Natural Convection Heat Transfer in a Cubic Cavity Submitted to Time-Periodic Sidewall Temperature

The laminar unsteady natural convection in a cubic cavity is comprehensively studied here using a high accuracy temporal-spatial pseudospectral method. In this study, the cavity is filled with air and one of its sidewalls is submitted to sinusoidally varying temperature, while constant lower temperature is imposed on the opposing sidewall and other sidewalls are adiabatic. Computations are performed to explore the effects of several influential factors on the fluid flow patterns and heat transfer performances within the cavity, including Rayleigh number and the amplitude and period of pulsating sidewall temperature. Numerical results reveal that the heat transfer enhancement is complexly determined by the above influential factors, and the heat transfer resonance is observed in the case of a large Rayleigh number and amplitude of pulsating sidewall temperature. The three-dimensional effects on fluid flow patterns and heat transfer are discussed. Finally, the backward heat transfer is quantitatively studied.     

复杂方腔内自然对流换热数值模拟分析

对一个内有绝热障碍物的复杂方腔的自然对流换热问题进行了数值计算分析，采用SIMPLE算法，运用类似处理孤岛的方法成功地处理了方腔内部的障碍物，并在此基础之上，对不同高度的障碍物和不同Ra数的方腔内的自然对流换热进行了模拟计算。计算结果表明障碍物的高度和Ra数对流动换热有着重要影响，但其影响对冷热壁面不一样。     

Magnetohydrodynamic natural convection in a vertical cylindrical cavity with sinusoidal upper wall temperature

A series of numerical simulations were performed in order to study liquid metal MHD natural convection in a vertical cylindrical container with a sinusoidal temperature distribution at the upper wall and the other surfaces being adiabatic. Starting from the basic hydrodynamic case, the effect of vertical (axial) and horizontal magnetic fields is assessed. Depending on the magnitude of the Rayleigh and Hartmann numbers, both turbulent and laminar (azimuthally symmetric or not) flows are observed. The results show that the increase of Rayleigh number promotes heat transfer by convection while the increase of Hartmann number favors heat conduction. The vertical magnetic field reduces the Nusselt number more than the horizontal. The circulation patterns for the most convective cases are confined close to the top corner of the container with the simultaneous formation of a secondary flow pattern at the bottom corner, while for the more conductive cases only one circulation pattern exists covering the entire domain.     

Natural convection in porous cavity with sinusoidal bottom wall temperature variation

Numerical study of natural convection in a porous cavity is carried out in the present paper. Natural convection is induced when the bottom wall is heated and the top wall is cooled while the vertical walls are adiabatic. The heated wall is assumed to have spatial sinusoidal temperature variation about a constant mean value which is higher than the cold top wall temperature. The non-dimensional governing equations are derived based on the Darcy model. The effects of the amplitude of the bottom wall temperature variation and the heat source length on the natural convection in the cavity are investigated for Rayleigh number range 20–500. It is found that the average Nusselt number increases when the length of the heat source or the amplitude of the temperature variation increases. It is observed that the heat transfer per unit area of the heat source decreases by increasing the length of the heated segment.     

Three dimensional lattice Boltzmann simulation for mixed convection of nanofluids in the presence of magnetic field

In the present study, a three dimensional thermal lattice Boltzmann model was developed to investigate the flow dynamics and mixed convection heat transfer of Al₂O₃/water nanofluid in a cubic cavity in the presence of magnetic field. The model was first validated with previous numerical and experimental results. Satisfactory agreement was obtained. Then the effects of Rayleigh number, nanoparticle volume fraction, Hartmann number and Richardson number on nanofluid flow dynamics and heat transfer were examined. Numerical results indicate that adding nanoparticles to pure water leads to heat transfer enhancement for low Rayleigh numbers. However, this enhancement might be weakened and even reversed for high Rayleigh numbers. In addition, the results show the external applied magnetic field has an effect of suppressing the convective heat transfer in the cavity. Moreover, the results demonstrate that the Richardson number in mixed convection has significant influences on both streamlines and temperature field.     

Impact of cavity chord shape on the free convection heat transfer rate in a triangular cavity

In this study, the effect of different chord shapes of a triangular cavity has been investigated on the natural convection heat transfer characteristics inside the cavity using the commercial ANSYS‐FLUENT software. Heat transfer phenomena have been regarded as very significant due to the widespread application of natural convection heat transfer in different engineering fields. According to the performed studies, the chord with partitions can considerably enhance the natural convection heat transfer rate inside the cavity. Four different types of partitions including zigzag, two types of rectangular and sinusoidal were considered on the chord of the triangular cavity. The dimensionless parameters investigated in the results include Rayleigh number, Prandtl number, and Nusselt number. The results comprise the isotherm lines, streamlines, velocity lines, local and average Nusselt numbers analyzed with regard to the chord type and Rayleigh number variation. The results revealed that the temperature trend is almost the same for all configurations. Furthermore, the average Nusselt number value in zigzag and sinusoidal is higher in comparison with other cases due to the larger heat transfer area. Finally, by examining the streamlines, isotherm and velocity lines, average and local Nusselt numbers, it was founded that the cavities with zigzag and sinusoidal chord shape have the better performance in terms of heat transfer rate.     

Natural convection in cavities with a thin fin on the hot wall

A numerical study has been carried out in differentially heated square cavities, which are formed by horizontal adiabatic walls and vertical isothermal walls. A thin fin is attached on the active wall. Heat transfer by natural convection is studied by numerically solving equations of mass, momentum and energy. Streamlines and isotherms are produced, heat and mass transfer is calculated. A parametric study is carried out using following parameters: Rayleigh number from 10⁴ to 10⁹, dimensionless thin fin length from 0.10 to 0.90, dimensionless thin fin position from 0 to 0.90, dimensionless conductivity ratio of thin fin from 0 (perfectly insulating) to 60. It is found that Nusselt number is an increasing function of Rayleigh number, and a decreasing function of fin length and relative conductivity ratio. There is always an optimum fin position, which is often at the center or near center of the cavity, which makes heat transfer by natural convection minimized. The heat transfer may be suppressed up to 38% by choosing appropriate thermal and geometrical fin parameters.     

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.     

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.     

On the aspect ratio for which the heat transfer in differentially heated cavities is maximum

A numerical study of two dimensional natural convection of air in rectangular, differentially heated cavities was conducted. For three Rayleigh numbers the aspect ratio S was varied. It was found that heat transfer between the active walls has a maximum at each Rayleigh number, which is located at values of S between 1 and 2. The aspect ratio for which the maximum heat transfer occurs is determined by the process of transition from a shallow cavity regime to a slender cavity regime.     

Non-Darcian effects on natural convection heat transfer in a wavy porous enclosure

A numerical investigation is carried out to analyze natural convection heat transfer inside a cavity with a sinusoidal vertical wavy wall and filled with a porous medium. The vertical walls are isothermal while the top and bottom horizontal straight walls are kept adiabatic. The transport equations are solved using the finite element formulation based on the Galerkin method of weighted residuals. The validity of the numerical code used is ascertained by comparing our results with previously published results. The importance of non-Darcian effects on convection in a wavy porous cavity is analyzed in this work. Different flow models for porous media such, as Brinkman-extended Darcy, Forchheimer-extended Darcy, and the generalized flow models, are considered. Results are presented in terms of streamlines, isotherms, and local heat transfer. The implications of Rayleigh number, number of wavy surface undulation and amplitude of the wavy surface on the flow structure and heat transfer characteristics are investigated in detail while the Prandtl number is considered equal to unity.     

Numerical study of natural convection in a vertical porous annulus with discrete heating

In this paper natural convection flows in a vertical annulus filled with a fluid-saturated porous medium has been investigated when the inner wall is subject to discrete heating. The outer wall is maintained isothermally at a lower temperature, while the top and bottom walls, and the unheated portions of the inner wall are kept adiabatic. Through the Brinkman-extended Darcy equation, the relative importance of discrete heating on natural convection in the porous annulus is examined. An implicit finite difference method has been used to solve the governing equations of the flow system. The analysis is carried out for a wide range of modified Rayleigh and Darcy numbers for different heat source lengths and locations. It is observed that placing of the heater in lower half of the inner wall rather than placing the heater near the top and bottom portions of the inner wall produces maximum heat transfer. The numerical results reveal that an increase in the radius ratio, modified Rayleigh number and Darcy number increases the heat transfer, while the heat transfer decreases with an increase in the length of the heater. The maximum temperature at the heater surface increases with an increase in the heater length, while it decreases when the modified Rayleigh number and Darcy number increases. Further, we find that the size and location of the heater effects the flow intensity and heat transfer rate in the annular cavity.     

Nanofluid multi-phase convective heat transfer in closed domain: Simulation with lattice Boltzmann method

The lattice Boltzmann method is applied to simulate the thermal field and flow field of nanofluid natural convection in a square cavity. The heat transfer characteristics of nanofluid are compared with that of water to explore nanofluid heat transfer mechanism. The flow field shows different characters at different Rayleigh number and the average Nusselt number is obtained changing with Rayleigh number.     

Modeling of conjugated heat transfer in a thick walled enclosure filled with nanofluid

The objective of this paper is to investigate the conjugated heat transfer in a thick walled cavity filled with copper-water nanofluid. The analysis uses a two-dimensional rectangular enclosure under conjugated convective-conductive heat transfer conditions and considers a range of Rayleigh numbers. The enclosure was subjected to a constant and uniform heat flux at the left thick wall generating a natural convection flow. The thicknesses of the other boundaries are assumed to be zero. The right wall is kept at a low constant temperature while the horizontal walls are assumed to be adiabatic. A moveable divider is located at the bottom wall of the cavity. The governing equations are derived based on the conceptual model in the Cartesian coordinate system. The study has been carried out for the Rayleigh number in the range of 10⁵ ≤ Ra ≤ 10⁸, and for the solid volume fraction at 0 ≤ ? ≤ 0.05. Results are presented in the form of streamlines, isotherms, average Nusselt number and input heat absorption by the nanofluid. The effects of solid volume fraction of nanofluids, the location of the divider and also the value of the ambient convective heat transfer coefficient on the hydrodynamic and thermal characteristics of flow have been analyzed. An increase in the average Nusselt number was found with the solid concentration for the whole range of Rayleigh number. In addition, results show that the position of the divider and the ambient convective heat transfer coefficient have a considerable effect on the heat transfer enhancement.     

Numerical modelling and optimisation of natural convection heat loss suppression in a solar cavity receiver with plate fins

This study details the numerical modelling and optimization of natural convection heat suppression in a solar cavity receiver with plate fins. The use of plate fins attached to the inner aperture surface is presented as a possible low cost means of suppressing natural convection heat loss in a cavity receiver. In the first part of the study a three-dimensional numerical model that captures the heat transfer and flow processes in the cavity receiver is analyzed, and the possibilities of optimization were then established. The model is laminar in the range of Rayleigh number, inclination angle, plate height and thickness considered. In the second part of the study, the geometric parameters considered were optimized using optimization programme with search algorithm. The results indicate that significant reduction on the natural convection heat loss can be achieved from cavity receivers by using plate fins, and an optimal plate fins configuration exit for minimal natural convection heat loss for a given range of Rayleigh number. Reduction of up to a maximum of 20% at 0° receiver inclination was observed. The results obtained provide a novel approach for improving design of cavity receiver for optimal performance.     

Natural convection heat transfer in partially open inclined square cavities

A numerical study has been carried out on inclined partially open square cavities, which are formed by adiabatic walls and a partial opening. The surface of the wall inside the cavity facing the partial opening is isothermal. Steady-state heat transfer by laminar natural convection in a two dimensional partially open cavity is studied by numerically solving equations of mass, momentum and energy. Streamlines and isotherms are produced, heat and mass transfer is calculated. A parametric study is carried out using following parameters: Rayleigh number from 10³ to 10⁶, dimensionless aperture size from 0.25 to 0.75, aperture position at high, center and low, and inclination of the opening from 0° (facing upward) to 120° (facing 30° downward). It is found that the volume flow rate and Nusselt number are an increasing function of Rayleigh number, aperture size and generally aperture position. Other parameters being constant, Nusselt number is a non-linear function of the inclination angle. Depending on the application, heat transfer can be maximized or minimized by selecting appropriate parameters, namely aperture size, aperture position and inclination angle at a given operation Rayleigh number.     

Combined Effects of Slip Motion and Boundary Conditions on Enhanced Heat Transfer in Natural Convection Flows of Enclosed Nanofluids

The experimental studies dealing with natural convection of nanofluids in differentially heated enclosures demonstrate that the addition of nanoparticles to a pure base liquid is substantially detrimental, which can be ascribed to the formation of two stagnant fluid layers near the top and bottom adiabatic walls. Thus, if the horizontal walls are differentially heated instead of being perfectly insulated, the consequent development of a pair of concentration boundary layers near them may possibly imply a heat transfer enhancement. In this connection, a two-phase mixture model is employed to perform a numerical study of laminar natural convection in a square cavity containing water suspensions of alumina nanoparticles with a diameter of 33 nm and an average volume fraction in the range 0.001–0.04, assuming that Brownian diffusion and thermophoresis are the primary slip mechanisms between solid and liquid phases. The cavity is differentially heated at sides, whereas the horizontal walls are assumed to be either adiabatic or one heated and the other cooled, with a Rayleigh number in the range 4 × 10⁵–3 × 10⁶. It is found that the heating-from-below configuration is featured by periodic heat transfer, with a rate remarkably higher than that typical of the pure base liquid.     

Laminar natural convection in an inclined cavity with a wavy wall

In the present work, a numerical study of the effect of a hot wavy wall of a laminar natural convection in an inclined square cavity, differentially heated, was carried out. This problem is solved by using the partial differential equations, which are the vorticity transport, heat transfer and stream function in curvilinear co-ordinates. The tests were performed for different inclination angles, amplitudes and Rayleigh numbers while the Prandtl number was kept constant. Two geometrical configurations were used namely one and three undulations.The results obtained show that the hot wall undulation affects the flow and the heat transfer rate in the cavity. The mean Nusselt number decreases comparing with the square cavity. The trend of the local heat transfer is wavy. The frequency of the latter is different from the undulated wall frequency.     

Entropy generation for natural convection by heated partitions in a cavity

Entropy generation for natural convection in a partitioned cavity, with adiabatic horizontal and isothermally cooled vertical walls, is studied numerically by both a FORTRAN code and the commercially available CFD-ACE software. Effects of the Rayleigh number, the position of the heated partition, and the dimensionless temperature difference on the local and average entropy generation rate are investigated. Proper scale analysis of the problem showed that, while fluid friction term has nearly no contribution to entropy production, the heat transfer irreversibility increases monotonically with the Nusselt number and the dimensionless temperature difference.     

Natural convection in enclosures with floor cooling subjected to a heated vertical wall

Natural convection in enclosures is extensively investigated due to its importance in many applications, such as heat transfer through double glazing windows, electronic cooling devices, geophysical applications, etc. Two configurations that have been extensively explored in the literature are the differentially heated enclosures and the Rayleigh–Benard problems. In the present work, a different kind of problem is investigated, namely the cross thermal boundary conditions. Three dimensional analyses were performed for an enclosure cooled from below with one vertical wall heated, and the other connecting walls were assumed to be adiabatic. The thermal condition at the ceiling is varied from an adiabatic one to a different degree of heating. The objective of this study is to simulate the comfort provided by floor cooling in a room. For comfort requirements, the interest is on determining the rate of heat transfer and the temperature distribution in the room. Also, the results have importance for other cooling applications such as electronic cooling and natural convection in freezers. Furthermore, the problem is academically interesting for understanding the fundamentals of natural convection. Based on the authors’ knowledge, the physics of this problem has not been explored by other people in such a detail. However, the application has been in practice from ancient times.The predicted results are interesting and have practical applications. For a certain configuration, where strong three dimensional recirculations were predicted, the flow is three dimensional, hence the two dimensional assumption is not valid. Also, it is found that the rate of rate transfer from the floor is a weak function of the investigated parameters, such as Rayleigh number.