Transient thermal characteristics of airborne electronic equipment with discrete hot bands in square cavities

This study is concerned with the thermal regulation of electronic circuits confined in a closed cubical air-filled cavity. The hot active wall, which represents the electronic equipment, is composed of three parallel discrete heat source bands subjected to a constant heat flux, separated by two adiabatic bands. The second active wall is an isothermal cold plate and is facing the hot wall. The cavity channel is considered adiabatic. Transient heat exchanges through 2D natural convection are analysed for several configurations obtained through varying the inclination angle of the active wall with respect to gravity. The numerical approach conducted with the finite volumes method allowed the derivation of the thermal and dynamic characteristics of the cavity. The thermal evolution of the sources does not show any local temperature peaks that could exceed the maximum allowable temperature set by the electronic components manufacturers. This guarantees the normal operation of the equipment. The numerical analysis is complemented by experimental measurements that validate the used model and allow the correct sizing of the airborne electronic circuits.     

Natural convection in a partially porous cavity: Roads to chaos

Abstract

A numerical study of a periodic and chaotic behavior of natural convection in a square cavity, with a porous layer is presented. The cavity under study consists of two opposite vertical walls of which the lower half walls are hot (hold high temperature) and the upper half walls are cold (hold low temperature), whereas the horizontal walls are adiabatic. The porous medium is located in the lower part of the cavity. The natural heat transfer and the Darcy Brinkman equations are solved by using the finite volume method and the TDMA. The results show that thermal natural convection evolves towards a deterministic chaos by following Curry York scenario.     

Laminar mixed convection in shallow inclined driven cavities with hot moving lid on top and cooled from bottom

Laminar mixed convective heat transfer in two-dimensional shallow rectangular driven cavities of aspect ratio 10 is studied numerically. The top moving lid of the cavity is at a higher temperature than the bottom wall. Computations are performed for Rayleigh numbers ranging from 10⁵ to 10⁷ keeping the Reynolds number fixed at 408.21, thus encompassing the dominating forced convection, mixed convection, and dominating natural convection flow regimes. The fluid Prandtl number is taken as 6 representing water. The effects of inclination of the cavity on the flow and thermal fields are investigated for inclination angles ranging from 0° to 30°. Interesting behaviours of the flow and thermal fields with increasing inclination are observed. The streamline and isotherm plots and the variation of the local and average Nusselt numbers at the hot and cold walls are presented. The average Nusselt number is found to increase with cavity inclination. The rate of increase of the average Nusselt number with cavity inclination is mild for dominating forced convection case while it is much steeper in dominating natural convection case.     

Effect of surface radiation on buoyant convection in vertical triangular cavities with variable aperture angles

The present investigation deals with the numerical computation of laminar natural convection with and without surface-to-surface radiation in a class of right-angled triangular cavities filled with air. The vertical walls are uniformly heated and the inclined walls are uniformly cooled while the upper connecting walls are adiabatic. The aperture angle φ located at the lower vertex of the triangular cavities between the vertical and the inclined walls identifies the shape of each cavity. This kind of cavity finds application in the miniaturization of cabinets housing electronic components constrained by space and/or weight severely. With a view at enhancing the heat transfer rates and/or reducing the size of cabinets, the influence that surface radiation exerts upon natural convection should be scrutinized. To this end, the finite volume method is implemented to perform the computational analysis of the above-described problem(s). Numerical results are reported for the local quantities, the velocity and temperature fields encompassing aperture angles φ that extend from 15° to 45° at two extreme Rayleigh numbers, Ra = 10³ and 10⁶. Additionally, the two global quantities, the mean convective Nusselt number and the mean radiative Nusselt number are reported in tabulated and graphical forms for the same controlling parameters. Overall, it was found that the competition between surface radiation and natural convection in right-angled triangular cavities filled with air plays a preponderant role. Finally, the analysis culminates with the construction of a comprehensive correlation equation for the total Nusselt number in terms of the controlling parameters which should be useful for engineering analysis and design. This correlation equation will undoubtedly provide a fast evaluation avenue to judge the cavity thermal performance.     

Numerical investigation on using inclined partitions to reduce natural convection inside the cavities of hollow bricks

Hollow bricks are widely used to build facades because of their light weight and high thermal resistance. The air-filled voids within the brick configuration elevates the block’s resistance to heat penetration. Suppressing the natural convection inside the voids increases the blocks thermal resistance. This paper presents a new approach to suppress the convection currents inside brick’s cavities by inserting cell dividers. A numerical study on the effect of inserting a folded sheet inside the cavities of the hollow buildings brick is presented. The folded sheet divides the cavity into several triangles producing a string of small convection cells.The mass, momentum and energy equations are solved for a section of a masonry brick represented by a partitioned squared cavity. The inclined partitions are conductive and are in perfect contact with the walls of the cavity. The two outer vertical sides of the brick section are assumed to be isothermal and the two horizontal sides are insulated. Air, the fluid filling the voids, is modeled as a Newtonian fluid with density defined based on Boussinesq approximation.The heat flux transported across the partitioned voids depends on the number of partitions used and their thermal conductivity. The heat flux through the cavity decreases as the number of partitions increases. Moreover, the convection is nearly diminished when the number partitions becomes six. One day simulation for a typical summer conditions shows that inclined partitions can reduce the heat flux by 37–42% depending on the number of partitions and their material.     

Transient natural 2D convection in a cylindrical cavity with the upper face cooled by thermoelectric Peltier effect following an exponential law

The present study is based on a numerical calculation involving the finite volume method. The transient 2D natural convection in vertical cylindrical cavities is addressed.Two cases have been examined. First we study the case of an adiabatic air-filled cavity whose upper face is submitted to a cooling following an exponential law observed experimentally, imposed by a Peltier’s module. Furthermore, we study the convection in an insuline-filled cylindrical cavity whose partition has a very weak thermal resistance.Space–time evolutions of temperature and velocity are presented, with the influence of the main representative parameters of the investigation. Local and mean thermal exchanges have been calculated, and we propose a Nusselt–Rayleigh type relation.The aim of this study is to determine the heat transfer in a long autonomy isothermal cavity designed for the conservation of insulin cartridges or any other product.     

平流层电子设备温度数值模拟

分析了平流层电子设备内外部热环境,考虑平流层大气对流、设备内部自然对流、太阳直射辐射、大气辐射、地面反射太阳辐射、地球红外辐射以及设备自身辐射等因素的基础上,建立了计算电子设备温度分布特征的对流、辐射耦合模型,模拟了其在不同功率、不同对流换热、不同环境条件下的温度分布。结果表明:对于平流层电子设备散热,对流换热和辐射换热都会影响电子设备的温度分布,尽管由于平流层大气压力低、对流换热弱,但对流换热量占到散热总量的60%以上,是散热的主要方式。因此,在平流层电子设备热设计时,可以优先考虑采取开孔等强化对流散热方法来控制设备的温度。最后,开展了平流层模拟环境的实验验证,典型工况实验值与计算值吻合较好,验证了计算模型的正确性。对平流层电子设备热设计有重要的指导意义。     

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.     

Combined Effect of Mixed Convection and Surface Radiation Heat Transfer for Thermally Developing Flow in Vertical Channels

Combined effect of laminar flow mixed convection and surface radiation heat transfer for thermally developing airflow in a vertical channel heated from a side has been experimentally examined with different thermal and geometric parameters. The channel boundary is made of two isothermal walls and two adiabatic walls, the isothermal parallel wall is heated uniformly and the opposite cold wall temperature is maintained equal to the inlet conditions. The heated wall temperature ranged from 55 to 100°C, Reynolds number ranged from 800 to 2900 and the heat flux was varied from 250 to 870 W/m². To cover the wide range of Reynolds numbers, two aspect ratios of square and rectangular section were used. Surface radiation from the internal walls is considered through two emissivities i.e. 0.05 and 0.85, to represent weak and strong radiation effects, respectively. From the experiments, surface temperature and Nusselt number distributions of convection and radiation heat transfer are obtained for different heat flux values. Flow structure inside the channel is visualized to observe the flow pattern. The results show the combined effect of laminar flow mixed convection and surface radiation on the total heat transfer rate within the channel. The accumulating buoyancy force and airflow moves together vertically in the upward direction to give significant heat transfer enhancement in the vertical orientation of the channel.     

Correlations for natural convective heat exchange in CPC solar collector cavities determined from experimental measurements

A detailed experimental study was undertaken to analyse the natural convective heat transfer in CPC cavities, a complex function of collector orientation, geometrical aspect ratios and thermal boundary conditions at the enclosure walls. Results are reported for CPC solar collectors with full-, three quarter- and half-height reflectors, C_R = 2 and a 100 mm wide flat plate absorber. Experiments were conducted using a purpose built solar simulator under controlled lab environment employing realistic boundary and thermal conditions. The effects of simultaneous tilting of the solar collectors about both transverse and longitudinal axes, truncation of the reflector walls and inlet water (collector heat removal fluid) temperature on the natural convective heat flow characteristics inside the CPC cavity have been determined. It is concluded that the correlations developed for prediction of natural convection characteristics in rectangular, annuli and V-trough enclosures are not appropriate for application to CPC solar collectors with divergence ranging from 150% to 300%. Based on the experimental data a correlation is presented to predict the natural convection heat loss from the absorber plate of solar collectors for a range of water inlet temperatures.     

TRANSIENT NATURAL CONVECTION IN A CAVITY WITH WALLS OF FINITE THICKNESS

Numerical studies are made of transient natural convection in a square cavity. The top and bottom end walls are thermally insulated. The vertical solid side walls are of finite thickness and of finite thermal conductivity. Flow is driven, from the motionless isothermal initial state, by impulsively increasing (decreasing) the temperature at the outer surface of one (the other) vertical side wall. Numerical solutions art sought to the time-dependent Navier-Stokes equations for the fluid and the solid regions. The ratios of thermophysical properties between solid and fluid are the significant parameters. As the thermal capacity ratio increases, the development of flow in the fluid region is retarded. The conductive and convective timescales are estimated. The effects of the thermal conductivity ratio and of the thickness of the side wall are delineated. The effect of the system Rayleigh number on transient heat transport is analyzed. The applicability of the approximate one-dimensional thermal conductance model to the transient features is scrutinized.     

Models for transient conduction in a flat plate subjected to a variable heat flux

This work presents analytical models allowing to identify the transient temperature distribution in a flat plate. The plate is exposed to a convective heat transfer on a face and to a heat flux on the other one. The heating flux is Heaviside (crenel type) and is maintained during a t₁ time. The heating phase is followed by a relaxation one. The theoretical method is original because it uses Green’s functions method to determine the analytical solutions of the heat propagation equation in the plate during the heating and relaxation phases. These analytical solutions allow to identify the temperature distribution as well as wall heat flux versus time. The results of our work can be useful at different levels: during the identification of parameters (such as the thermal conductivity or the thermal diffusivity of a plate), during the identification of the boundary conditions (like the heating flux or the convection coefficient) in industrial processes using this kind of systems, or even with educational intents for teaching transient conduction.     

Analysis of heat losses from a trapezoidal cavity used for Linear Fresnel Reflector system

A Computational study to investigate the heat loss due to radiation and steady laminar natural convection flow in a trapezoidal cavity having eight absorber tubes for a Linear Fresnel Reflector (LFR) solar thermal system with uniformly heated tubes and adiabatic top wall and side walls has been performed. The losses due to convection and radiation were considered from the bottom glass cover. The results are validated with experimental data. Radiative component of losses from the cavity was found to be dominant which contributes around 80–90%. Heat loss characteristics have been studied for cavities of different depths. Simulations have been carried out for various values of heat transfer coefficient based on the wind speed below the glass surface. Effect of emissivities of the tubes on the heat loss has also been simulated. Flow pattern and isotherms inside the cavity for various depths have been analyzed. Finally, the correlation between the total average Nusselt number and its influencing parameters has been obtained for the proposed cavity.     

Numerical analysis of fluid flow due to mixed convection in a lid-driven cavity having a heated circular hollow cylinder

Mixed convection heat transfer in a lid-driven cavity along with a heated circular hollow cylinder positioned at the center of the cavity has been analyzed numerically. The present study simulates a realistic system such as air-cooled electronic equipment with a heat component or an oven with heater. A Galerkin weighted residual finite element method with a Newton–Raphson iterative algorithm is adopted to solve the governing equations. The computation is carried out for wide ranges of the Richardson numbers, cylinder diameter and solid fluid thermal conductivity ratio. Results are presented in the form of streamlines, isothermal lines, average Nusselt number at the heated surface and fluid temperature in the cavity for the mentioned parameters. It is found that the flow field and temperature distribution strongly depend on the cylinder diameter and also the solid–fluid thermal conductivity ratio at the three convective regimes.     

Natural convection on inclined QFN32 electronic package generating constant volumetric heat flux

Qualification and quantification of the natural convective phenomena are examined in the case of a Quad Flat Non-lead (QFN32). This active electronic package is inclined with respect to the horizontal plane by an angle varying between 0° and 90° corresponding to the horizontal and vertical position respectively. It generates during its operation a constant volumetric heat flux leading to Rayleigh numbers varying in the range 1.31x10⁷ ‐ 1.01x10⁸. The walls of the large air-filled cubic cavity containing this device are maintained isothermal. The temperature and velocity fields are presented for different combinations of the Rayleigh number and inclination angle. The convective heat transfer concerning the whole component exchange surface is determined for all the treated configurations. Correlations of Nusselt–Rayleigh type are proposed. They allow optimizing the thermal design of electronic assemblies used in various engineering domains.     

Solutal thermodiffusion in binary mixture in the presence of g-jitter

The phenomenon of mass flux in a mixture due to a temperature gradient is known as the Soret effect or thermal diffusion. This effect is usually small but can be quite important in the analysis of compositional variation in hydrocarbon reservoirs. Diffusion-dominated experiments on-board the International Space Station will be greatly affected by convective flow due to the residual acceleration field and/or to oscillatory g-jitters caused by several sources. In this paper we are interested in investigating the flow due to thermal diffusion for different oscillatory g-jitters. The model considered is a rectangular rigid cavity filled with a binary mixture of methane and normal butane, subject to a temperature difference on its end walls and radiation heat transfer on the lateral ones. The non-linear differential equations for the mass-thermo-vibrational problem are derived in the case of a unique mode oscillatory acceleration. The full transient Navier–Stokes equations coupled with the mass and heat transfer formulations and the equation of state of the fluid are solved numerically using the finite element technique. Results revealed that the thermal diffusion is important and drives a strong convection. Convection is enhanced and therefore temperature and species profiles distortion from purely diffusive condition increases when a parallel g-jitter is added to the residual gravity, in a destabilizing configuration. The numerical study shows that both residual gravity and g-jitter may be detrimental but also beneficial to achieve purely diffusive conditions, according to the orientation of the vibration direction and the residual gravity vector, relative to the direction of the main density gradient. For the different configurations investigated, the g-jitter is found to reduce compositional variation. When the stable regime is attained, thermal and compositional quantities fluctuate following a mode whose frequency is equal to that of the initially imposed vibration. Even if the temperature fluctuation at a given point remains small, the compositional variation due to residual g-jitter convection is not negligible.     

Numerical study of the natural convection of nanofluids based on mineral oil with properties evaluated experimentally

This paper deals with the numerical simulation of natural convection inside a closed cavity of multi-walled carbon nanotubes and diamond nanoparticles dispersed in pure mineral oil. The data of the thermal conductivity and viscosity of the nanofluids were obtained experimentally, while specific heat and density were evaluated by the first law of thermodynamic and mass conservation principle, respectively. The physical model considered is a 2D cavity with adiabatic horizontal walls, where the left vertical wall with high temperature and the right vertical wall with low temperature and all walls with no-slip boundary conditions. The simulations were performed in a numerical code based on the Finite Volume Method-FVM, where second order temporal and spatial schemes were used. The results showed that only the Nusselt number for MWCNT based nanofluids increased in comparison to the mineral oil for the same Grashof number. However, the comparison between the convective coefficient for nanofluids and mineral oil showed that nanofluids presented better convection characteristics, for the same Grashof number. Furthermore, the diamond nanofluid with higher volumetric concentration presented the maximum increase of the convection coefficient, about 23%, though this nanofluid did not presentthe higher Nusselt number in comparison to the other nanofluids analyzed.     

Conjugate heat transfer in an enclosure under the condition of internal mass transfer and in the presence of the local heat source

Conjugate convective–conductive heat transfer in a rectangular enclosure under the condition of mass transfer within cavity with local heat and contaminant sources is numerically investigated. Mathematical model, describing a two-dimensional and laminar natural convection in a cavity with heat-conducting walls, is formulated in terms of the dimensionless stream function, vorticity, temperature and solute concentration. The main attention is paid to the effects of Grashof number (Gr), Buoyancy ratio (Br) and transient factor on flow modes, heat and mass transfer.     

Non-gray radiative convective conductive modeling of a double glass window with a cavity filled with a mixture of absorbing gases

Coupled radiation and natural convection heat transfer occurs in vertical enclosures with walls at different temperatures filled with gas media. In glass window thermal insulation applications in hot climates, infrared absorbing gases appear as an alternative to improve their thermal performance. The thermal modeling of glass windows filled with non-gray absorbing gases is somewhat difficult due to the spectral variation of the absorption coefficients of the gases and the phenomena of natural convection. In this work, the cumulative wavenumber (CW) model is used to treat the spectral properties of mixtures of absorbing gases and the radiative transport equation is solved using CW model and the discrete ordinates method. Due to the range of temperature variation, the mixture of gases is considered as homogeneous. The absorption coefficients were obtained from the database HITRAN. First, the natural convection in a cavity with high aspect ratio is modeled using a CFD code and the local and global Nusselt numbers are computed and compared with available empirical correlations. Also, the flow pattern for different Rayleigh numbers is analyzed. Then, the heat transfer in the gas domain is approximated by a radiative conductive model with specified heat flux at boundaries which is equivalent to convective transport at the walls surroundings. The energy equation in its two-dimensional form is solved by the finite volume technique. Three types of gas mixtures, highly absorbing, medium and transparent are investigated, to determinate their effectiveness in reducing heat gain by the gas ambient. Reflective glasses are also considered. The numerical method to solve radiative heat transport equation in gray and non-gray participant media was validated previously. The temperatures distributions in the gas and the glass domain are computed and the thermal performance of the gas mixtures is evaluated and discussed. Also, comparison with pure radiative conductive model is shown.     

Integral transform solution for natural convection in three-dimensional porous cavities: Aspect ratio effects

Three-dimensional natural convection in box-like cavities filled with a porous material is revisited, by considering a transient formulation for the energy balance and a quasi-steady formulation for the flow problem. The Generalized Integral Transform Technique (GITT) is employed in the hybrid numerical-analytical solution of the Darcy law based model for vertical cavities (insulated vertical walls with differentially prescribed horizontal wall temperatures), employing the vorticity-vector potential formulation. Comparisons with previously reported numerical solutions are performed and the transition between conductive and convective states is illustrated, centering on the aspect ratio influence on the flow and heat transfer phenomena. A set of reference results for the steady-state behavior under different aspect ratio is provided for covalidation purposes.