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.     

Pool boiling of R-123/oil mixtures on enhanced tubes having different pore sizes

The effect of enhanced geometry (pore diameter, gap width) is investigated on the pool boiling of R-123/oil mixture for the enhanced tubes having pores with connecting gaps. Tubes having different pore diameters (and corresponding gap widths) are specially made. Significant heat transfer degradation by oil is observed for the present enhanced tubes. At 5% oil concentration, the degradation is 26–49% for T_sat = 4.4 °C. The degradation increases 50–67% for T_sat = 26.7 °C. The heat transfer degradation is significant even with small amount of oil (20–38% degradation at 1% oil concentration for T_sat = 4.4 °C), probably due to the accumulation of oil in sub-tunnels. The pore size (or gap width) has a significant effect on the heat transfer degradation. The maximum degradation is observed for d_p = 0.20 mm tube at T_sat = 4.4 °C, and d_p = 0.23 mm tube at T_sat = 26.7 °C. The minimum degradation is observed for d_p = 0.27 mm tube for both saturation temperatures. It appears that the oil removal is facilitated for the larger pore diameter (along with larger gap) tube. The highest heat transfer coefficient with oil is obtained for d_p = 0.23 mm tube, which yielded the highest heat transfer coefficient for pure R-123. The optimum tube significantly (more than 3 times) outperforms the smooth tube even with oil. The heat transfer degradation increases as the heat flux decreases.     

Investigation of natural circulation in cavities with uniform heat generation for different Prandtl number fluids

Natural convection in enclosures with uniform heat generation and isothermal side walls is studied here. For the rectangular enclosure, two-dimensional conservation equations are solved using SIMPLE algorithm. Parametric studies are conducted to examine the effects of orientation of the cavity, fluid properties (Pr number), and aspect ratio for Rayleigh numbers up to 10⁶. For a horizontal square cavity, the flow becomes periodically oscillating at Ra = 5 × 10⁴ and chaotic at Ra = 8 × 10⁵. With a slight increase in the inclination angle, the oscillations die and for inclination angles greater than 15⁰, the flow attain a steady state over a range of Ra. It is found that for tall cavities (aspect ratio > 1), the steady-state solution is obtained for all values of Ra considered here. However, for wide cavities (aspect ratio < 1), an oscillatory flow regime is observed. The maximum temperature within the cavity is calculated for the range of Ra, aspect ratio and Pr number. Correlations for the maximum cavity temperature is presented here. The values of critical Rayleigh number at which the convection sets in the rectangular cavity are also studied and two distinct criteria are determined to evaluate the critical Rayleigh number. Further, a three-dimensional simulation is performed for a cubic cavity. It is found that the steady state solutions are obtained for all Rayleigh number, except at Ra = 10⁶. This is in contrast to the predictions for a two-dimensional square cavity, which has an oscillatory zone from Ra = 5 × 10⁴ onwards.     

Thermo-bioconvection in a suspension of gravitactic micro-organisms in vertical cylinders

We investigate the effect of heating or cooling from below at constant temperature and constant heat flux on the development of gravitactic bioconvection in vertical cylinders with stress free sidewalls. The governing equations are the continuity equation, the Navier–Stokes equations with the Boussinesq approximation, the diffusion equation for the motile micro-organisms and the energy equation. The control volume method is used to solve numerically the complete set of governing equations. The governing parameters are the thermal and bioconvection Rayleigh numbers, the bioconvection Peclet number, the Lewis number, the Schmidt number and the aspect ratio. We found that subcritical bifurcations of bioconvection became supercritical bifurcations when the thermal Rayleigh number Ra_T is different than zero. For Ra_T < 0, i.e. for cooling from below, we have opposing buoyancy forces, the convection is decreased and the critical thermo-bioconvection Rayleigh number is increased with respect to that of bioconvection. For Ra_T > 0, i.e. for heating from below, we have cooperating buoyancy forces, the convection is increased and the critical thermo-bioconvection Rayleigh number is decreased with respect to that of bioconvection. Heating and cooling from below at constant temperature and heat flux modify considerably the pattern formation of the gravitactic bioconvection.     

Natural convection effects on heat and mass transfer in a curvilinear triangular cavity

Finite element method is used in this study to analyze the effects of buoyancy ratio and Lewis number on heat and mass transfer in a triangular cavity with zig-zag shaped bottom wall. Buoyancy ratio is defined as the ratio of Grashof number of solutal and thermal. Inclined walls of the cavity have lower temperature and concentration according to zig-zag shaped bottom wall. Enclosed space consists mostly of an absorber plate and two inclined glass covers that form a cavity. Both high temperature and high concentrations are applied to bottom corrugated wall. Computations were done for different values of buoyancy ratio (?10 ? Br ? 10), Lewis number (0.1 ? Le ? 20) and thermal Rayleigh number (10⁴ ? Ra_T ? 10⁶). Streamlines, isotherms, iso-concentration, average Nusselt and Sherwood numbers are obtained. It is found that average Nusselt and Sherwood numbers increase by 89.18% and 101.91% respectively as Br increases from ?10 to 20 at Ra_T = 10⁶. Also, average Nusselt decreases by 16.22% and Sherwood numbers increases by 144.84% as Le increases from 0.1 to 20 at this Rayleigh number.     

Experimental investigation of mixed convection heat transfer from longitudinal fins in a horizontal rectangular channel

Mixed convection heat transfer from longitudinal fins inside a horizontal channel has been investigated for a wide range of modified Rayleigh numbers and different fin heights and spacings. An experimental parametric study was made to investigate effects of fin spacing, fin height and magnitude of heat flux on mixed convection heat transfer from rectangular fin arrays heated from below in a horizontal channel. The optimum fin spacing to obtain maximum heat transfer has also been investigated. During the experiments constant heat flux boundary condition was realized and air was used as the working fluid. The velocity of fluid entering channel was kept nearly constant (0.15 ? w_in ? 0.16 m/s) using a flow rate control valve so that Reynolds number was always about Re = 1500. Experiments were conducted for modified Rayleigh numbers 3 × 10⁷ < Ra¹ < 8 × 10⁸ and Richardson number 0.4 < Ri < 5. Dimensionless fin spacing was varied from S/H = 0.04 to S/H = 0.018 and fin height was varied from H_f/H = 0.25 to H_f/H = 0.80. For mixed convection heat transfer, the results obtained from experimental study show that the optimum fin spacing which yields the maximum heat transfer is S = 8–9 mm and optimum fin spacing depends on the value of Ra¹.     

Critical condition for Rayleigh-Bénard convection of Bingham fluids in rectangular enclosures

Two-dimensional steady-state numerical simulations have been conducted for laminar Rayleigh-Bénard convection of Bingham fluids in rectangular enclosures to analyse the critical Rayleigh number Ra_crit for which convection ceases to influence the thermal transport and thermal conduction becomes the principal heat transfer mechanism. The influences of Bingham number Bn on the critical Rayleigh number Ra_crit have been investigated for different values of aspect ratio (height: length) AR (ranging from 1/4 to 4) and nominal Prandtl number Pr (ranging from 10 to 500) for both constant wall temperature (CWT) and constant wall heat flux (CWHF) boundary conditions for the horizontal walls. It has been found that Ra_crit increases with increasing values of Bn and AR, regardless of the boundary condition. The values of Ra_crit have been found to be greater in the case of CWT boundary condition than in the CWHF configuration for AR ≤ 1, whereas an opposite trend is obtained for AR > 1 for Bingham fluids. Additionally, Ra_crit has been found be insensitive to the change of Pr for Newtonian fluids (i.e. Bn = 0), whereas Ra_crit increases with increasing Pr for Bingham fluids irrespective of the boundary condition. A detailed scaling analysis has also been performed to elucidate the effects of Bn ,Pr , AR on Ra_crit for Bingham fluids. The results of scaling analysis and numerical findings have been utilised to propose a new correlation for Ra_crit for both Newtonian and Bingham fluids in the case of both CWT and CWHF boundary conditions.     

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.     

Entropy generation in natural convection in a symmetrically and uniformly heated vertical channel

In this study numerical predictions of local and global entropy generation rates in natural convection in air in a vertical channel symmetrically heated at uniform heat flux are reported. Results of entropy generation analysis are obtained by solving the entropy generation equation based on the velocity and temperature data. The analyzed regime is two-dimensional, laminar and steady state. The numerical procedure expands an existing computer code on natural convection in vertical channels. Results in terms of fields and profiles of local entropy generation, for various Rayleigh number, Ra, and aspect ratio values, L/b, are given. The distributions of local values show different behaviours for the different Ra values. A correlation between global entropy generation rates, Rayleigh number and aspect ratio is proposed in the ranges 10³ ⩽ Ra ⩽ 10⁶ and 5 ⩽ L/b ⩽ 20.     

Thermal lattice-BGK model based on large-eddy simulation of turbulent natural convection due to internal heat generation

To simulate turbulent convection at high Rayleigh number (Ra), we propose a new thermal lattice-BGK (LBGK) model based on large eddy simulation (LES). Two-dimensional numerical simulations of natural convection with internal heat generation in a square cavity were performed at Ra from 10⁶ to 10¹³ with Prandtl numbers (Pr) at 0.25 and 0.60. Simulation results indicate that our model is fit to simulate high Ra flow for its better numerical stability. At Ra = 10¹³, a global turbulent has occurred. With a further increase in Ra, the flow will arrive in a fully turbulence regime. The Nusselt–Rayleigh relationship is also discussed.     

Experimental study of natural convection in PV roof solar collector

The aim of this paper is to propose the PV roof solar collector (PV-RSC) to investigate the natural convection heat transfer and estimated the convective heat transfer coefficient in the channel. The experimental set-up was composed of a PV panel on the upper layer and the lower layer is aluminum plate of the channel. The inclination angle and air gap of channel were fixed at 30° and 15 cm, respectively. The channel width is 0.7 m, and length is 1.2 m. The data analysis were confirmed the effect of radiative exchange influent to natural convection within the channel. On the basis of the experimental results, an empirical formula is found; the Nu as a function of Ra_s sin30, that is Nu_s = 0.3282 (Ra_s sin30)^0.2249. The correlation obtained to range 3 × 10⁸ < Ra_s sin30 < 7 × 10⁸. A comparison between PV-RSC and normal PV panel, it was confirmed that the PV-RSC could be generated electric power than that normal PV panel by about 30 W; and also the percentage of power generation increase was rising about 25% throughout the day.     

Heat flow visualization for natural convection in rhombic enclosures due to isothermal and non-isothermal heating at the bottom wall

Analysis has been carried out for the energy distribution and thermal mixing in steady laminar natural convective flow through the rhombic enclosures with various inclination angles, φ for various industrial applications. Simulations are carried out for various regimes of Prandtl (Pr) and Rayleigh (Ra) numbers. Dimensionless streamfunctions and heatfunctions are used to visualize the flow and energy distribution, respectively. Multiple flow circulations are observed at Pr = 0.015 and 0.7 for all φs at Ra = 10⁵. On the other hand, two asymmetric flow circulation cells are found to occupy the entire cavity for φ = 75° at higher Pr (Pr = 7.2 and 1000) and Ra (Ra = 10⁵). Heatlines are found to be parallel circular arcs connecting the cold and hot walls for the conduction dominant heat transfer at Ra = 10³. The enhanced convective heat transfer is explained with dense heatlines and convective loop of heatlines at Ra = 10⁵. Heatlines clearly demonstrate that the left wall receives heat from the bottom wall as heatlines directly connect both the walls whereas the convective heat circulation cells play lead role to distribute the heat along the right wall, especially for smaller φs. On the other hand, the heat flow is evenly distributed to both side walls at higher φs via convection as well as direct conductive transport. Significant convective heat transfer from the bottom hot wall to the left cold wall occurs for φ = 30° cavity whereas the heat transfer to the right cold wall is maximum for φ = 75° irrespective of Pr. Average Nusselt number studies also show that φ = 30° cavity gives maximum heat transfer rate from the bottom to left wall irrespective of Pr in isothermal heating case. On the other hand, enhanced thermal mixing occurs at φ = 75° for both isothermal and non-isothermal heating strategies except at Pr = 0.015 in isothermal heating case.     

Numerical study of heat transfer by natural convection and surface thermal radiation in an open cavity receiver

In this work the numerical results of natural convection and surface thermal radiation in an open cavity receiver considering large temperature differences and variable fluid properties are presented. Numerical calculations were conducted for Rayleigh number (Ra) values in the range of 10⁴–10⁶. The temperature difference between the hot wall and the bulk fluid (ΔT) was varied between 100 and 400 K, and was represented as a dimensionless temperature difference (φ) for the purpose of generalization of the trends observed. Noticeable differences are observed between the streamlines and temperature fields obtained for φ = 1.333 (ΔT = 400 K) and φ = 0.333 (ΔT = 100 K). The total average Nusselt number in the cavity increased by 79.8% (Ra = 10⁶) and 88.0% (Ra = 10⁴) as φ was varied from 0.333 to 1.333. Furthermore the results indicate that for large temperature differences (0.667 ? φ ? 1.333) the radiative heat transfer is more important that convective heat transfer.     

Natural convection heat transfer in horizontal and vertical closed narrow enclosures with heated rectangular finned base plate

Natural convection heat transfer and fluid flow characteristics in horizontal and vertical narrow enclosures with heated rectangular finned base plate have been experimentally investigated at a wide range of Rayleigh number (Ra) for different fin spacings and fin lengths. Quantitative comparisons of finned surface effectiveness (ε) and heat transfer rate between horizontal and vertical enclosures have been reported. In comparison with enclosure of a bare base plate, insertion of heat conducting fins always enhances heat transfer rate. Optimization of fin-array geometry has been addressed. The results gave an optimum fin spacing at which Nusselt number (Nu_H) and finned surface effectiveness (ε) are maximum. It has been found that: (1) increasing fin length increases Nu_H and ε; (2) increasing Ra increasesNu_H for any fin-array geometries and (3) for any fin-array geometry and at Ra > 10,000, increasing Ra decreases ε while for fin-array geometries of large fin spacing and at Ra < 10,000, increasing Ra increases ε. Useful design guidelines have been suggested. Correlations of Nu_H have been developed for horizontal and vertical enclosures. Correlations predictions have been compared with previous data and good agreement was found.     

Numerical simulation of liquid metals in differentially heated enclosure undergoing orthogonal rotation

In this work a numerical investigation has been performed to examine the characteristics of mixed convective heat transfer in square enclosures undergoing orthogonal rotation i.e. rotation axis and gravity axis are orthogonal to each other. A semi implicit finite difference code on a collocated grid is used to solve the momentum and energy equations subject to Boussinesq approximation. The study is carried out for a wide range of operating parameters such as Rayleigh number (Ra), Taylor number (Ta), Rotational Rayleigh number (Ra_w) for a fixed Prandtl number (Pr). The numerical experiments have been carried out for a fixed Pr = 0.01, Ra varies from 10⁵ to 10⁷ while Ta and Ra_w vary from almost 0 to 10⁹. Results reveal that significant increase or decrease in heat transfer rates can be achieved by the rotational effects, mainly influenced by centrifugal force.     

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.     

Turbulent Rayleigh–Bénard convection of water in cubical cavities: A numerical and experimental study

Experimental measurements and numerical simulations of natural convection in a cubical cavity heated from below and cooled from above are reported at turbulent Rayleigh numbers using water as a convective fluid (Pr = 6.0). Direct numerical simulations were carried out considering the Boussinesq approximation with a second-order finite volume code (10⁷ ⩽ Ra ⩽ 10⁸). The particle image velocimetry technique was used to measure the velocity field at Ra = 10⁷, Ra = 7 × 10⁷ and Ra = 10⁸ and there was general agreement between the predicted time averaged local velocities and those experimentally measured if the heat conduction through the sidewalls was considered in the simulations.     

Magnetic field and internal heat generation effects on the free convection in a rectangular cavity filled with a porous medium

A numerical investigation of the steady magnetohydrodynamics free convection in a rectangular cavity filled with a fluid-saturated porous medium and with internal heat generation has been performed. A uniform magnetic field, inclined at an angle γ with respect to the horizontal plane, is externally imposed. The values of the governing parameters are the inclined angle γ = 0, π/6, π/4 and π/2, Hartmann number Ha = 0, 1, 5, 10 and 50, Rayleigh number Ra = 10, 100, 10³ and 10⁵, and the aspect ratio a = 0.01, 0.2, 0.5 and 1 (square cavity). It is shown that the intensity of the core convection is considerably affected by the considered parameters. It is also found that the local Nusselt number Nu_Y decreases on the bottom wall as γ increases (magnetic field changes its direction from the horizontal to the vertical direction) and vice versa for the top wall of the cavity. The reported results are in good agreement with the available published work in the literature.     

Heatlines based natural convection analysis in tilted isosceles triangular enclosures with linearly heated inclined walls: effect of various orientations

Natural convection in isosceles triangular enclosures with various configurations (case 1 — inverted, case 2 — straight and case 3 — tilted) is studied via heatline analysis for linear heating of inclined walls. Detailed analysis and comparison for various base angles (φ = 45°, 60°) of triangular enclosures have been carried out for a range of fluids (Pr = 0.015 − 1000) within Ra = 10³ − 10⁵ using Galerkin finite element method. The heat flow distributions indicate conduction dominant heat transfer at low Ra (Ra = 10³) for case 1 and case 2 whereas in case 3, convective heat flow is observed due to high buoyancy force. As Ra increases, enhanced thermal mixing is observed at the core of the cavity. Wall to wall heat transfer occurs at walls AB and AC due to linear heating boundary condition in all the cases. Although the distributions of fluid flow and heat flow are qualitatively similar for φ = 45° and 60°, the intensity of fluid flow and heat flow decreases as φ increases. Strength of fluid flow and heat flow circulation cells is found to be higher in case 3 for identical parameters. Results show that upper side wall (AC) for case 3 exhibits higher heat transfer rates whereas heat transfer rates for walls AB and AC are the same for case 1 and case 2. Also Nu_AB is higher for case 2 followed by case 1 and case 3 at the middle portion of wall AB. Thus to achieve high heat transfer from fluid to wall at the central region, case 2 and case 3 configurations may be recommended at high Ra (Ra = 10⁵) and Pr, irrespective of φ.     

Natural convection in a partially open square cavity with internal heat source: An analysis of the opening mass flow

A steady buoyancy-driven flow of air in a partially open square 2D cavity with internal heat source, adiabatic bottom and top walls, and vertical walls maintained at different constant temperatures is investigated numerically in this work. A heat source with 1% of the cavity volume is present in the center of the bottom wall. The cold right wall contains a partial opening occupying 25%, 50% or 75% of the wall. The influence of the temperature gradient between the verticals walls was analyzed for Ra_e = 10³–10⁵, while the influence of the heat source was evaluated through the relation R = Ra_i/Ra_e, investigated at between 400 and 2000. Interesting results were obtained. For a low Rayleigh number, it is found that the isotherm plots are smooth and follow a parabolic shape indicating the dominance of the heat source. But as the Ra_e increases, the flow slowly becomes dominated by the temperature difference between the walls. It is also observed that multiple strong secondary circulations are formed for fluids with a small Ra_e whereas these features are absent at higher Ra_e. The comprehensive analysis is concluded with horizontal air velocity and temperature plots for the opening. The numerical results show a significant influence of the opening on the heat transfer in the cavity.