Natural convection heat transfer in an anisotropic porous cavity heated from side (2nd report,experiment using a Hele‐Shaw cell)

Natural convection heat transfer and flow structure in an anisotropic porous medium of square cavity saturated with a Boussinesq fluid has been studied experimentally using a Hele‐Shaw cell. The permeability ratio defined by K = K_y/K_x was set to three different values: 0.4, 1, and 2.5. The convection patterns at the three permeability ratios are visualized at several different Rayleigh numbers by a pH indicator method. When K is 0.25, the visualized flow is mainly in the vertical direction. On the contrary, for K = 4 the convecting flow is in the horizontal direction. The average heat transfer coefficients are also measured, and the corresponding Nusselt numbers are plotted as a function of K. It is found that the corresponding Nusselt numbers are correlated with (KRa)^1/2. The experimental results of the flow pattern and heat transfer are in good agreement with those obtained by our previous theory. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(6): 463–474, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10046     

Numerical simulation of natural convection heat transfer from a heated square cylinder in a square cavity filled with micropolar fluid

A numerical investigation has been performed to visualize the magnetohydrodynamic natural convective heat transfer from a heated square cylinder situated within a square enclosure subjected to nonuniform temperature distributions on the left wall. The flow inside the enclosure is unsteady, incompressible, and laminar and the working fluid is micropolar fluid with constant Prandtl number (Pr = 7). The governing equations of the flow problem are the conservation of mass, energy, and linear momentum, as well as the angular momentum equations. Governing equations formulated in dimensionless velocity and pressure form has been solved by Marker and Cell method with second-order accuracy finite difference scheme. Comprehensive verification of the utilized numerical method and mathematical model has shown a good agreement with numerical data of other authors. The results are discussed in terms of the distribution of streamlines and isotherms and surface-averaged Nusselt number, for combinations of Rayleigh number, Ra (10³–10⁶), Vortex viscosity parameter, K (0–5), and Ha parameter (0–50). It has been shown that an increase in the vortex viscosity parameter leads to attenuation of the convective flow and heat transfer inside the cavity.     

Rayleigh–Bénard convection in a supercritical fluid along its critical isochore in a shallow cavity

We perform a numerical investigation of the Rayleigh–Bénard convection in supercritical nitrogen in a shallow enclosure with an aspect ratio of 4. The transient and steady-state fluid behaviors over a wide range of initial distances to the critical point along the critical isochore are obtained and analyzed in response to modest homogeneous bottom heating. On account of the fluid layer being extremely thin, density stratification is notably excluded from consideration herein, which leads to the dominating role of the Rayleigh criterion in the onset of convection. Following the Boussinesq approximation, we find the power law scaling relationships over five decades of the Rayleigh number (Ra) for various transient quantities including the exponential growth rate of the mean enstrophy in the cavity and the characteristic times of the development of convective motion. The correlation of the Nusselt number versus the Rayleigh number shows asymptotic features at the two ends of the Ra spectrum, which incidentally correspond to different convection patterns. Under the regime of high Ra, the heat transfer through the fluid cavity is enhanced by the turbulent bursts of thermal plumes from the boundary layers. On the other hand, under the regime of low Ra, it is the orderly multicellular flow that moves heat from the bottom of the layer to the top, which includes a transition from a four-cell structure to a six-cell structure with decreasing Ra.     

Parallel Finite Volume Method Simulation of Three-Dimensional Fluid Flow and Convective Heat Transfer for Viscoplastic Non-Newtonian Fluids

Three-dimensional fluid mechanics and heat transfer for viscoplastic flows are described by finite volume method, FVM. The open multi-processing approach has been implemented to parallelize the numerical code. Results for the elapsed times, speed-ups and efficiencies are presented. The code was used to describe the natural convection (Ra = 10⁴; 10⁶) and the lid-driven cavity (Re = 100; 1000) processes with Bingham, Casson and Herschel–Bulkley fluids (Bn = 0.01; 1.0). Results describing isotherms, velocity distributions and streamtraces, as a function of Ra, Re, Pr and Bn numbers are shown. The grid size analysis shows that different sizes are required to obtain precise results for Nusselt number and friction factor.     

Natural convective heat transfer in square enclosures heated from below

The paper deals with the results of an experimental and numerical study of free convective heat transfer in a square enclosure characterized by a discrete heater located on the lower wall and cooled from the lateral walls.The study analysed how the heat transfer develops inside the cavity at the increasing of the heat source length.The experimental data are obtained by measuring the temperature distribution in the air layer by real-time and double-exposure holographic interferometry while the commercial finite volumes code Fluent 6.0 is used for the numerical study. Convection has been studied for Rayleigh number from 10³ to 10⁶. Different convective forms are obtained depending on Ra and on the heat source length.The local Nusselt number is evaluated on the heat source surface and it shows a symmetrical form raising near the heat source borders. Graphs of the local Nusselt number on the heat source and of the average Nusselt number at several Ra are finally presented.     

A thermal nonequilibrium model to natural convection inside non-Darcy porous layer surrounded by horizontal heated plates with periodic boundary temperatures

This article displays a numerical investigation on natural convection within non-Darcy porous layer surrounded by two horizontal surfaces having sinusoidal temperature profiles with difference in phase and wave number. The Darcy–Brinkman–Forchheimer model and local thermal nonequilibrium condition have been employed. Simulations have been performed for wide ranges of inertia coefficient (10^–4 ≤ Fs/Pr* ≤ 10^–2), thermal conductivity ratio (0.1 ≤ K _r ≤ 100), phase difference (0 ≤ β ≤ π), modified Rayleigh number (200 ≤ Ra* ≤ 1000), wavelength (3 ≤ k ≤ 12), and nondimensional heat transfer coefficient (0.1 ≤ H ≤ 100). Results demonstrate that Nusselt number highly relies on Fs/Pr*, K _r, β, Ra*, and k as compared to H. A considerable enhancement in fluid, solid, and overall Nusselt numbers has been observed with diminishing Fs/Pr* and β and increasing k, K _r, and H. The raising in β has a significant impact on Nu for smaller k and this effect is almost ignored when k > 12. The increase in Ra*, K _r, β, and H and decrease in Fs/Pr* and k acts to reduce the severity of nonequilibrium zone and increase the size of thermal equilibrium zone. The influence of H on nonequilibrium area is more evident than K _r.     

CFD-based analysis of entropy generation due to mean and fluctuating fields during turbulent natural convection in a square enclosure

The current study aims to numerically investigate the entropy generation during the natural convection flow of air in a square cavity. The governing equations for the conservation of mass, momentum, energy, and turbulence are solved using a control volume-based technique employing the commercial code Fluent. Runs have been performed for both laminar and turbulent flow regimes by varying the Rayleigh number (Ra) from 10³ to 10¹⁰. On the other hand, various viscous distribution coefficients (ϕ = 10⁻⁴, 10⁻³, and 10⁻²) and constant Prandtl number (Pr = 0.71) were considered. Given the conflicting perspectives in the literature regarding the entropy generation under turbulent regimes, more research is needed to better understand the impact that the fluctuating flow has on entropy production. The four terms of entropy generation inherent to turbulent natural convection (entropy generation due to dissipation in the mean and the fluctuating velocity fields in addition to the heat flux due to the mean and the fluctuating temperature) are computed in the present work and compared to calculations based on only mean values of temperature and velocity gradients. It was found that taking into account the fluctuating terms of temperatures and velocities augment the total entropy generation by 10.10%, 14.43%, and, 17.70%, up to 32.60%, respectively, for Ra = 5 × 10⁸, Ra = 10⁹, Ra = 1.58 × 10⁹, and Ra = 10¹⁰. The gain shows the tendency to increase with the Rayleigh number. Thus, the fluctuating terms cannot be neglected particularly for high Rayleigh numbers. Furthermore, unlike entropy production due to the mean flow field, numerical outcomes reveal that the generated irreversibilities due to fluctuating flow are located around the upper hot and the lower cold corners of the heated walls. In addition, a numerical relationship between the first and the second laws of thermodynamics has been derived. A promising result that emerged from this study has shown that the Nusselt number and therefore the first law of thermodynamics is sufficient to estimate the heat part of entropy generation without the necessity of using the second law.     

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.     

Effects of thermal boundary conditions on natural convection flows within a square cavity

A numerical study to investigate the steady laminar natural convection flow in a square cavity with uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls has been performed. A penalty finite element method with bi-quadratic rectangular elements has been used to solve the governing mass, momentum and energy equations. The numerical procedure adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number Ra, 10³ ⩽ Ra ⩽ 10⁵ and Prandtl number Pr, 0.7 ⩽ Pr ⩽ 10) with respect to continuous and discontinuous Dirichlet boundary conditions. Non-uniform heating of the bottom wall produces greater heat transfer rates at the center of the bottom wall than the uniform heating case for all Rayleigh numbers; however, average Nusselt numbers show overall lower heat transfer rates for the non-uniform heating case. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominated regimes, power law correlations between average Nusselt number and Rayleigh numbers are presented.     

The role of a partition on free convection in a trapezoidal shaped building

Heat transfer and fluid flow in a partitioned trapezoidal-shaped building are carried out. The finite-volume computational procedure is adopted for numerical simulations. The inclined wall of the building is uniformly heated; the vertical wall is the cold wall, whereas the top and bottom walls are adiabatic. The ranges of parameters studied are the Rayleigh number, Ra (10³ ≤ Ra ≤ 10⁶), the location of the partition, d (0.3L ≤ d ≤ 0.9L), and the partition height, h (0.3H ≤ h ≤ 0.9H). The results are presented for different locations and height of the partition in an enclosure in terms of temperature patterns, streamline curves, and the local and overall Nusselt numbers. It is noticed that when the height of the partition increases beyond 0.3H irrespective of the position of the partition, the heat transfer decreases drastically for all Rayleigh numbers. The comfort zones are located in the cavity for different partition heights. Correlations are developed for Nusselt numbers in terms of the Rayleigh number and height of the partition.     

Non—Darcian and Anisotropic Effects on Natural Convection in Horizontal Porous Media Enclosure

Natural convection heat transfer in a horizontal enclosure filled with anisotropic porous media,being isothermally heated at bettom and cooled at top while the vertical walls being adiabatic,is numerically studied by applying the Brinkman model-a modified form of Darcy model giving consideratioin to the viscous effect.The results show that:(1)a larger permeability ratio(K^*) causes a lower flow intensity in the enclosure and a smaller Nusselt number,all Nusselt numbers approach unity in the limit of K^*→∞;a larger thermal conductivity ratio(λ^*) causes a stranger distortion of isotherms in the enclosure and a higher flow velocity near the walls,all the Nusselt numbers approach unity in the limit of λ^*-→0,the permeability and thermal conductivity ratios generally have opposing effects on the Nusselt number.(2) an increasing Darcy number decreases the flow intensity and heat tansfer rates,which is more significant at a lower permeability ratio.In particular,with K^*≤0.25,the Nusselt number for Da=10^-3 would differ from that of Darcy flow up to an amount of 30%,an analysis neglecting the non-Darican effect will inevitably be of considerable error.     

Enhanced thermal performance and entropy generation analysis in a novel cavity design with circular cylinder

Analyzing fluid dynamics and heat transfer holds significant importance in the design and enhancement of engineering systems. The current investigation utilizes the finite element method to explore natural convection and heat transfer intricacies within a novel cavity containing an inner circular cylinder under steady and laminar flow conditions. The principal aim of this study is to assess the impact of Rayleigh number (Ra), Bejan number (Be), and the presence of adiabatic, hot, and cold cylinders on heat transfer, entropy generation, and fluid flow. The range of Ra considered in this investigation spans from 10³ to 10⁶, while the Prandtl number for the air is fixed at 0.71. The findings illustrate that the presence of a cylinder leads to higher Be as Ra increase, compared to scenarios where no cylinder is present. This observation suggests that buoyancy forces dominate in the absence of a cylinder, resulting in significantly enhanced convective heat transfer efficiency. However, the presence of a heated cylinder within the tooth-shaped cavity exerts a substantial influence on the overall thermal performance of the system. Notably, the average Nusselt Number (Nu) experiences a remarkable increase of 41.97% under the influence of a heated cylinder, when compared to situations where a cold cylinder is present. This elevated average Nu signifies improved heat transfer characteristics, ultimately resulting in an overall improvement in the thermal system's efficiency.     

Natural convective heat transfer and fluid flow in a porous medium filled corrugated enclosure: Effect of discrete heat sources

In this work, we investigate the two-dimensional unsteady natural convective fluid flow problem in a porous-corrugated enclosure with a fixed sinusoidal heated upper wall. The corrugations of the enclosure are discretely heated while vertical walls are maintained isothermally cold. Subject to where the heat sources are located, five different cases are taken into consideration. The vorticity–streamfunction equations are discretized using a transformation-free higher order compact approach, and the hybrid BiCGSTAB technique is used to solve the system of algebraic equations that derives from the numerical discretization. To validate our findings, we first compare them to previously published numerical and experimental data. The numerically simulated outcomes are then examined over a variety of essential parameters, such as the Darcy (10⁻⁵ ≤ Da ≤ 10⁻¹), Rayleigh (10³ ≤ Ra ≤ 10⁶), and Prandtl (0.1 ≤ Pr ≤ 10) numbers. Symmetric and asymmetric fluid flow phenomena are observed. Asymmetric flow phenomenon can be caused by miscible or non-miscible movements of lighter fluids by heavier fluids, or almost exclusively by nonuniform buoyancy-driven forces caused by density variations that have arisen because of variations in fluid temperature. The averaged Nusselt value for Case 1 and Case 5 exhibits the highest percentage ratio. The thermal boundary layer is strongly affected by compression, dispersion, suppression, the zone of stratification, and the outweighing of isotherms. The simulated results are visualized by stream functions, isotherms, local and averaged Nusselt number plots.     

Internal gravity wave resonance of thermal convection fields in rectangular cavities with heat‐flux vibration (effects of aspect ratio on the fields)

In this paper the thermal convection field and its resonance phenomena in a rectangular cavity with heat‐flux vibration are numerically examined and the results are compared with those of a square cavity. As in the case of α=1, the critical angular velocity at which the relative amplitude of the midplane Nusselt number α_m has a local maximum agrees very well with the resonance angular velocity of the internal gravity wave ω_r, estimated by the theoretical equation proposed by Thorpe, even when the aspect ratio is α=5 and the Prandtl number is Pr=0.71 for a range of the Rayleigh number Ra. However, α_m has two local maxima for a larger Ra, which is peculiar to the case of larger α. The time variation of sub‐components of the fluctuating component of the midplane Nusselt number shows that the phase at the maximum value of α_m agrees well with that of the sub‐component of velocity for the first resonance angular velocity ω_r. For the other angular velocity ω_r2, the phase of α_m agrees with that of the sub‐component of temperature. Moreover, we found that the boundary angular velocity ω₀ between the first two of the five ω regions, which classify the thermal convection fields against ω, can be expressed by a function of α, Ra, and Pr and that α_m is independent of α and Ra for a relatively wide range of ω/ω₀. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(3): 158– 171, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20149     

Transient thermo-solutal convection of water near 4 °C with opposing gradients in a square cavity

A numerical study of two-dimensional thermo-solutal convection of water in a square cavity heated from below and salted from above for various value of Lewis number is conducted. The maximum density associated with water around 4 °C occurs inside the cavity, as the top wall is maintained at 0 °C while the bottom wall temperature varies in the range 8–12 °C. The maximum density region acts as an obstacle to prohibit convectional heat, mass, and momentum transfer. These effects are investigated numerically in the domain −5 × 10² < Ra_T < 2 × 10⁴, 1 × 10⁵ < Ra_S < 8 × 10⁶ and L = 0.015 m length of square cavity where Ra is the Rayleigh number of the fluid. The effect of Lewis number on the heat, mass, and momentum transfer is also systematically studied. For certain range of parameters, it is interesting to find that the flow pattern may change inversely from rolling (fluid particles raise along both vertical side walls and fall along the vertical center line) to plume motion (fluid particles raise along the vertical center line and fall along both side walls) as the bottom wall temperature and top wall concentration increase. Further increase in the value of Rayleigh number results in oscillating two cell flow structure in the cavity. It is found that there is a temporal maximum absolute value of average Nusselt and Sherwood number followed by a temporal minimum absolute value of average Nusselt and Sherwood number in a small time interval (0 < t < 300 s) and the steady state is reached after a certain time interval at the bottom wall. These time intervals are reduced with increasing Lewis number. Also, critical Grashof number which accounts for oscillatory heat and mass transfer with Lewis number is studied and it reveals that an increase in Lewis number results in slowing down oscillation and oscillation cycle becomes shorter with increasing species Grashof number.     

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.     

Non‐Darcy assisted flow along a channel with an open cavity filled with water–TiO2 nanofluid

Numerical investigation on forced (assisted) convection heat transfer in a two‐dimensional horizontal porous channel with an open cavity is studied in this article. A non‐uniform heat flux is considered to be located on the bottom surface of the cavity. The rest of the surfaces are taken to be perfectly insulated. The physical domain is filled with a water‐based nanofluid containing TiO₂ nanoparticles. The fluid enters from the left and exits from the right with initial velocity U_i and temperature T_i. Governing equations are discretized using the penalty finite element method. The simulation is carried out for a wide range of Reynolds number Re (= 10–500) and Darcy number Da (= 10^?5–∞). Results are presented in the form of streamlines, isothermal lines, local and average Nusselt numbers, average temperatures of the fluid, horizontal and vertical velocities at mid‐height of the channel and mean velocity fields for various Re and Da. The enhancement of heat transfer rate is caused by the increasing Re and falling Da. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21046     

Numerical analysis of conjugate heat transfer in a partially open square cavity with a vertical heat source

Conjugate heat transfer in partially open square cavity with a vertical heat source has been numerically studied. The cavity has an opening on the top with several lengths and three different positions. The other walls of cavity were assumed adiabatic. The heat source was located on the bottom wall of cavity and it has got a width such as Printed Circuit Boards (PCB). Steady state heat transfer by laminar natural convection and conduction is studied numerically by solving two dimensional forms of governing equations with finite difference method. The results were reported for various governing parameters such as Rayleigh number (10³ ≤ Ra ≤ 10⁶), conductivity ratio, opening position, opening length, PCB distance and PCB height. The numerical results were discussed with streamlines, isotherms, Nusselt number and velocity profiles on x- and y-directions. It is found that ventilation position has a significant effect on heat transfer.     

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.