Conjugate natural convection in a square cavity with finite thickness horizontal walls

The effect of conduction of horizontal walls on natural convection heat transfer in a square cavity is numerically investigated. The vertical walls of the cavity are at different constant temperatures while the outer surfaces of horizontal walls are insulated. A code based on vorticity–stream function is written to solve the governing equations simultaneously over the entire computational domain. The dimensionless wall thickness of cavity is taken as 0.1. The steady state results are obtained for wide ranges of Rayleigh number (10³ < Ra < 10⁶) and thermal conductivity ratio (0 < K < 50). The variation of heat transfer rate through the cavity and horizontal walls with Rayleigh number and conductivity ratio is analyzed. It is found that although the horizontal walls do not directly reduce temperature difference between the vertical walls of cavity, they decrease heat transfer rate across the cavity particularly for high values of Rayleigh number and thermal conductivity ratio. Heatline visualization technique is a useful application for conjugate heat transfer problems as shown in this study.     

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

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

Experimental benchmark data for turbulent natural convection in an air filled square cavity

An experimental study of low-level turbulence natural convection in an air filled vertical square cavity was conducted. The cavity was 0.75 m high × 0.75 m wide × 1.5 m deep giving 2D flow. The hot and cold walls of the cavity were isothermal at 50 and 10 °C respectively giving a Rayleigh number of 1.58 × 10⁹. The local velocity and temperature were simultaneously measured at different locations in the cavity and both mean and fluctuation quantities are presented, i.e. ū, u^′_rms, v?, v^′_rms, , T^′_rms, , and . The local and average Nusselt numbers, the wall shear stress as well as the turbulent kinetic energy and the dissipation rate of the temperature variance are also presented. The experiments were conducted with very high accuracy and as such the results can form experimental benchmark data and will be useful for validation of computational fluid dynamics codes.     

Effect of aspect ratio on entropy generation in a rectangular cavity with differentially heated vertical walls

In the present study, entropy generation in rectangular cavities with the same area but different aspect ratios is numerically investigated. The vertical walls of the cavities are at different constant temperatures while the horizontal walls are adiabatic. Heat transfer between vertical walls occurs by laminar natural convection. Based on the obtained dimensionless velocity and temperature values, the distributions of local entropy generation due to heat transfer and fluid friction, the local Bejan number and local entropy generation number are determined and related maps are plotted. The variation of the total entropy generation and average Bejan number for the whole cavity volume at different aspect ratios for different values of the Rayleigh number and irreversibility distribution ratio are also evaluated. It is found that for a cavity with high value of Rayleigh number (i.e., Ra = 10⁵), the total entropy generation due to fluid friction and total entropy generation number increase with increasing aspect ratio, attain a maximum and then decrease. The present results are compared with reported solutions and excellent agreement is observed. The study is performed for 10² < Ra < 10⁵, 10^− 4 < ? < 10^− 2, and Pr = 0.7.     

Natural convection in right-angle porous trapezoidal enclosure partially cooled from inclined wall

A numerical study is conducted to investigate the steady free convection flow in a two-dimensional right-angle trapezoidal enclosure filled with a fluid-saturated porous medium. The left vertical wall of the cavity is heated; the inclined wall is partially cooled; and the remaining walls are insulated (adiabatic). Three different cases are considered. While in Case I the cooler wall is located adjacent to the top wall, in Case II it is located in the middle inclined wall. In Case III, it is located adjacent to the bottom wall. Flow and heat transfer characteristics are studied for a range of parameters: the Rayleigh number, Ra, 100 ≤ Ra ≤ 1000; and the aspect ration, AR = 0.25, 0.50 and 0.75. Numerical results indicate that there exist significant changes in the flow and temperature fields as compared with those of a differentially heated square porous cavity. These results lead, in particular, to the prediction of a position of minimum heat transfer across the cavity, which is of interest in the thermal insulation of buildings and other areas of technology.     

Magnetohydrodynamic natural convection in trapezoidal cavities

A computational numerical work has been done to see the effects of magnetic field on natural convection for a trapezoidal enclosure. Both inclined walls and bottom wall have constant temperature where the bottom wall temperature is higher than the inclined walls. Top wall of the cavity is adiabatic. To investigate the effects, finite element method is used to solve the governing equations for different parameters such as Rayleigh number, Hartmann number and inclination angle of inclined wall of the enclosure. It is found that heat transfer decreased by 20.70% and 16.15% as φ increases from 0 to 60 at Ra = 10⁵ and 10⁶ respectively. On the other hand, heat transfer decreased by 20.28% and 13.42% as Ha increases from 0 to 50 for Ra = 10⁵ and 10⁶ respectively.     

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.     

Experimental and numerical studies on periodic convection flow and heat transfer in a lid-driven arc-shape cavity

This paper presents experimental and numerical studies on periodic convection flow and heat transfer in a lid-driven arc-shape cavity with temperature differential. Three cases were considered: Gr = 2 × 10⁵, 5 × 10⁵ and 1.2 × 10⁶ at Re = 100 (Gr = Grashof number; Re = Reynolds number). The mathematical model was proposed in our previous study. The current study performs an experiment to validate this model, to corroborate the existence of the periodic flow, and to more deeply probe the internal flow and temperature characteristics. The experimental setup primarily comprised an arc-shape cavity, a moving lid, a thermo-system, a smoke generator and an image acquisition system. The periodic convection flow in the cavity was visualized using kerosene smoke. The numerical and experimental results consistently reveal that the periodic flow pattern was observed in the case with Gr = 5 × 10⁵, whereas the steady-state flow pattern took place in the other two cases (Gr = 2 × 10⁵ and Gr = 1.2 × 10⁶). The numerical simulation produced reasonable and satisfactory agreement with the experiment for the periodic flow pattern and period. The difference between the predicted and measured periods is less than 5%. The transport properties, such as average kinetic energy, overall Nusselt number, stream function, phase space trajectory, local kinetic energy, velocity history and temperature distribution, were further analyzed and discussed in this paper. The proposed numerical simulation not only confirms the experimental observation, but also enhances the understanding of periodic convection in an arc-shape cavity subjected to a moving lid and temperature differential.     

Experimental analysis of solar thermal storage in a water tank with open side inlets

This paper investigates thermal mixing caused by the inflow from one or two round, horizontal, buoyant jets in a water storage tank, which is part of a thermal solar installation. A set of experiments was carried out in a rectangular tank with a capacity of 0.3 m³, with one or two constant temperature inflows. As a result, two correlations based on temperature measurements have been developed. One of the correlations predicts the size of a zone of homogenous temperature, referred to herein as the mixing zone, which develops when a single hot inflow impinges on the opposite wall of the tank. The other identifies the degree of mixing resulting from the interaction between a hot inflow and a cold inflow located below the hot one. The correlations are combined with energy balances to predict the amount of hot water available in a tank with open side inlets and the corresponding temperatures of the outflows. Outdoor measurements were also performed in a solar installation, in which a commercial water storage tank with a 1.5 m³ capacity, heated by a solar collector array with a useful surface area of 42.2 m², drives a LiBr-H₂O absorption chiller. Comparison of the predicted and measured outflow temperatures under a variety of weather conditions shows a maximum difference of 3 °C.     

Experimental study of natural convection heat transfer of air in a cube below atmospheric pressure

Experimental study was carried out on the temperature profile of natural convection of air in a 50 mm cube with the temperature difference of 30 K between two opposing vertical walls. The objective is to investigate the essential aspect of heat transfer in the wide range of Rayleigh number (Ra) by lowering the pressure. The pressure was varied from 5.40 kPa (40.5 mmHg) to 99.99 kPa (750.0 mmHg). These correspond to Ra=1.04×10³ to 3.56 × 10⁵. The results show that the temperature distribution and Nusselt number approach those of conduction state as the pressure decreases.     

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.     

Natural convective characteristics of a heat source module at different angles in the closed and ventilated cabinets

A numerical analysis is performed to study the characteristics of heat transfer from a block heat source module at different angles in two-dimensional cabinets. Great efforts are carried out to conduct the effects of thermal interaction between the air steams inside and outside the cabinet on the conjugate conduction–natural convection phenomena. Moreover, the enhancement of cooling performance of the heat source module through the construction of air vents on cabinet wall is rigorously examined. The computation domain covers the cabinet and the surrounding area, and the temperature and velocity fields of the cabinet and surrounding area are solved simultaneously. Comparing the results for cases with and without the consideration of thermal interaction between the air streams, the difference in hot spot temperature of module can be up to 26% for Pr = 0.7, K_bf = K_wf = 100, 0 ≦ K_pf ≦ 100, 10⁵ ≦ Ra ≦ 10⁷ and φ = 0°, 90°, 270°. The maximum reduction in hot spot temperature is about 41% when two air vents are constructed on the cabinet wall. The variation of module angle results in the maximum difference of the hot spot temperature is 17% for closed cabinet, and 10% for ventilated cabinet. In addition, the hot spot temperatures for cases with K_pf = 10 are about two times of that for K_pf = 100.     

Investigation of buoyancy-driven flow and heat transfer in a trapezoidal cavity filled with water–Cu nanofluid

A numerical study is conducted to investigate the transport mechanism of free convection in a trapezoidal enclosure filled with water–Cu nanofluid. The horizontal walls of the enclosure are insulated while the inclined walls are kept at constant but different temperatures. The numerical approach is based on the finite element technique with Galerkin's weighted residual simulation. Solutions are obtained for a wide range of the aspect ratio (AR) and Prandtl number (Pr) with Rayleigh number (Ra = 10⁵) and solid volume fraction (? = 0.05). The streamlines, isotherm plots and the variation of the average Nusselt number at the left hot wall are presented and discussed. It is found that both AR and Pr affect the fluid flow and heat transfer in the enclosure. A correlation is also developed graphically for the average Nusselt number as a function of the Prandtl number as well as the cavity aspect ratio.     

Control of mixed convection in lid-driven enclosures using conductive triangular fins

Control of mixed convection (combined forced and natural convection) in a lid-driven square cavity is performed using a short triangular conductive fin. A numerical technique is used to simulate the flow and temperature fields. The vertical walls of the cavity are differentially heated. Both the top lid and the bottom wall are adiabatic. The fin is located on one of the motionless walls of the cavity. Three different cases have been studied based on the location of the fin. In this context, Cases I, II and III refer to the fin on the left, bottom and right walls, respectively. Results are presented for +x and −x directions of the top lid in horizontal axis and different Richardson numbers as Ri = 0.1, 1.0 and 10.0. It is observed that the triangular fin is a good control parameter for heat transfer, temperature distribution and flow field.     

Computational analysis of mixed convection in a channel with a cavity heated from different sides

A computational work is performed in this paper to analyze the heat transfer, temperature distribution and flow field in a channel with a cavity heated from different sides. Flow inlets to the channel are uniform. Constant magnetic field is applied to the channel as Ha = 10, Prandtl number is chosen as Pr = 0.7 and Reynolds number is fixed at Re = 100. Finite element method is used to solve governing equations. Three different cases were considered based on heater position in the cavity at the left vertical side (Case 1), bottom side (Case 2) and right vertical side (Case 3). It is found that the highest heat transfer is obtained when the isothermal heater is located at the right vertical wall.     

Transient natural convection in parallelogrammic enclosures with isothermal hot wall. Experimental and numerical study applied to on-board electronics

This work treats 2D transient natural convection in closed cavities of parallelogrammic section. Such cavities are formed by two vertical, active walls maintained at different temperatures_, connected by a closing channel that can be inclined at an angle α with respect to the horizontal. The channel is adiabatic, the angle of tilt α being defined by the inclination of the upper and lower walls while the fitting lateral ones denote the parallelogram-shape section of the cavity. We present the temperature fields and the flow lines at some representative instants of the transient state for all angles treated. The temporal evolution of the maximum Nusselt number and maximum velocity near the hot wall are determined for all the angles and compared to those of the square cavity. The evolution of the local Nusselt number on the active hot wall is also presented for the transient and steady states, what constitutes the main original contribution of the present work. Numerical results are complemented by experimental thermal measurements at steady state. The small deviation found between measurements and calculations serve to validate the model used and to properly size real devices. This study is done for several Rayleigh numbers Ra whose high values, varying between 10⁵ and 10⁹, are representative of engineering assemblies, as it is the case of on-board electronics.     

Heat transfer in porous cavity under the influence of radiation and viscous dissipation

Heat transfer under the influence of radiation and viscous dissipation in a square cavity filled with saturated porous medium is analysed. The flow is assumed to follow Darcy law. The governing equations are non-dimensionalised and solved numerically using finite element method. Left vertical surface of the square cavity is maintained at isothermal temperature T_h and right vertical surface at T_c. Results are presented in terms of Nusselt number at hot and cold wall of the cavity for various values of viscous dissipation parameter and radiation parameter. It is seen that the average Nusselt number at hot as well as cold wall increases with increase in radiation parameter.     

Computation of combined natural-convection and radiation heat-transfer in a cavity having a square body at its center

This paper describes a numerical study of the radiation-natural convection interactions in a differentially-heated cavity with an inner body. A specifically developed numerical model, based on the finite-volume method, is used for the solutions of the governing differential-equations. The SIMPLER algorithm for the pressure–velocity coupling is adopted. The fluid (air) is perfectly transparent to the radiation. The surface emissivity ε, the Rayleigh number Ra, and the thermal conductivity ratio R_k were varied parametrically. For Pr = 0.71 and relatively wide ranges of the other parameters, results are reported in terms of isotherms, streamlines, average Nusselt-numbers across the enclosure, local Nusselt-numbers at the hot and cold walls, vertical and horizontal median velocities and horizontal walls, temperature distributions. It is found that: (i) the radiation exchange homogenizes the temperature inside the cavity and produces an increase in the average Nusselt-number, particularly when R_k and Ra are high and (ii) the average Nusselt-number increases with increasing surface emissivity, especially at high Rayleigh numbers.     

2D transient natural convection in diode cavities containing an electronic equipment with discrete active bands under constant heat flux

The thermal behavior of airborne electronic equipment submitted to natural convection in closed parallelogrammic air-filled cavities is examined in this study. The cold active wall of the enclosure is maintained isothermal. The hot wall, representing the electronic device, is composed of three parallel discrete bands generating a constant heat flux, separated by two adiabatic bands of equal dimensions. Both walls remain always vertical. The channel is considered adiabatic and the aspect ratio of the cavity is equal to unity. Many configurations are examined while varying the inclination angle of the top and bottom walls of the channel. When the angle is positive the convective heat transfer is favored in comparison with the case of the right cavity, but, on the contrary, it is reduced for negative angles. The resultant enclosures are so called diode cavities in the convective heat transfer sense of the word. The experimental part of the study is achieved with a setup based on electrical data and temperature measurements on the walls. The numerical approach using the finite volume method allows to complete the experimental results with the thermal and dynamical characteristics of the 2D flow. The temperature fields show the thermal behavior of the device during the transient phase after switching it on. The convective results concerning the imposed heat flux treated in this study differ from those corresponding to impose the temperature on the hot bands. The distribution and evolution of the Nusselt number allow to characterize the natural convection occurring in the cavity. The results of this work are consistent with previous studies and allow to predict the thermal behavior of the electronic equipment during the transient phase.     

Mixed convection heat transfer in a ventilated cavity with hot obstacle: Effect of nanofluid and outlet port location

In the present study, the lattice Boltzmann method is implemented to investigate the effect of suspension of nanoparticles on mixed convection in a square cavity with inlet and outlet ports and hot obstacle in the center of the cavity. The effect of outlet port location is examined on heat transfer rate then the effect of nanoparticles is inspected for volume fraction of nanoparticles in the range of 0 to 0.03 at the different position of outlet port. The study was carried out for different Richardson numbers ranging from 0.1 to 10. Grashof number is assumed to be constant (10⁴) so that the Richardson number changes with Reynolds number. The isothermal boundary condition is assumed for obstacle walls and the cavity walls are adiabatic. The result is presented by isotherms, streamlines, and local and average Nusselt numbers. The maximum heat transfer rate occurs when the outlet port is located at P2 for Ri = 0.1 and P1 for Ri = 1, Ri = 10, respectively. Results show that by adding the nanoparticles to base fluid and increasing the volume concentration of nanoparticles the heat transfer rate is enhanced at different Richardson numbers and outlet port positions. But this phenomenon is not observed at Ri = 10 when the outlet port is located at P1.