Three-dimensional Free Convection Research Articles

Effect of magnetic field on particle deposition in a modeled room

In this work, the three-dimensional free convection flow in a modeled room was studied for various Grashof numbers (Gr = 2 × 104 and 2 × 105) and Hartmann numbers (Ha = 0 and 100) by the lattice Boltzmann method (LBM), and the effect of magnetic field on the flow and temperature field was investigated. For consideration of the effect of magnetic field on particle behavior in a three-dimensional modeled room, 50,000 particles with sizes of 1 and 10 μm were injected into the room. The number of deposited particles on the different walls of the room was obtained, and it was observed that by increasing the Grashof number, the total number of deposited particles for both particle sizes and both Hartmann numbers enhances. Moreover, for Ha = 100, the number of deposited 10 μm particles on the walls increases. Therefore the number of suspended particles in the modeled room decreases, which is environmentally desirable. However, the number of deposited 1 μm particles on the walls decreases in the presence of the magnetic field. Furthermore, it was found that the gravity force has a significant effect on the particle deposition, as the number of deposited 10 μm particles on the floor is much larger than 1 μm particles.

Heat transfer and entropy generation analysis of water-Fe3O4/CNT hybrid magnetic nanofluid flow in a trapezoidal wavy enclosure containing porous media with the Galerkin finite element method

The present study addresses theoretically and computationally the performance of electrically conducting water-Fe3O4/CNT hybrid nanofluid in three-dimensional free convection and entropy generation in a wavy-walled trapezoidal enclosure. The enclosure has two layers—a hybrid nanoliquid layer and a permeable medium layer. A transverse magnetic field is acting in the upward direction. Newtonian flow is considered, and the modified Navier–Stokes equations are employed with Lorentz hydromagnetic body force, Darcian and Forchheimer drag force terms. The wavy side walls are heated while the top and vertical walls are adiabatic. An elliptic cylindrical cooled fin is positioned at the center of the cavity, and several different tilting angles of the fin are considered. The transformed, non-dimensional systems of coupled nonlinear partial differential equations with their corresponding boundary conditions are solved numerically with the Galerkin Finite Element Method (FEM) using the COMSOL Multiphysics software platform. The impact of Darcy number, Hartmann number, volume fraction, undulation number of the wavy wall and Rayleigh number (thermal buoyancy parameter) on the streamlines, isotherms and Bejan number contours are investigated. Extensive visualization of the thermal flow characteristics is included. With increasing Hartmann and Rayleigh numbers, the average Bejan number is reduced strongly whereas the average Nusselt number is only depleted significantly at very high values of Rayleigh and high Hartmann numbers. With increasing undulation number, a slight elevation in average Bejan number at intermediate Rayleigh numbers is noticed, whereas the average Nusselt number is substantially boosted, and the effect is maximized at a very high Rayleigh number where the average Nusselt number was increased by 35%. An increment in Darcy number (i.e., reduction in permeability of the porous medium layer) is observed to considerably elevate the average Nusselt number at high values of the Rayleigh number up to 20%, whereas the contrary response is computed in average Bejan number, where it showed a reduction by 10 times. The simulations apply to hybrid magnetic nanofluid fuel cells and electromagnetic nanomaterials processing in cavities.

Unsteady Three-Dimensional Free Convection Flow Near the Stagnation Point Over a General Curved Isothermal Surface in a Nanofluid

This study deals with an unsteady three-dimensional free convection flow near the stagnation point region over a general curved isothermal surface placed in a nanofluid. Nanofluids are great scientific interest because these new thermal transport phenomena surpass the fundamental limits of conventional macroscopic theories of suspensions. Since the heat and mass transfer are very extensive in the industry, the unsteady three-dimensional body near stagnation point can give a significant impact on the heat transfer process. The main objective of the present study is to investigate the effects of some governing parameters on the skin friction coefficients, local Nusselt and local sheerwood numbers as well as related profiles of unsteady free convection in a nanofluid. The momentum equations in x-and y-directions, energy balance equation, and nanoparticle concentration equation are reduced to a set of four fully-coupled nonlinear differential equations under appropriate similarity transformations. The well-known technique Keller-box method is used numerically for different values of governing parameters entering these equations. Further, the present results have been compared with the previous published results for a particular case and the comparisons are found to be in good agreement. The skin friction, local Nusselt number and Sherwood number is increases with an increase in curvature parameter. Rising values of the Lewis number and Brownian motion parameter has enhanced the flow while rising values of the buoyancy and thermophoresis parameter will decelerate the flow. The temperature profile is increases when Brownian motion, buoyancy and thermophoresis parameter increases and concentration profile increase with an increases in buoyancy and thermophoresis parameter.

Numerical Study of Periodic Magnetic Field Effect on 3D Natural Convection of MWCNT-Water/Nanofluid with Consideration of Aggregation

In this paper, a numerical study is performed to investigate the effect of a periodic magnetic field on three-dimensional free convection of MWCNT (Mutli-Walled Carbone Nanotubes)-water/nanofluid. Time-dependent governing equations are solved using the finite volume method under unsteady magnetic field oriented in the x-direction for various Hartmann numbers, oscillation periods, and nanoparticle volume fractions. The aggregation effect is considered in the evaluation of the MWCNT-water/nanofluid thermophysical properties. It is found that oscillation period, the magnitude of the magnetic field, and adding nanoparticles have an important effect on heat transfer, temperature field, and flow structure.

TWO- AND THREE-DIMENSIONAL TRANSIENT ANALYSIS OF FLOW AND HEAT TRANSFER IN STRUCTURES WITH DOMICAL AND CURVED ROOFS

The aim of this study is to investigate transient buoyancy driven free convection heat transfer in domical (with a dome) structures or curved roofs is numerically. Two- and three-dimensional turbulent free convection are considered for the Rayleigh number intervals (10 8 ≤ Ra ≤10 10 ). The aspect ratios of H/L =1 and 2, with respect to the heated length, are considered. The heating is provided from a lateral surface while cooling is from opposing lateral surface. The hot and cold surfaces are kept isothermal, and all other surfaces are adiabatic. The Boussineq approximation is used for modeling the buoyancy flow. The RNG k- e turbulence model is used. The pertinent transient equations are solved using Fluent 6.3.26 software. The flow of air (streamlines) and temperature distribution (isotherms) are produced. The mean Nusselt number is evaluated over the isothermal hot wall is computed, and the results are analyzed with respect to the flow and geometric variations. The mean Nusselt number using the 2-D simulations indicate that the mean Nusselt number does not significantly change with H/L ratio. The 3-D simulations yield higher mean Nusselt numbers, but they are smaller than those of obtained for flat top enclosures.

Effects of Variable Viscosity and Thermal Conductivity on MHD Flow Past a Vertically Moving Porous Plate with Viscous and Joule Dissipation

effects of variable viscosity and thermal conductivity on a three-dimensional free convection flow past a uniformly moving porous vertical plate with viscous dissipation and Joule heating in presence of a uniform transverse magnetic field have been studied numerically. The governing boundary layer equations with associated boundary conditions are converted to non-dimensional form. The Magnetic Reynolds number is considered small enough to neglect the induced hydro magnetic effect. The resulting non-linear partial differential equations are then solved using an iterative method for an implicit finite difference scheme. Effects of various flow governing parameters on the fluid velocity, temperature, concentration fields are presented graphically. Further, the coefficient of skin-friction, rate of heat transfer and rate of mass transfer at the plate are presented in tabular form. Keywordsviscosity and thermal conductivity, Joule heating, viscous dissipation, MHD, free convection, mass and heat transfer.

Stationary free convection problem with radiative heat exchange

We prove the solvability of the three-dimensional stationary free convection problem with regard of radiative heat exchange. We show that the set of solutions is homeomorphic to a compact set in a finite-dimensional space. Sufficient conditions for the uniqueness of the solution are obtained.

Free convection nanofluid flow in the stagnation-point region of a three-dimensional body.

Analytical results are presented for a steady three-dimensional free convection flow in the stagnation point region over a general curved isothermal surface placed in a nanofluid. The momentum equations in x- and y-directions, energy balance equation, and nanoparticle concentration equation are reduced to a set of four fully coupled nonlinear differential equations under appropriate similarity transformations. The well known technique optimal homotopy analysis method (OHAM) is used to obtain the exact solution explicitly, whose convergence is then checked in detail. Besides, the effects of the physical parameters, such as the Lewis number, the Brownian motion parameter, the thermophoresis parameter, and the buoyancy ratio on the profiles of velocities, temperature, and concentration, are studied and discussed. Furthermore the local skin friction coefficients in x- and y-directions, the local Nusselt number, and the local Sherwood number are examined for various values of the physical parameters.

Three-dimensional free convection MHD flow in a vertical channel through a porous medium with heat source and chemical reaction

An analysis is made to study the three-dimensional MHD free convection flow in a vertical channel through a porous medium with heat source and chemical reaction. The flow phenomenon is characterized by magnetic parameters (M), Darcy number (Kp), Reynolds number (Re), source parameter (S), Grashof number for heat transfer (Gr), Grashof number for mass transfer (Gc), Prandtl number (Pr), Schmidt number (Sc), and chemical reaction parameter (Kc). Approximate solutions of the velocity, temperature, and concentration are obtained using a perturbation technique. The effect of these parameters on the velocity, temperature and concentrations distribution is discussed and some interesting results are presented.

Three-dimensional laminar convection in a parallelepiped with heating of two side walls

Three-dimensional laminar free convection in a parallelepiped with heating of two side walls with variation of the height-to-width aspect ratio over a wide range A x = L/H = 0.1–5 is investigated numerically. The Rayleigh number changed over the range Ra = 103−106. The influence of the volume geometry on the three-dimensional flow structure and heat transfer is studied. It is shown that the three-dimensional character of the flow has a profound effect on heat transmission at a small aspect ratio parameter (A x < 1). For longer length volumes, the whole coefficient of heat emission does not depend on the height-to-width aspect ratio of the enclosure and can be determined from a 2D-approach.

Three-Dimensional Free Convection Flow with Radiation in the Slip Flow Regime

Three-Dimensional Free Convection Flow with Radiation in the Slip Flow Regime

Three-Dimensional Free Convection Flow in a Vertical Channel Filled with a Porous Medium

Three-Dimensional Free Convection Flow in a Vertical Channel Filled with a Porous Medium

Three-Dimensional Free Convection Flow of a Viscous Fluid through a Nonhomogeneous Porous Medium

Three-Dimensional Free Convection Flow of a Viscous Fluid through a Nonhomogeneous Porous Medium

Thermal-diffusion and diffusion-thermo effects on combined heat and mass transfer by hydromagnetic three-dimensional free convection over a permeable stretching surface with radiation

Abstract The thermal-diffusion and diffusion-thermo effects on the heat and mass transfer characteristics of free convection past a continuously stretching permeable surface in the presence of magnetic field, blowing/suction and radiation are studied. The fluid viscosity is assumed to vary with temperature. The resulting, governing three-dimensional equations are transformed using a similarity transformation and then solved numerically by the shooting method. Comparison with previously published work is performed and full agreement is obtained. A parametric study showing the effects of variable viscosity parameter β, magnetic parameter M, Dufour number Df, Soret number Sr, radiation parameter R and blowing/suction parameter f 0 on the velocity, temperature, and concentration field of a hydrogen–air mixture as a non-chemical reacting fluid pair, as well as the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number is carried out. These are illustrated graphically and in tabular form to depict special features of the solutions.

Series solutions of unsteady free convection flow in the stagnation-point region of a three-dimensional body

The unsteady three-dimensional free convection flow in the stagnation-point region on a general curved isothermal surface placed in an ambient fluid is studied. By introducing new similarity transformations, the momentum and energy balance equations are reduced to a set of three fully coupled nonlinear partial differential equations. These equations are solved analytically for some various values of the ratio of the two principal radii of curvature. The accurate series solutions are obtained which are uniformly valid for all dimensionless time in the whole spatial region 0 ⩽ η < ∞ .

Three-Dimensional Heat and Mass Transfer Flow of a Viscous Fluid with Periodic Suction Velocity

In this paper, three-dimensional unsteady free convection and mass transfer flow of an incompressible, viscous liquid through a porous medium past an infinite vertical porous plate is presented. It is considered that the plate is subjected to a time-dependent periodic suction velocity normal to the plate. Approximate solutions for the velocity, temperature, and concentration fields are obtained by using the series expansion method and considering e as a reference parameter. Expressions for the skin friction, rate of heat transfer, and mass transfers are also derived. The results obtained are discussed for the cooling and heating cases of the porous plate.

Three-Dimensional Free Convection Flow and Heat Transfer Past a Vertical Channel

Three-Dimensional Free Convection Flow and Heat Transfer Past a Vertical Channel

Three-dimensional flow of a viscous fluid with heat and mass transfer

Three-dimensional unsteady free convection and mass transfer flow of an incompressible, viscous liquid through a porous medium past an infinite vertical flat plate subjected to a time-dependent suction velocity normal to the plate is studied. The equations encountered into the problem are solved using perturbation technique to obtain the velocity, temperature and concentration fields considering ɛ as reference parameter. Expressions for the skin-friction, rate of heat and mass transfers are also obtained. Two cases of most common interest viz. cooling case ( G r > 0) and heating case ( G r < 0) are discussed.

Three-dimensional convective cooling in a vertical channel with flush-mounted heat sources

Three-dimensional free convection in a vertical channel with spatially periodic, flush-mounted heat sources is investigated by a spectral element method. All numerical solutions are obtained using a time-accurate finite-difference integration scheme capable of capturing temporal instabilities that spontaneously appear at large values of Grashof number, Gr. In addition, the leading order approximation of the 3-D solution for small Gr is derived and compared with the numerical solutions. The agreement is excellent for sufficiently small Gr. Computations are carried out for a Boussinesq fluid, Prandtl number, Pr=0.71, non-dimensional reference temperature, Θ ∗ b =0.12 and values of Grashof number in the range 0.1⩽ Gr⩽5×10 4. For given aspect ratios, and for sufficiently small values of Grashof number, the solution evolves to a unique, time-independent state that exhibits the maximum symmetry consistent with the boundary conditions. At Gr ∗≃28 ,000, self-sustained oscillations appear spontaneously in the flow and thermal fields. For time-dependent solutions ( Gr⩾Gr ∗ ) the symmetry of the flow and temperature fields breaks down. Temperature and velocity distributions as well as maximum temperature, maximum velocity and local Nusselt number distributions are presented for the values of Grashof number studied. For time-dependent flows, instantaneous as well as averaged-in-time solutions are discussed.

Three-dimensional free convection in molten gallium

Convective flow of molten gallium is studied in a small-aspect-ratio rectangular, differentially heated enclosure. The three-dimensional nature of the steady flow is clearly demonstrated by quantitative comparison between experimental temperature measurements, which give an indication of the strength of the convective flow, and the results of numerical simulations. The three-dimensional flow structure is characterized by cross-flows which are an order of magnitude smaller than the main circulation, and spread from the endwall regions to the entire enclosure when the Grashof number is increased beyond Gr = 104. The mergence of these effects in the centre of the enclosure leads to a complex central divergent flow structure which underpins the observed transition to oscillatory convection.