabatic. The governing two-dimensional flow equations have been solved by using Galarkin weighted residual finite element technique. The investigations are conducted for different values of Rayleigh number (Ra), Reynolds number (Re) and Hartmann number (Ha). Various characteristics such as streamlines, isotherms and heat transfer rate in terms of the average Nusselt number (Nu), the Drag force (D) and average bulk temperature (θ_av) are presented. The results indicate that the mentioned parameters strongly affect the flow phenomenon and temperature field inside the cavity whereas in the channel these effects are less significant.     

Numerical simulation of nanoparticle shape and thermal ray on a CuO/C2H6O2–H2O hybrid base nanofluid inside a porous enclosure using Darcy's law

In this study, the physical aspects of magnetohydrodynamic flow and heat transfer of a hybrid base nanofluid in a porous medium under the effect of the shape, thermal radiation, and Lorentz force have been examined using the finite element method. Copper oxide (CuO) of various shapes was dispersed into ethylene glycol 50%‐water 50% (likewise for Fe₃O₄). The Darcy model is chosen because of the porous medium. The effect of changeable, diverse parameters, for example, Hartmann number (Ha), volume fraction (), radiation parameter (), and buoyancy force (Ra), on the streamlines, temperature gradient, and Nusselt number are shown through contours. Outputs show that the Fe₃O₄ nanoparticles have a smaller temperature gradient than that of CuO nanoparticles. The Nusselt number decreases for a larger (Ha) number, but increases for a larger Ra, Rd. The blade shaped nanoparticle has a larger impact on increasing compared with that of other shapes.     

Natural convection in a square cavity filled with a porous medium: Effects of various thermal boundary conditions

Natural convection flows in a square cavity filled with a porous matrix has been studied numerically using penalty finite element method for uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls. Darcy–Forchheimer model is used to simulate the momentum transfer in the porous medium. The numerical procedure is adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number Ra, 10³ ⩽ Ra ⩽ 10⁶, Darcy number Da, 10⁻⁵ ⩽ Da ⩽ 10⁻³, and Prandtl number Pr, 0.71 ⩽ Pr ⩽ 10) with respect to continuous and discontinuous thermal boundary conditions. Numerical results are presented in terms of stream functions, temperature profiles and Nusselt numbers. Non-uniform heating of the bottom wall produces greater heat transfer rate at the center of the bottom wall than uniform heating case for all Rayleigh numbers but average Nusselt number shows overall lower heat transfer rate for non-uniform heating case. It has been found that the heat transfer is primarily due to conduction for Da ⩽ 10⁻⁵ irrespective of Ra and Pr. The conductive heat transfer regime as a function of Ra has also been reported for Da ⩾ 10⁻⁴. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominated regimes the power law correlations between average Nusselt number and Rayleigh numbers are presented.     

Two phase simulation of nanofluid flow and heat transfer using heatline analysis

In this study Control Volume based Finite Element Method is applied to solve the problem of natural convection heat transfer in an enclosure filled with nanofluid. The important effect of Brownian motion and thermophoresis has been included in the model of nanofluid. The inner sinusoidal and outer circular walls are maintained at constant temperatures while the two other walls are thermally insulated. The heat transfer between cold and hot regions of the enclosure cannot be well understood by using isotherm patterns so heatline visualization technique is used to find the direction and intensity of heat transfer in a domain. Effects of thermal Rayleigh number (Ra), buoyancy ratio number (Nr) and Lewis number (Le) on streamline, isotherm, isoconcentration and heatline are examined. The results indicate that the average Nusselt number decreases as buoyancy ratio number increases until it reaches a minimum value and then starts increasing. As Lewis number increases, this minimum value occurs at higher buoyancy ratio number.     

Non-Darcy effects in buoyancy driven flows in an enclosure filled with vertically layered porous media

Natural convection in an enclosure filled with two layers of porous media is investigated numerically. Constant heat flux is imposed on the left vertical wall and the right wall is assumed to be at a low temperature. The focus of the work is on the validity of the Darcy model when various combinations of fluid Rayleigh number, Darcy number and permeability ratios are considered for fixed values of the modified Rayleigh numbers. It is found that the boundary effects (Brinkman term) have significant importance at higher modified Rayleigh numbers (Rayleigh number based on permeability, Ra_m). Calculations are performed for a modified Rayleigh number up to 10⁵. The results showed that, for the investigated range of parameters, the flow structure and heat transfer could be different than what Darcy model predicts. Two circulations are predicted for Ra_f=1×10⁸, for two different cases, Da=1×10⁻³, K_r=1000 and Da=1×10⁻⁴, K_r=100 (K_r=K₁/K₂). For K_r>1, increasing permeability ratio decreases flow penetration from layer 1 to layer 2 while reverse is true for K_r<1. For low Ra_m (Ra_m?10³) and K_r=1000, the heat transfer is conductive in the right layer, while this is true for the left layer for K_r=0.001. It is possible to obtain no-slip velocity boundary conditions both at the walls and at the interface between the porous layers even for very low permeability.     

Brownian Motion Effects on Natural Convection of Alumina–Water Nanofluid in 2‐D Enclosure

This article reports a numerical study of natural convection heat transfer in a differentially heated enclosure filled with a Al₂O₃–water nanofluid. Fluent v6.3 is used to simulate nanofluid flow. Simulations have been carried out for the pertinent parameters in the following ranges: the Rayleigh number, Ra = 10⁶, 10⁷, and the volumetric fraction of alumina nanoparticles, ? = 0 ? 4%. The effect of Brownian motion on the heat transfer is considered and examined. The numerical results show a decrease in heat transfer with an increase in particle volume fraction. Similar to experimental results, the Nusselt number increases with the Rayleigh number in the numerical results. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21121     

Influence of anisotropy on convection in porous media with nonuniform thermal gradient

Effect of anisotropy on the onset of natural convection heat transfer in a fluid saturated porous horizontal cavity subjected to nonuniform thermal gradients is investigated analytically. The porous layer is heated from the bottom by a constant heat flux while the other surfaces are being insulated. The horizontal boundaries are either rigid/rigid or stress-free/stress-free. The hydrodynamic anisotropy of the porous matrix is considered. The principal directions of the permeability are oriented in a direction that is oblique to the gravity. Based on a parallel flow assumption, closed-form solution for the flow and heat transfer variables, valid for the onset of convection corresponding to vanishingly small wave number, is obtained in terms of the Darcy-Rayleigh number Ra, the Darcy number Da, and the anisotropic parameters K^* and θ. The critical Rayleigh number for the onset of convection arising from sudden heating and cooling at the boundaries is also predicted. The limiting cases Da→∞ (for a viscous pure fluid) and Da→0 (for anisotropic porous media) completed all results. It is demonstrated that effects of anisotropic parameters are strongly significant.     

Hydromagnetic effect on mixed convection in a lid-driven cavity with sinusoidal corrugated bottom surface

The present numerical simulation is conducted to analyze the mixed convection flow and heat transfer in a lid-driven cavity with sinusoidal wavy bottom surface in presence of transverse magnetic field. The enclosure is saturated with electrically conducting fluid. The cavity vertical walls are insulated while the wavy bottom surface is maintained at a uniform temperature higher than the top lid. In addition, the transport equations are solved by using the finite element formulation based on the Galerkin method of weighted residuals. The implications of Reynolds number (Re), Hartmann number (Ha) and number of undulations (λ) on the flow structure and heat transfer characteristics are investigated in detail while, Prandtl number (Pr) and Rayleigh number (Ra) are considered fixed. The trend of the local heat transfer is found to follow a wavy pattern. The results of this investigation illustrate that the average Nusselt number (Nu) at the heated surface increases with an increase of the number of waves as well as the Reynolds number, while decreases with increasing Hartmann number.     

Heat generation effects in natural convection inside a porous annulus

The interplay between internal heat generation and externally driven natural convection inside a porous medium annulus is studied in detail using numerical methods. The axisymmetric domain is bounded with adiabatic top and bottom walls and differentially heated side walls sustaining steady natural convection of a fluid with Prandtl number, Pr = 5, through a porous matrix of volumetric porosity, ? = 0.4. The generalized momentum equation with Brinkman–Darcy–Forchheimer terms and the local thermal non-equilibrium based two-energy equation model are solved to determine the flow and the temperature distribution. Beyond a critical heat generation value defined using an internal Rayleigh number, Ra_I,cr^?, the convection transits from unicellular to bicellular mode, as the annulus T_max becomes higher than the fixed hot-wall temperature. The Ra_I,cr^? increases proportionately when the permeability based external Rayleigh number Ra_E^? and the solid–fluid thermal conductivity ratio γ are independently increased. A correlation is proposed to predict the overall annulus Nu as a function of Ra_E^?, Ra_I^?, Da and γ. It predicts the results within ± 20% accuracy.     

Numerical simulation of natural convection of nanofluid in a square enclosure: Effects due to uncertainties of viscosity and thermal conductivity

The present study aims to identify effects due to uncertainties in effective dynamic viscosity and thermal conductivity of nanofluid on laminar natural convection heat transfer in a square enclosure. Numerical simulations have been undertaken incorporating a homogeneous solid–liquid mixture formulation for the two-dimensional buoyancy-driven convection in the enclosure filled with alumina–water nanofluid. Two different formulas from the literature are each considered for the effective viscosity and thermal conductivity of the nanofluid. Simulations have been carried out for the pertinent parameters in the following ranges: the Rayleigh number, Ra_f = 10³–10⁶ and the volumetric fraction of alumina nanoparticles, ? = 0–4%. Significant difference in the effective dynamic viscosity enhancement of the nanofluid calculated from the two adopted formulas, other than that in the thermal conductivity enhancement, was found to play as a major factor, thereby leading to contradictory results concerning the heat transfer efficacy of using nanofluid in the enclosure.     

Prandtl number effect on cooling performance of a heated cylinder in an enclosure filled with nanofluid

Natural convection heat transfer from a heated cylinder contained in a square enclosure filled with water–Cu nanofluid is investigated numerically. The main objective of this study is to explore the influence of pertinent parameters such as Prandtl number (Pr) and diameter (D) of the heated body on the flow and heat transfer performance of nanofluids while Rayleigh number (Ra) and the solid particle volume fraction (?) of nanoparticle are considered fixed. The results obtained from finite element method clearly indicate that heat transfer augmentation is possible using highly viscous nanofluid resulting in the compactness of many industrial devices.     

Magnetic field effect on the unsteady free convection flow in a square cavity filled with a porous medium with a constant heat generation

The effects of an inclined magnetic field and heat generation on unsteady free convection within a square cavity filled with a fluid-saturated porous medium have been investigated numerically. The top and bottom horizontal walls of the enclosure are adiabatic whereas the vertical walls are kept at constant but different temperatures. The physical problems are represented mathematically by a set of partial differential equations along with the corresponding boundary conditions. By using an implicit finite-difference scheme, namely the ADI method (Alternative Direction Implicit), the non-dimensional governing equations are numerically solved. The influential parameters are the Rayleigh number Ra, the inclination angle γ of the magnetic field relative to the gravity vector g, the Hartmann number Ha and the heat generation parameter Q. In the present study, the obtained results are presented in terms of streamlines, isotherms and average Nusselt number along the hot wall. The result shows that with increasing Ha, the diffusive heat transfer become prominent even though the Rayleigh number increases.