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.     

Experimental investigation of buoyant flows in inclined differentially heated cavities

This experimental investigation focuses on the effects of angle of inclination on buoyancy-driven flows inside tall, rectangular, differentially-heated cavities. It considers a rectangular cavity with an aspect ratio of 28.6, with its two long sides maintained at different temperatures and the two short, end-walls, thermally insulated. The spanwise aspect ratio is 6.82 and the side walls are also thermally insulated. The Rayleigh number, based on the temperature difference and spacing between the long sides, is 0.86 × 10⁶ for most cases and the working fluid is air (Prandtl number 0.71). Experimental data, for the flow and the thermal fields, using laser Doppler anemomentry and thermocouple traverses respectively, are presented for the cavity inclined at 60° and 15° to the horizontal, for both stable (the hot surface being the upper surface) and unstable orientations. The 15° stable case is investigated at a higher Rayleigh number of 1.54 × 10⁶ and some additional data for the 15° unstable case are also presented at this higher value of Rayleigh number. For moderate angles of inclination, the flow is two-dimensional and the effects of inclination are primarily confined to the fluctuating fields. For large angles of inclination, the flow becomes three-dimensional. In the unstable 15° angle of inclination case a set of four longitudinal vortices are formed over the entire length of the cavity, with four counter-rotating re-circulation cells within the cross-section parallel to the thermally active walls. The stable 15° angle of inclination leads to the formation of two longitudinal vortices and two re-circulation cells. At the 15° angle (stable and unstable), the enhanced mixing leads to uniform temperature in the cavity core and thus to only minor deviations from two-dimensionality in the thermal field. A modest rise in Rayleigh number, in the 15° unstable case, does not affect the mean motion, but causes an increase in the normalised turbulence intensities.     

Empirical Nu–Ra–Fo relationships for natural convection in air-filled hemispherical enclosures. Isothermal and inclined disk with dome oriented downwards

Correlations of Nusselt–Rayleigh–Fourier type proposed in this work allow quantifying of the transient convective heat transfer occurring in air-filled hemispherical cavities. The disk, initially at ambient temperature, is suddenly heated and kept isothermal. Throughout the heating process, the dome is maintained at ambient temperature. The radius of the cavity, associated with the temperature difference imposed between the disk and the dome, involves a large Rayleigh number range, varying between 10⁴ and 5 × 10⁸. The disk can be inclined with respect to the horizontal plane at an angle varying between 90° (vertical disk) and 180° (horizontal disk with dome downwards) by steps of 10°. The numerical approach is based on the finite volume method. The proposed empirical relationships in transient regime are linked to the steady state Nusselt–Rayleigh ones. They are obtained via the analysis of results corresponding to many combinations of the Rayleigh number and the disk inclination angle. The relationships are new since the considered geometry associated with the inclinations of the isothermal disk has not been treated previously. They constitute an important tool for the thermal design of engineering systems involved as they allow determining the convective heat transfer during the transient regime. They can be applied in several fields such as nuclear technology, solar energy, security and safety electronics, building, domotics or aeronautics.     

Free convection in ZnO-Water nanofluid-filled and tilted hemispherical enclosures containing a cubic electronic device

The present work deals with free convection within nanofluid-filled hemispherical enclosure whose base (disc) can be inclined with respect to the horizontal plane by an angle ranging from 0° to 180° (horizontal disc with dome facing upwards and downwards respectively). A cubic active electronic component positioned at the center of the disc generates important heat fluxes leading to high Rayleigh number values ranging from 5.21 × 10⁷ to 7.29 × 10¹⁰. The used nanofluid is a mixture Water-ZnO with a volume fraction varying between 0 (pure water) and 10%. The 3D numerical approach is done by means of the volume control method based on the SIMPLE algorithm, and using a one-phase model. The dynamic and thermal fields are presented for several geometric and thermal configurations. The natural convective heat transfer is quantified by means of the average Nusselt Number whose evolution versus the inclination angle, the Rayleigh Number and the volume fraction is presented and commented on for all considered cases. Correlations of the Nusselt-Rayleigh-Prandtl-inclination angle type are proposed to determine the natural convective heat transfer in this assembly corresponding to applications in electronics.     

Computational analysis of natural convection in a parallelogrammic cavity with a hot concentric circular cylinder moving at different vertical locations

A finite volume numerical simulation of natural convection in a parallelogrammic air-filled cavity having a heated concentric circular cylinder is performed. The left and right sidewalls of the cavity are maintained at a uniform cold temperature, while both upper and lower walls of it are considered thermally insulated. A wide range of significant parameters such as Rayleigh number, inclination angle and cylinder vertical locations are considered in the present study. Comparison with previously published works is made and found to be an excellent agreement. The results show that the strength of the flow circulation and the thickness of thermal boundary layer around the hot circular cylinder are increased dramatically when the Rayleigh number increases. Also, to increase the flow circulation inside the parallelogrammic cavity, it is recommended to make the inner cylinder moves downward until it reaches to [δ = − 0.2] and the parallelogrammic cavity sidewalls inclined to [Φ = 15°]. Moreover, it is found that for various values of the inclination angle, the average Nusselt numbers at inner cylinder surface and at both cavity sidewalls, decrease when the cylinder moves upward, while they increase when the cylinder moves downward.     

On thermal control of devices contained in inclined hemispherical cavities with dome oriented downwards and subjected to transient natural convection

In this study, relationships of Nusselt–Rayleigh–Fourier type are proposed for the case of air-filled hemispherical cavity whose dome is oriented downwards and maintained isothermal. Its disk is subjected to a constant heat flux and inclined at an angle varying between 90° (vertical position) and 180° (disk horizontal with dome oriented downwards). The numerical approach is performed in transient regime by means of the finite volume method for Rayleigh numbers in the range of 10⁴ − 5 × 10⁸. These results are confirmed at steady state by measurements done for some configurations in a previous study for the same Rayleigh and inclination ranges. Otherwise, they complete other surveys considering inclination angles varying between 0° (horizontal cavity with dome oriented upwards) and 90° (vertical cavity) for a wider range of Rayleigh numbers. The correlations allow thermal control of devices submitted to natural convection in hemispherical cavities during the time preceding the steady state after their switch on.     

Convective instability of a vertical thermal boundary layer in a differentially heated cavity

The convective instability of a vertical thermal boundary layer adjacent to the sidewall of a water-filled differentially heated cavity over a range of Rayleigh numbers (5 × 10⁷–3.44 × 10⁹) is investigated using direct stability analysis. The results show that the dominant frequency of the convective instability changes as perturbations travel downstream due to the presence of the horizontal boundaries, which is different from that of the vertical thermal boundary layer adjacent to an infinite or semi-infinite thermal wall. The features of the convective instability of the vertical thermal boundary layer adjacent to the sidewall are described, and the dependence of the dominant frequency on the Rayleigh number is obtained. Furthermore, the dependence of the flow rate and heat transfer through the cavity on the Rayleigh number is quantified by numerical results.     

Heat transfer by free convection from the inside surface of the vertical and inclined elliptic tube

Free convection from the inside surface of vertical and inclined elliptic tubes of axis ratio (a:b) 2:1 with a uniformly heated surface (constant heat flux) is investigated experimentally. The effects of orientation angle (α) and inclination angle (ϕ) on the heat transfer coefficient were studied. The orientation angle (α) is varied from 0° (when the major axis is horizontal) to 90° (when the major axis is vertical) with steps of 15°. The inclination angle (ϕ) is measured from the horizontal and varied from 15° to 75° with steps of 15°. The vertical position is considered as a special case of the inclined case when ϕ = 90. The experiments covered a range of Rayleigh number, Ra from 2.6 × 10⁶ to 3.6 × 10⁷. The local and average Nusselt numbers are estimated for different orientation angles and inclination angles at different Rayleigh numbers. The results obtained showed that the local Nu increased with the increase of axial distance from the lower end of the elliptic tube until a maximum value near the upper end, and then, it gradually decreased. The average Nu increases with the increase of α or ϕ at the same Ra. The results obtained are correlated by dimensionless groups and with the available data of the inclined and vertical elliptic tubes.     

Natural convective flow in an inclined lid-driven enclosure with a heated thin plate in the middle

Natural convection heat transfer from a heated thin plate located in the middle of a lid-driven inclined square enclosure has been analyzed numerically. Left and right of the cavity are adiabatic, the two horizontal walls have constant temperature lower than the plate’s temperature. The study is formulated in terms of the vorticity-stream function procedure and numerical solution was performed using a fully higher-order compact (FHOC) finite difference scheme on the 9-point 2D stencil. Air was chosen as a working fluid (Pr = 0.71). Two cases are considered depending on the position of heated thin plate (Case I, horizontal position; Case II, vertical position). Governing parameters, which are effective on flow field and temperature distribution, are Rayleigh number values (Ra) ranging from 10³ to 10⁵ and inclination angles γ (0° ? γ < 360°). The fluid flow, heat transfer and heat transport characteristics were illustrated by streamlines, isotherms and Nusselt number (Nu). It is found that fluid flow and temperature fields strongly depend on Rayleigh numbers and inclination angles. Further, for the vertical located position of thin plate heat transfer becomes more enhanced with lower γ at various Rayleigh numbers.     

Quantification of natural convective heat transfer within air-filled hemispherical cavities. Isothermal tilted disk with dome oriented upwards and wide Ra range

This work quantifies the natural convective heat transfer occurring in hemispherical air-filled cavities whose disk is inclined at an angle varying between 0° and 90°. This active hot disk as well as the dome are maintained isothermal at different temperatures. The numerical approach by means of the control volume method allows the examination of the dynamical phenomena that occurs in many configurations obtained by varying the temperature difference between the two active walls and the radius of the hemisphere. Convective heat transfer at the hot wall is represented by the average Nusselt number associated to Rayleigh numbers varying between 10⁴ and 2.55 × 10¹². By taking into account all the studied configurations, correlations between these two dimensionless numbers are established for the set of considered inclination angles. Comparisons with results from other studies for the case of horizontal cavity show a good agreement. The relationships presented here cover the laminar, transitional and turbulent heat transfer regimes. They complement previous studies with the condition of heat flux imposed on the disk. The wide range of Rayleigh numbers considered in this survey and its association with the large inclination angle range allow the application of the correlations to various engineering fields such as nuclear technology, solar energy, building, embarked electronics, architecture, safety or domotics.     

Natural convection of microparticle suspensions in thin enclosures

Natural convection experiments were performed with aluminum oxide microparticle aqueous suspensions in thin enclosures of circular planform at angles of inclination to the horizontal of 90°, 30° and 0°. The average size of the aluminum oxide particles was about 250 nm, and volume fractions of 1.31% and 2.72% were used. The aspect ratio varied from 50.7 to 10.9, and the maximum Raleigh number was 3 × 10⁵. No effect of particles on the Nusselt number–Rayleigh number relation was found for the vertical enclosure at 90°. However at 30° and 0° (horizontal) there was a decrease in Nusselt number compared to pure water, which was pronounced at lower Rayleigh number and higher particle concentrations. This anomalous behavior is attributed to sedimentation.     

Sensitivity analysis for MHD effects and inclination angles on natural convection heat transfer and entropy generation of Al2O3-water nanofluid in square cavity by Response Surface Methodology

The natural convection heat transfer and entropy generation of Al₂O₃-water nanofluid, in a square cavity with inclination angle θ and the presence of a constant axial magnetic field B₀ are examined in this paper. The governing equations are solved numerically by finite volume method. Also an effective parameters analysis was performed by using of the Response Surface Methodology (RSM). The effects of the Rayleigh number (10³, 10⁴, 10⁵ and 10⁶), Hartmann number (0, 10, 30 and 50) and also inclination angles (0°, 30°, 60° and 90°) are investigated. It is observed that the mean Nusselt number and the total entropy generation increase when the Rayleigh number increases. It is also found that, regardless of the Ha parameter, by increasing of the inclination angles, the mean Nusselt number and entropy generation rate increase until inclination angle 30° and then they decrease. Also, for low Ra numbers, by increasing the Ha parameter, the mean Nusselt number increases until Ha = 10 and then decreases. The analysis showed that the sensitivity of the Nusselt number and the entropy generation to Ha parameter was too small, and as a result it was negligible. Also, the sensitivity of the mean Nusselt number and the entropy generation to inclination angle, θ, increases by increasing of this angle. It is also observed that the mean Nusselt number and the entropy generation were more sensitive to the inclination angle θ than the Ha parameter.     

Radiative effects on natural convection in vertical convergent channels

Natural convection in air, in a convergent channel, uniformly heated at the principal walls, is experimentally investigated, in order to analyze the effects of the radiative heat transfer. Results in terms of wall temperature profiles as a function of the walls inclination angle, the spacing between the walls, the heat flux, are given for two values of the wall emissivity. Flow visualization is carried out to show the peculiar pattern of the flow between the plates in several configurations. The comparison between two wall emissivity values, 0.10 and 0.90, shows that the effect of thermal radiation is more pronounced for larger convergence angles. For a wall emissivity equal to 0.90 and for small values of the minimum channel spacing, heat transfer in slightly convergent vertical channels is stronger than in a vertical parallel channel. Flow visualization points out a recirculating zone in the upper part of the channel for small values of the minimum channel spacing and for converging angles equal to 5° and 10°. Nusselt numbers and dimensionless maximum temperatures are then evaluated and correlated to the Rayleigh number, in the investigated range from 5 to 5 × 10⁸ and 0° ? θ ? 10°. A very good agreement between experimental data and correlations is observed for the dimensionless parameters based on the maximum channel spacing. Comparisons between experimental and numerical data are also performed and a good relationship is observed.     

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).     

Single-phase heat transfer in the high temperature multiple porous insulation

An experimental study of steady state flow and heat transfer has been conducted for the multiple plate porous insulation used in the reactor pressure vessels of ‘Magnox’ nuclear power stations. The insulation pack studied, consisting of seven dimpled stainless steel sheets and six plane stainless steel sheets, was of the type installed in the Sizewell A plant. A large scale experimental test facility, based on the guarded hot plate method, was used for measuring the effective thermal conductivity of Magnox reactor pressure vessel insulation, which consists of alternate layers of plain steel foil and dimpled foil. The measurements were made both with the fluid within the insulation pack nominally stationary and with an imposed flow through it, simulating leakage through the insulation pack. The experimental conditions corresponded to a heat flux of 75–1000 W/m², fluid pressures of atmospheric to 5 bar gauge, pack orientations in range of 0°–45° relative to the horizontal, leakage velocities ranging from 0.05 m/s to 0.20 m/s and inlet air bulk temperatures ranging from 18 °C to 290 °C. Local values of effective thermal conductivity of 0.04–0.23 W/m K were obtained for the above experimental conditions. The heat transfer modes in the insulation pack were conduction through the contacting metallic foils, thermal radiation across the gas gaps, and conduction and convection in the air. The effective thermal conductivity of the porous insulation increased with increasing air pressure, inclination angle, and air velocity. Buoyancy effects increased with increasing inclination angle and air pressure.     

Numerical investigation for natural convection of a nanofluid in an inclined L-shaped cavity in the presence of an inclined magnetic field

The problem of natural convection in an inclined L-shaped enclosure filled with Cu/water nanofluid that operates under differentially heated walls in the presence of an inclined magnetic field is presented in this paper. The fully implicit finite difference method is used to solve the governing equations. A comparison with previously published results in special case of the present study is performed and a very good agreement is found. Heat transfer and fluid flow are examined for parameters of the Hartmann number (0 ≤ Ha ≤ 100), the nanoparticles volume fraction (0% ≤ ϕ ≤ 20%), the cavity inclination angle (0° ≤ ϑ ≤ 300°), the magnetic field inclination angle (0° ≤ γ ≤ 270°), the cavity aspect ratio (0.25 ≤ AR ≤ 0.6) and the Rayleigh number (10³ ≤ Ra ≤ 10⁶). It is found that, the presence of the magnetic field in the fluid region causes a significant reduction in the fluid flow and heat transfer characteristics. Also, a good enhancement in the heat transfer rate can be obtained by adding the copper nanoparticles to the base fluid.     

Combined convection heat transfer for thermally developing aiding flow in an inclined circular cylinder with constant heat flux

Experiments have been conducted to study the local and average heat transfer by mixed convection for hydrodynamically fully developed, thermally developing and thermally fully developed laminar air flow in an inclined circular cylinder. The experimental setup consists of aluminum cylinder as test section with 30 mm inside diameter and 900 mm heated length (L/D = 30), is subjected to a constant wall heat flux boundary condition. The investigation covers Reynolds number range from 400 to 1600, heat flux is varied from 70 W/m² to 400 W/m² and cylinder angles of inclination including 30°, 45° and 60°. The hydrodynamically fully developed condition has been achieved by using aluminum entrance section pipes (calming sections) having the same inside diameter as test section pipe but with variable lengths. The entrance sections included two long calming sections, one with length of 180 cm (L/D = 60), another one with length of 240 cm (L/D = 80) and two short calming sections with lengths of 60 cm (L/D = 20), 120 cm (L/D = 40). The results present the surface temperature distribution along the cylinder length, the local and average Nusselt number distribution with the dimensionless axial distance Z⁺. For all entrance sections, the results showed an increase in the Nusselt number values as the heat flux increases and as the angle of cylinder inclination moves from θ = 60° inclined cylinder to θ = 0° horizontal cylinder. The mixed convection regime has been bounded by the convenient selection of Re number range and the heat flux range, so that the obtained Richardson numbers (Ri) is varied approximately from 0.13 to 7.125. The average Nusselt numbers have been correlated with the (Rayleigh numbers/Reynolds numbers) in empirical correlations.     

Lattice Boltzmann simulation of natural convection heat transfer in an elliptical-triangular annulus

A numerical study for steady-state, laminar natural convection in a horizontal annulus between a heated triangular inner cylinder and cold elliptical outer cylinder was investigated using lattice Boltzmann method. Both inner and outer surfaces are maintained at the constant temperature and air is the working fluid. Study is carried out for Rayleigh numbers ranging from 1.0 × 10³ to 5.0 × 10⁵. The effects of different aspect ratios and elliptical cylinder orientation were studied at different Rayleigh numbers. The local and average Nusselt numbers and percentage of increment heat transfer rate were presented. The average Nusselt number was correlated. The results show that by decreasing the value of aspect ratio and/or increasing the Rayleigh number, the Nusselt number increases. Also the heat transfer rate increases when the ellipse positioned vertically.     

Natural convection heat transfer of molten salts around a vertically aligned horizontal cylinder set

The heat transfer from the vertical arrays of a set of equally spaced cylinders in molten salts is studied numerically to obtain the laminar natural convection heat transfer mechanism of molten salts around a vertically aligned horizontal cylinder set. Simulations are performed for arrays of 2–10 horizontal cylinders at a Rayleigh number based on a cylinder diameter between 2 × 10³ and 5 × 10⁵. Results show that the natural convective heat transfer of molten salts from the bottom cylinder of the array remains the same as that from a single cylinder. By contrast, the downstream cylinders may either be enhanced or reduced mainly depending on their location in the array and on the tube spacing. Heat transfer dimensionless correlating equations are proposed for any individual cylinder in the two vertically aligned horizontal cylinders. The heat transfer mechanism from the horizontal cylinders set in a vertical array is also simulated, and the results show that cylinder spacing can influence the average heat transfer rate around the whole tube array. Thus, in real applications, adjusting the cylinder spacing better enhances the average heat transfer from the whole tube array.     

Start-up,heat transfer and flow characteristics of silicon-based micro pulsating heat pipes

A simultaneous visualization and measurement study has been carried out to investigate the start-up, heat transfer and flow characteristics of three silicon-based micro pulsating heat pipes (MPHPs) with the trapezoidal cross-section having hydraulic diameters of 251 μm (#1), 352 μm (#2) and 394 μm (#3), respectively. Experiments were performed under different working fluids, filling ratios, inclination angles (bottom heating mode) and heating power inputs. It is found that (1) the silicon-based MPHPs could start up within 200 s when charged with R113 or FC-72, but they failed to start up at all inclination angle when charged with water or ethanol having lower (dP/dT)_sat, higher viscosity, higher latent heat and higher surface tension at the same temperature. During the start-up period, no obvious nucleation was observed. After the start-up period, MPHPs entered the operation period. The silicon-based MPHP could operate normally even at a Bond number of 0.26 and a hydraulic diameter of 251 μm, both smaller than the corresponding values in literatures; (2) the thermal performance of MPHPs depends greatly on the type of working fluid, filling ratio and inclination angle. At the lower power input, MPHPs charged with R113 showed better thermal performance than that charged with FC-72, however, the latter exceeded the former at the higher power input. For the same working fluid, there existed an optimal filling ratio corresponding to the best thermal performance of MPHPs, which was about 52%, 55% and 47% for MPHPs #1, #2 and #3 at the vertical orientation (90°), respectively. When the MPHPs turned from the vertical to the horizontal orientation, the thermal performance tended to be decreased, indicating that the gravity effect cannot be ignored in these silicon-based MPHPs. In MPHP #3 at the inclination angle from 70° to 90°, there appeared a special thermal resistance curve with two local maximum points, which is absent in the traditional PHPs; (3) in the operation period of larger MPHP #3, nucleation boiling, bulk circulation and injection flow were all observed, while these flow patterns were absent in the smaller MPHPs #1 and #2. Intense liquid film evaporation, instead of bubbles’ generation and expansion which usually activated the oscillation flow in macro-PHPs, drove the two-phase flow in the smaller MPHPs #1 and #2.