The effect of the position of the heated thin porous fin on the laminar natural convection heat transfer in a differentially heated cavity

Laminar natural convection heat transfer in a differentially heated cavity with two thin porous fins attached to the hot wall and bottom insulated surface was studied numerically for various pertinent parameters. Such parameters include Richardson number, Darcy number, thermal conductivity ratio, and location of the porous fin. The left wall of the cavity is assumed to be uniformly heated while the right wall is kept at a lower temperature. In addition, the horizontal walls of the cavity were considered insulated. Furthermore, the governing transport equations within the porous media were written according to the volume-average theory. The governing equations are solved using a finite element formulation based on the Galerkin method of weighted residuals. The results of this investigation showed that the presence of a horizontal porous fin increases the average Nusselt number when compared with the differentially heated cavity for various Richardson numbers and thermal conductivity ratios. However, a vertical porous fin attached to the bottom insulated surface exhibited a lower average Nusselt number than the no-fin case.     

Magnetizing force modeled and numerically solved for natural convection of air in a cubic enclosure: effect of the direction of the magnetic field

Magnetizing force is modeled by considering magnetic susceptibility as a function of temperature and is included in a momentum balance equation as an external force term in addition to the buoyant force term. Under ideal gas behavior, the magnetizing force term can be represented by a new and simple non-dimensional parameter group γ, which represents the ratio of magnetizing force to the gravitational force. This magnetizing force acts on material of high magnetic susceptibility, like oxygen gas in a temperature gradient field, and affects the convection in addition to gravity. Sample computation was carried out for air in a cubic box that is heated from one vertical wall and cooled from the opposing wall, and has the other four walls thermally insulated. With an increase in the magnetic strength, the upward and downward natural convection in the gravity field becomes horizontal circulation under a cusp-shaped magnetic field.     

BUOYANT CONVECTION IN A CAVITY WITH A BAFFLE UNDER TIME-PERIODIC WALL TEMPERATURE

A numerical study is made of buoyant convection at high Rayleigh number in a square cavity that contains a horizontal baffle at midheight. The horizontal walls of the cavity are insulated. At the cold left vertical wall, the nondimensional temperature is constant θ = 0, and at the hot right vertical wall, the wall temperature is time periodic, θ     

Comparison of Mixed Convection in a Square Cavity with an Oscillating versus a Constant Velocity Wall

This article presents a numerical investigation of unsteady laminar mixed convection heat transfer in a two-dimensional square cavity. The cavity is configured such that one of the vertical walls is cooled and slides either with a constant speed or with a sinusoidal oscillation. A portion of the opposite stationery wall is heated by a constant temperature heat source while, the remaining walls of the cavity are thermally insulated. Different configurations of sliding wall movement and a series of Richardson numbers and Strouhal numbers are tested. The results indicate that the direction and magnitude of the sliding wall velocity affect the heat transfer rate. At low Richardson numbers, the average heat transfer rate for the cavity with an oscillating wall is found to be lower compared to that for the cavity with a constant velocity wall. In addition, at a fixed Richardson number, as the Strouhal number decreases the oscillation frequency of average Nusselt number on the vertical walls decreases; however, the oscillation amplitude of average Nusselt number increases.     

Effect of Various Thermal Boundary Conditions on Natural Convection in a Trapezoidal Cavity with Linearly Heated Side Wall(s)

A penalty finite-element-based study has been carried out for natural-convection flow in a trapezoidal cavity with uniformly heated bottom wall and linearly heated and/or cooled vertical wall(s) in the presence of an insulated top wall. For linearly heated side walls, symmetry in flow patterns is observed, whereas secondary circulation is observed for the linearly heated left wall and cooled right wall. The local Nusselt number indicates reversal of heat flow at the side walls or the left wall. The average Nusselt number versus Rayleigh number illustrates that the overall heat transfer rate at the bottom wall is larger for the linearly heated left wall and cooled right wall.     

Natural convection in three-dimensional porous cavities: integral transform method

A transient three-dimensional Darcy model of natural convection in porous medium filled cavities is studied, using a vorticity-vector potential formulation and the generalized integral transform technique (GITT). A general formulation and solution methodology for vertical cavities (insulated vertical walls with differential horizontal wall temperatures) is developed. Results for cubic cavities are presented while evaluating the Rayleigh number effects for stable situations, observing the transient evolution of the heat transfer process. The convergence behavior of the proposed eigenfunction expansion solution is investigated and comparisons with previously reported steady-state solutions are critically performed.     

Numerical simulation of free convection heat transfer in a vertical annular cavity with discrete heating

The main objective of this article is to investigate the effect of discrete heating on convection heat transfer in a vertical cylindrical annulus. In this analysis, the inner wall of the cavity has two discrete flush-mounted heat sources and the outer wall is isothermally cooled at a lower temperature and top and bottom walls are thermally insulated. The governing equations are solved using an implicit finite difference technique to investigate the influence of each parameter and in particular the radii ratio. The numerical results reveal that the heat transfer rate is always higher at the bottom heater. Also, the rate of heat transfer increases with radii ratio but decreases with aspect ratio. Further, the present results are in excellent agreement with the existing benchmark solutions.     

Natural convection heat transfer in a partially opened cavity filled with porous media

This paper examines the steady natural convection in a partially opened enclosure filled with porous media using the Brinkman–Forchheimer model. Whilst the part of the left vertical wall of the cavity is heated, the other walls are adiabatic or thermally insulated Based upon numerical predictions, the effects of pertinent parameters such as Grashof number, Darcy number, porosity, length of the heated wall and the location center of the opened cavity are examined. It is found that as the Grashof number increases, due to strengthening buoyancy driven flows, the local Nusselt number from partially heated vertical wall, at a given position on this wall increases. This, in turn, increases the temperature of the heated wall. The results of this study can be used in the design of an effective cooling system for electronic components to help ensure effective and safe operational conditions.     

Natural convection in divided trapezoidal cavities filled with fluid saturated porous media

A numerical work was performed to determine the heat transfer and fluid flow due to buoyancy forces in divided trapezoidal enclosures filled with fluid saturated porous media. In the present investigation, bottom wall was non-uniformly heated while two vertical walls were insulated and the top wall was maintained at constant cold temperature. The divider had constant thermal conductivity. Flow patterns and temperature distribution were obtained by solving numerically the governing equations, using Darcy's law. Results are presented for different values of the governing parameters, such as Rayleigh number for a porous medium, location of the partition, thickness of the partition and thermal conductivity ratio between solid and fluid media. It was observed that the conduction mode of heat transfer became dominant inside the cavity for higher thickness of the partition, low Rayleigh numbers, and low thermal conductivity ratio.     

Surface radiation effect on convection in a closed enclosure driven by a discrete heater

This paper is aimed at presenting the changes experienced by a convective flow in a closed square enclosure when surface radiation is taken into account. The flow is driven by a centrally placed discrete heater in an air filled two dimensional square enclosure. Symmetrically cooled isothermal vertical walls and insulated horizontal walls are considered. The governing coupled partial differential equations were solved using a finite volume method on a uniformly staggered grid system. The resulting augmentation of fluid velocities and the factors causing them are discussed.     

Fluid–structure interaction analysis of mixed convection heat transfer in a lid-driven cavity with a flexible bottom wall

A numerical investigation of steady laminar mixed convection heat transfer in a lid driven cavity with a flexible bottom surface is analyzed. A stable thermal stratification configuration was considered by imposing a vertical temperature gradient while the vertical walls were considered to be insulated. In addition, the transport equations were solved using a finite element formulation based on the Galerkin method of weighted residuals. In essence, a fully coupled fluid–structure interaction (FSI) analysis was utilized in this investigation. Moreover, the fluid domain is described by an Arbitrary-Lagrangian–Eulerian (ALE) formulation that is fully coupled to the structure domain. Comparisons of streamlines, isotherms, bottom wall displacement and average Nusselt number were made between rigid and flexible bottom walls. The results of this investigation revealed that the elasticity of the bottom wall surface plays a significant role on the heat transfer enhancement. Furthermore, the contribution of the forced convection heat transfer to that offered by natural convection heat transfer has a profound effect on the behavior of the flexible wall as well as the momentum and energy transport processes within the cavity. This investigation paves the road for future research studies to consider flexible walls when augmentation of heat transfer is sought.     

Numerical Study of Laminar Natural Convection in a Side-Heated Trapezoidal Cavity at Various Inclined Heated Sidewalls

Steady natural convection of air flow in a two-dimensional side-heated trapezoidal room was investigated numerically using a non-orthogonal, collocated finite-volume grid system. The considered geometry has an inclined left heated sidewall, a vertical right cooled sidewall, and two insulated horizontal upper and lower walls. Computations are performed for seven values of the heated sloping wall angle, three different values of aspect ratio, and five Rayleigh number values. Results are displayed in terms of streamlines, isotherms, and both local and average Nusselt number values. The principal result of this work is the great dependence of the flow fields and the heat transfer on the inclination angle, the aspect ratio, and the Rayleigh number. A correlation between the average Nusselt number, Rayleigh number, heated sloping wall angle, and aspect ratio is proposed.     

Neural-finite difference method (NFDM) in development of improved differential approximation (IDA) and its application for coupled conduction and radiation heat transfer in a square enclosure: An experimental validation

The present numerical and experimental analysis addresses coupled conduction and radiation heat transfer (CCR) in differentially heated vertical isothermal walls and horizontal insulated walls of a square enclosure with absorbing, emitting and isotropic scattering participating gray medium. The P₁ approximation solution is utilized as the input signal to the neuron model. The computational domain is treated by the neural-finite difference method (NFDM) with ray tracing technique of ray emission model (REM) for the development of improved differential approximation (IDA). The output results are validated with the results of DOM. The practical implementation of IDA for wide range of radiative parameters are illustrated and examined. Experiments have been performed in a square enclosure with solid isothermal walls made of aluminum and insulated walls with bakelite, thus forming air filled cavity. Finally, the consistence of isotherm pattern of the numerical work with the interferogram captured by Mach–Zehnder interferometer corroborates the IDA theory and its realistic approach.     

Differentially heated cubical cavity using energy pathlines and field synergy

The article deals with the natural convective flow of air in a cubical cavity which is analyzed numerically. Isothermal temperature is maintained on the vertical walls where the temperature of the left wall is more than the right wall and all other walls are assumed to be kept insulated. In this present article, upwind, QUICK, SUPERBEE, and self‐filtered central differencing schemes are compared based on their accuracy and computational time with a numerical example. An attempt has been made to analyze the flow behavior inside the cavity using vortex corelines, streamlines, isotherms energy pathlines, and field synergy by varying the Rayleigh number (Ra) from 10³ to 10⁶. In the vicinity of isothermal vertical walls, the velocity, and temperature boundary layers become thinner as Ra increases. The energy pathlines are in oscillating nature when Ra increases to 10⁵ and above. The field synergy principle implies by improving the synergy between the velocity and temperature, the heat transfer gets enhanced with the less increased flow resistance.     

HYDROMAGNETIC COMBINED CONVECTION FLOW IN A VERTICAL LID-DRIVEN CAVITY WITH INTERNAL HEAT GENERATION OR ABSORPTION

The problem of unsteady, laminar, combined forced-free convection flow in a square cavity in the presence of internal heat generation or absorption and a magnetic field is formulated. Both the top and bottom horizontal walls of the cavity are insulated while the left and right vertical walls are kept at constant and different temperatures. The left vertical wall is moving in its own plane at a constant speed while all other walls are fixed. A uniform magnetic field is applied in the horizontal direction normal to the moving wall. A temperature-dependent heat source or sink is assumed to exist within the cavity. The governing equations and conditions are solved numerically by the finite-volume approach along with the alternating direct implicit (ADI) procedure. Two cases of thermal boundary conditions corresponding to aiding and opposing flows are considered. Comparisons with previously published work are performed and the results are found to be in excellent agreement. A parametric study is conducted and a set of representative graphical results is presented and discussed to illustrate the influence of the physical parameters on the solution.     

Interactions of thermally induced acoustic waves with buoyancy induced flows in rectangular enclosures

Acoustic waves are generated when a compressible-fluid is exposed to a rapidly varying heat flux along a confining wall. For an enclosure, these waves reverberate and eventually decay. Buoyancy-induced flows generated within an enclosure can be affected by the acoustic waves generated. The interactions of the acoustic waves produced by rapid heating of a wall with the buoyancy-induced flow in air filled rectangular enclosures are investigated numerically. For the present simulations, the bottom wall of the enclosure is heated rapidly with varying heating rates, while the top wall is held at the initial temperature of the air. The vertical walls of the enclosure are considered insulated. The compressible unsteady Navier–Stokes equations are solved by an explicit flux-corrected transport algorithm for the convection terms and by a central-differencing scheme for the viscous and conduction terms.     

Experimental and Numerical Investigation on a Water-Filled Cavity Natural Convection to Find the Proper Thermal Boundary Conditions for Simulations

In this study, the laminar natural convection flow inside a water-filled cavity with differentially heated vertical walls is investigated experimentally and numerically. Both of the walls are heated and cooled by two special heat exchangers that are attached to the walls and the rest are insulated. The main purpose of each test is to reach a uniform constant temperature on both of the heated and cooled walls. Early tests for an air-filled cavity showed that a uniform temperature on the walls is feasible, while a different trend was observed for a water-filled cavity with a nonuniform distribution of temperature. ANSYS FLUENT 15 employed four approaches in terms of boundary conditions for computational purposes. None of the three-dimensional (3D) and two-dimensional (2D) models of the cavity with a uniform wall temperature (the wall average temperature from the experiment) were suitable for predicting the Nusselt number. Therefore, it was essential to use the full model to properly predict the real distribution of temperature and Nusselt number on the walls. The 3D model of the cavity with a nonuniform wall temperature, which was borrowed from the experiment, also provided good results for the Nusselt number, but a measured temperature was still needed from the experiments. The 2D simulation's findings showed a weakness in properly capturing the streamlines for all ranges of Rayleigh numbers.     

Integral transform solution for natural convection in three-dimensional porous cavities: Aspect ratio effects

Three-dimensional natural convection in box-like cavities filled with a porous material is revisited, by considering a transient formulation for the energy balance and a quasi-steady formulation for the flow problem. The Generalized Integral Transform Technique (GITT) is employed in the hybrid numerical-analytical solution of the Darcy law based model for vertical cavities (insulated vertical walls with differentially prescribed horizontal wall temperatures), employing the vorticity-vector potential formulation. Comparisons with previously reported numerical solutions are performed and the transition between conductive and convective states is illustrated, centering on the aspect ratio influence on the flow and heat transfer phenomena. A set of reference results for the steady-state behavior under different aspect ratio is provided for covalidation purposes.     

TRANSIENT NATURAL CONVECTION IN A CAVITY WITH WALLS OF FINITE THICKNESS

Numerical studies are made of transient natural convection in a square cavity. The top and bottom end walls are thermally insulated. The vertical solid side walls are of finite thickness and of finite thermal conductivity. Flow is driven, from the motionless isothermal initial state, by impulsively increasing (decreasing) the temperature at the outer surface of one (the other) vertical side wall. Numerical solutions art sought to the time-dependent Navier-Stokes equations for the fluid and the solid regions. The ratios of thermophysical properties between solid and fluid are the significant parameters. As the thermal capacity ratio increases, the development of flow in the fluid region is retarded. The conductive and convective timescales are estimated. The effects of the thermal conductivity ratio and of the thickness of the side wall are delineated. The effect of the system Rayleigh number on transient heat transport is analyzed. The applicability of the approximate one-dimensional thermal conductance model to the transient features is scrutinized.     

Convective Heat Transfer in a Vertical Rectangular Duct Filled with a Nanofluid

An analysis is performed to study natural convective heat transfer in a vertical rectangular duct filled with a nanofluid. One of the vertical walls of the duct is cooled by a constant temperature, while the other wall is heated by a constant temperature. The other two sides of the duct are thermally insulated. The transport equations for a Newtonian fluid are solved numerically with a finite volume method of second‐order accuracy. The influence of pertinent parameters such as Grashof number, Brinkman number, aspect ratio and solid volume fraction on the heat transfer characteristics of natural convection is studied. Results for the volumetric flow rate and skin friction for Copper and Diamond nanoparticles are also drawn. The Nusselt number for various types of nanoparticle such as silver, copper, diamond and titanium oxide are also tabulated. The results indicate that inclusion of nanoparticles into pure water improves its heat transfer performance; however, there is an optimum solid volume fraction which maximizes the heat transfer rate.