A numerical study of laminar natural convective heat transfer around a horizontal cylinder inside a concentric air-filled triangular enclosure

A numerical investigation of steady-state laminar natural convective heat transfer around a horizontal cylinder to its concentric triangular enclosure was carried out. The enclosure was filled with air and both the inner and outer cylinders were maintained at uniform temperatures. The buoyancy effect was modeled by applying the Boussinesq approximation of density to the momentum equation and the governing equations were iteratively solved using the control volume approach. The effects of the Rayleigh number and the aspect ratio were examined. Flow and thermal fields were exhibited by means of streamlines and isotherms, respectively. Variations of the maximum value of the dimensionless stream function and the local and average Nusselt numbers were also presented. The average Nusselt number was correlated to the Rayleigh number based on curve-fitting for each aspect ratio. At the highest Rayleigh number studied, the effects of different inclination angles of the enclosure and various cross-section geometries of the inner cylinder were investigated. The computed results indicated that at constant aspect ratio, both the inclination angle and cross-section geometry have insignificant effects on the overall heat transfer rates though the flow patterns are significantly modified.     

EFFECTS OF ADAPTIVITY ON FINITE ELEMENT SCHEMES FOR TURBULENT HEAT TRANSFER AND FLOW PREDICTIONS

This article reports convection heat transfer in a short and tall annular enclosure with two discrete isoflux heat sources of different lengths. The discrete heat sources are mounted at the inner wall and the outer wall is maintained at a lower temperature, whereas the top and bottom walls and the unheated portions of the inner wall are kept at adiabatic. An implicit finite-difference method is employed to solve the vorticity–stream function formulations of the governing equations. The significant influence of the discrete heaters on the flow and heat transfer is analyzed for a wide range of modified Rayleigh numbers, aspect ratio, and length ratio (?) of heat sources. Our numerical results reveal that the average Nusselt number decreases with aspect ratio, whereas the magnitude of maximum temperature increases with the aspect ratio. For most of the parametric cases considered in the present study, the heat transfer rate is found to be higher at the bottom heater than at the top heater except for ? = 0.5. The effect of heater length ratio on the heat transfer rate is noticeable for unit aspect ratio, whereas its effect is insignificant as the aspect ratio increases. Furthermore, it was found that the maximum temperature is found generally at the top heater except for the case ? = 0.5, where the maximum temperature is found at the bottom heater.     

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.     

Natural Convection in a Vertical Annuli with Discrete Heat Sources

In this article, we numerically study natural convection heat transfer in a cylindrical annular cavity with discrete heat sources on the inner wall, whereas the outer wall is isothermally cooled at a lower temperature, and the top wall, the bottom wall, and unheated portions of the inner wall are assumed to be thermally insulated. To investigate the effect of discrete heating on the natural convection heat transfer, at most two heating sources located near the top and bottom walls are considered, and the size and location of these discrete heaters are varied in the enclosure. The governing equations are solved numerically by an implicit finite difference method. The effect of heater placements, heater lengths, aspect ratio, radii ratio, and modified Rayleigh number on the flow and heat transfer in the annuli are analyzed. Our numerical results show that when the size of the heater is smaller, the heat transfer rates are higher. We also found that the heat transfer in the annular cavity increases with radii ratio and modified Rayleigh number, and can be enhanced by placing a heater with the smaller length near the bottom surface.     

Effect of aspect ratio on natural convection in an inclined rectangular enclosure with sinusoidal boundary condition

The aim of the present numerical study is to understand the natural convection flow and heat transfer in an inclined rectangular enclosure with sinusoidal temperature profile on the left wall. The top and bottom walls of the enclosure are kept to be adiabatic. The finite difference method is used to solve the governing equations with a range of inclination angles, aspect ratios and Rayleigh numbers. The results are presented in the form of streamlines, isotherms and Nusselt numbers. The heat transfer increases first then decreases with increasing the inclination of the enclosure for all aspect ratio and Rayleigh number. Increasing the aspect ratio shows a decreasing trend of the heat transfer for all Rayleigh numbers considered. A correlation equation is also introduced for the heat transfer analysis in this study.     

Mixed Convection of Nanofluid Flows in a Square Lid-Driven Cavity Heated Partially From Both the Bottom and Side Walls

This article presents the results of a numerical study on mixed convection within a square lid-driven which was heated simultaneously by two finite heat sources on the bottom and side walls, and also filled with nanofluids. The results were presented for different nanofluids. The governing equations were solved using a finite volume approach by the SIMPLE algorithm. The effects of the Rayleigh number, Reynolds number, the solid volume fraction, the dimensions of heaters, and their locations on the streamlines and isotherms contours were investigated accurately. Also, the effects of the above parameters on the average Nusselt number along two heat sources were precisely presented. Moreover, variations of the average Nusselt number of two heaters were considered whenever one heater was fixed and the location of the other heater was varied along the wall. In addition, variations of the length of one heater on the average Nusselt number were also studied whenever the length of the other heater was fixed.     

Free convective heat transfer in an enclosure with an internal louvered blind

A numerical study has been conducted of free convection in a tall vertical enclosure with an internal louvered metal blind. The study considers the effects of Rayleigh number, enclosure aspect ratio, and blind geometry on the convective heat transfer. The numerical model has been validated against experimental measurements and the results have been presented in terms of an empirical correlation for the average Nusselt number. The correlation is applicable to an enclosure with an internal metal blind. It has been shown that the Nusselt number correlation can be combined with a simple one-dimensional model to closely predict the enclosure U-value.     

Three-Dimensional Numerical Study of Natural Convective Heat Transfer of Liquid in a Cubic Enclosure

ABSTRACT

Steady-state laminar natural convection in a cubic enclosure with a cold vertical wall and two hot square heaters with constant temperature on the opposite wall is studied numerically. The enclosure is filled with various liquids. Three-dimensional Navier–Stokes Equations are solved by employing the SIMPLE algorithm. Computations are performed for a range of Rayleigh number from 10³ to 10⁷ while enclosure aspect ratio varies from 0.05 to 1.6. The effects of Rayleigh number, enclosure aspect ratio, and Prandtl number on heat transfer characteristics are studied in detail. The results show that the flow field is very complex and heat transfer from the two heaters is not the same. The effects of Prandtl number are negligible in the range from 5 to 140 with other parameters kept constant. This allows the use of liquids such as water for studying other dielectric liquids, provided the flow geometry and other nondimensional parameters are similar. The overall Nusselt number increases markedly with Rayleigh number. It is also affected by enclosure aspect ratio. It attains the maximum value when aspect ratio is in the range of 0.1–0.2 and decreases as enclosure aspect ratio varies from 0.2 to 1.6. Also, various settings of cooling face and arrangement of heaters are investigated, and the results show that they have considerable effects on heat transfer of both heaters.     

Study of buoyancy-induced flows subjected to partially heated sources on the left and bottom walls in a square enclosure

In this paper, numerical simulations of laminar, steady, two-dimensional natural convection flows in a square enclosure with discrete heat sources on the left and bottom walls are presented using a finite-volume method. Two different orientated wall boundary conditions are designed to investigate the natural convection features. The computational results are expressed in the form of streamlines and isothermal lines for Rayleigh numbers ranging from 10² to 10⁷ in the cavity. In the course of study, a combination of third-order and exponential interpolating profile based on the convective boundedness criterion is proposed and tested against the partially heated cavity flow up to the highest Rayleigh number 10⁷. The effects of thermal strength and heating length on the hydrodynamic and thermal fields inside the enclosure are also presented. Numerical results indicate that the average Nusselt number increases as Rayleigh number increases for both cases. Moreover, it is seen that the effect of the heat transfer rate due to the heating strength on the left wall is different from the one on the bottom. For the heater size effect, it is observed that by increasing the length of heat source segment, the heat transfer rate is gradually increased for both cases.     

Acknowledgment

An experimental and numerical study has been carried out in order to investigate mixed and natural convection heat transfer in a two-dimensional enclosure. A discrete isothermal heat source is located at one of the vertical walls. Also, two ventilation ports are at the bottom and on top of the opposite wall. A forced flow condition was imposed by providing an inlet of air at the bottom port. A Mach–Zehnder interferometer was used to visualize the temperature field within the enclosure and to determine the local and average heat transfer characteristics of the heat source. Five heater positions on the vertical wall and different Rayleigh numbers (4.5 × 10⁵ to 1.15 × 10⁶) and Reynolds numbers (120 to 1600) were considered in the experiments. A finite volume code has been developed based on the SIMPLE algorithm and hybrid discretization scheme for the numerical study. It is observed that the interaction of natural convection with the forced flow leads to various flow fields depending on the Richardson number, Reynolds number and the heater position. Also, results show different trends for variation of the average Nusselt number with the heater position at low and high Reynolds numbers. An optimum position for the heat source, at which the maximum heat transfer is achieved, exists for high Reynolds numbers and has been found to be at the middle of the vertical wall.     

Natural convection of water-based nanofluids in an inclined enclosure with a heat source

This study investigates natural convection heat transfer of water-based nanofluids in an inclined square enclosure where the left vertical side is heated with a constant heat flux, the right side is cooled, and the other sides are kept adiabatic. The governing equations are solved using polynomial differential quadrature (PDQ) method. Calculations were performed for inclination angles from 0° to 90°, solid volume fractions ranging from 0% to 20%, constant heat flux heaters of lengths 0.25, 0.50 and 1.0, and a Rayleigh number varying from 10⁴ to 10⁶. The ratio of the nanolayer thickness to the original particle radius is kept at a constant value of 0.1. The heat source is placed at the center of the left wall. Five types of nanoparticles are taken into consideration: Cu, Ag, CuO, Al₂O₃, and TiO₂. The results show that the average heat transfer rate increases significantly as particle volume fraction and Rayleigh number increase. The results also show that the length of the heater is also an important parameter affecting the flow and temperature fields. The average heat transfer decreases with an increase in the length of the heater. As the heater length is increased, the average heat transfer rate starts to decrease for a smaller inclination angle (it starts to decrease with inclination at 90° for ? = 0.25, 60° for ? = 0.50, 45° for ? = 1.0, respectively).     

Heatline Analysis on Heat Transfer and Convective Flow of Nanofluids in an Inclined Enclosure

This article presents a heatline method to analyse the transport mechanism of heat transfer and convective flow of nanofluids in an inclined square enclosure, where a heated thin plate located in the middle of the enclosure. The fluid flow, heat transfer, and heat transport characteristics are illustrated using streamlines, isotherms, Nusselt number and heatlines. Results show that fluid flow and temperature fields strongly depend on Rayleigh number, inclination angle, solid volume fraction, types of nanoparticles and the plate length, and the maximum strength of heatfunction increases as the inclination angle and Rayleigh number increase.     

Numerical Investigation of the Entropy Generation Due to Natural Convection in a Partially Heated Square Cavity Filled With Nanofluids

A comprehensive numerical investigation has been carried out on the heat transfer performance and entropy generation within a rectangular cavity containing nanofluid. The cavity consists of two heat sources located on the bottom and a side wall. The effects of influential parameters including type and concentration of nanoparticles, radius of corner, width and thickness of heaters, heater distance from corners and aspect ratio of the enclosure were studied. The results showed that the Nusselt number enhanced by increasing the aspect ratio of the cavity, the distance of heaters from the corners, and concentration of nanoparticle and applying Cu as nanoparticle while it reduced by increasing the radius of the corner and the width and thickness of the heat sources. The entropy generation was found to be profoundly minimized by lowering the Rayleigh number. In addition, the entropy generation was attenuated by increasing the Eckert number, corner radius, the distance from the corner and concentration of nanoparticles and using Al₂O₃ as nanoparticle. On the other hand, increasing the aspect ratio of the cavity, width and thickness of the heaters augmented the entropy generation. Interestingly, the entropy generation of the system was lowered by just increasing the distance of one heater from the corner, whereas increasing the thickness and width of one heater resulted in larger entropy generation. This study provides valuable insight into the change in the amount of heat transfer and entropy by altering the geometry as well as fluid properties.     

Numerical Investigation of Unsteady Natural Convection in an Inclined Square Enclosure With Heat-Generating Porous Medium

The unsteady laminar natural convection in an inclined square enclosure with heat-generating porous medium whose heat varies by a cosine function is investigated by a thermal equilibrium model and the Brinkman–Darcy–Forchheimer model numerically, with the four cooled walls of closure as isothermal. The numerical code based on the finite-volume method has been validated by reference data before it was adopted. Influence of dimensionless frequency and inclination angle on heat transfer characteristics in a square enclosure, such as flow distribution, isotherm, averaged Nusselt number on each wall, and time-averaged Nusselt number, are discussed, with specified value for Rayleigh number = 10⁸, Darcy number = 10^?4, Prandtl number = 7, porosity = 0.4, and specific heat ratio = 1. It is found that when the internal heat source varies by cosine, the Nusselt numbers of the four walls oscillate with the same frequency as the internal heat source; however, phase difference occurs. Moreover, frequency has little impact on time-averaged Nusselt number of the four walls, which is different from the phenomenon discovered in natural convection with suitable periodic varying wall temperature boundary condition. Moreover, inclination angle plays an important role in the heat transfer characteristics of the walls studied.     

Laminar natural convection in an inclined complicated cavity with spatially variable wall temperature

Natural convection in two-dimensional enclosure with three flat and one wavy walls is numerically investigated. One wall is having a sinusoidal temperature profile. Other three walls including the wavy wall are maintained at constant cold temperature. This problem is solved by SIMPLE algorithm with deferred QUICK scheme in curvilinear co-ordinates. The tests were carried out for different inclination angles, amplitudes and Rayleigh numbers while the Prandtl number was kept constant. The geometrical configurations considered were namely one-, two- and three-undulations.The results obtained show that the angle of inclination affects the flow and heat transfer rate in the cavity. With increase in amplitude, the average Nusselt number on the wavy wall is appreciably high at low Rayleigh number. Increasing the number of undulations beyond two is not beneficial. The trend of local Nusselt number is wavy.     

Effects of the inclination angle on natural convection heat transfer and entropy generation in a square porous enclosure

ABSTRACT

In this paper, we analyze numerically the effects of the inclination angle on natural convection heat transfer and entropy generation characteristics in a two-dimensional square enclosure saturated with a porous medium. There is a significant alteration in Nusselt number with the orientation of the enclosure at higher values of Rayleigh number. It reveals that the variation of entropy generation rate with the inclination angle is significant for higher values of Darcy number. The dominant source of irreversibility is due to heat transfer at low values of Darcy number, whereas entropy generation due to fluid flow dominates over that due to heat transfer for larger values of Darcy number.     

Three-Dimensional Study of Natural Convection in a Horizontal Channel With Discrete Heaters on One of Its Vertical Walls

Three-dimensional natural convection in a horizontal channel with an array of discrete flush-mounted heaters on one of its vertical walls is numerically studied. Effects of thermal conductivities of substrate and heaters and convection on outer sides of the channel walls on heat transfer are examined. The substrate affects heat transfer in a wider range of thermal conductivities than do the heaters. At lower heater thermal conductivities a higher heat portion is transferred by direct convection from the heaters to the adjacent coolant. However, higher substrate conductivity is associated with higher heat portion transferred through the substrate. The innermost heater column is found to become the hottest heater column due to the lower coolant accessibility. The heat transfer in the channel is strongly influenced by convection on the outer sides of the channel walls. Correlations are presented for dimensionless temperature maximum and average Nusselt number.     

Numerical investigation of laminar natural convective heat transfer from a horizontal triangular cylinder to its concentric cylindrical enclosure

A numerical simulation was conducted to investigate the steady laminar natural convective heat transfer for air within the horizontal annulus between a heated triangular cylinder and its circular cylindrical enclosure. The Boussinesq approximation was applied to model the buoyancy-driven effect and the governing equations were solved using the finite volume method. Four different Rayleigh numbers and four different radius ratios were considered, and four different inclination angles for the inner triangular cylinder were investigated as well. The computed flow and temperature fields were demonstrated in the form of streamlines and isotherms. Variations of the maximum stream function and the local and average Nusselt numbers were displayed as functions of the above-mentioned parameters. Correlations of the average Nusselt number were proposed based on curve fitting. At constant radius ratio, inclination angles of the inner triangular cylinder are found to have negligible effects on the average Nusselt number.     

Numerical Studies on Natural Convection in a Trapezoidal Enclosure With Discrete Heating

Abstract

A steady state laminar natural convection flow in a trapezoidal enclosure with discretely heated bottom wall, adiabatic top wall, and constant temperature cold inclined walls is performed. The finite volume based commercial code “ANSYS-FLUENT” is used to investigate the influence of discrete heating on natural convection flows in a trapezoidal cavity. The numerical solution of the problem covers various Rayleigh numbers ranging from 10³ to 10⁶, non-dimensional heating length ranging from 0.2 to 0.8 and Prandtl number is 0.7. The performance of the present numerical approach is represented in the form of streamfunction, temperature profile and Nusselt number. Heat transfer increases with increase of Rayleigh numbers at the corners of the cavity for same heating length from center of the bottom wall. However, the heat transfer rate is less and almost constant for the Rayleigh numbers considered. It is found that the average Nusselt number monotonically increases with increase of Rayleigh number and length of heat source. The variation of local and average Nusselt numbers is more significant for larger length of heating than smaller one. The heat transfer correlations useful for practical design problems have been predicted.     

Laminar natural convection in an inclined complicated cavity with spatially variable wall temperature

Natural convection in two-dimensional enclosure with three flat and one wavy walls is numerically investigated. One wall is having a sinusoidal temperature profile. Other three walls including the wavy wall are maintained at constant cold temperature. This problem is solved by SIMPLE algorithm with deferred QUICK scheme in curvilinear co-ordinates. The tests were carried out for different inclination angles, amplitudes and Rayleigh numbers while the Prandtl number was kept constant. The geometrical configurations considered were namely one, two and three undulations.The results obtained show that the angle of inclination affects the flow and heat transfer rate in the cavity. With increase in amplitude, the average Nusselt number on the wavy wall is appreciably high at low Rayleigh number. Increasing the number of undulations beyond two is not beneficial. The trend of local Nusselt number is wavy.