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The purpose of this paper is to propose correlations between Nusselt and Rayleigh numbers for the case of inclined and closed air-filled hemispherical cavities. The disk of such cavities is subjected to a constant heat flux. The study covers a wide range of Rayleigh numbers from 5×107 to 2.55×1012.

Correlations are obtained from numerical approach validated by experimental measurements on some configurations, valid for several angles of inclination of the cavity between 0° (horizontal disk) and 90° (vertical disk) in steps of 15°.

The statistical analysis of a large number of calculations leads to reliable results covering laminar, transitional and turbulent natural convection heat transfer zones.

The proposed correlations provide solutions for applications in several fields of engineering such as solar energy, aerospace, building, safety and security.

The new relations proposed are the first published for high Rayleigh numbers for this type of geometry. They supplement the knowledge of natural convection in hemispherical inclined cavities and constitute a useful tool for application in various engineering areas as solar energy (thermal collector, still, pyranometer, albedometer, pyrgeometer), aerospace (embarked electronics), building, safety and security (controlling and recording sensors).

The purpose of this study is to determine the thermal behavior of a hemispherical electronic device contained in a concentric hemispherical enclosure, cooled by means of free convection through a porous medium saturated with a water–copper nanofluid. Influence of various parameters on the thermal state of this device is processed in this work. The high power generated by the dome leads to a Rayleigh number varying in the 5.2 × 10⁷-7.29 × 10¹⁰ range. The volume fraction of the monophasic nanofluid varies between 0 (pure water) and 10 per cent while the base of the hemispherical cavity (disc) is inclined between 0° (horizontal disc with dome facing upward) and 180° (horizontal disc with dome facing downward).

The three-dimensional numerical approach is carried out by means of the volume control method associated to the SIMPLE algorithm.

The work shows that the average temperature of the active component increases with the Rayleigh number according to a conventional law of the power type. The increase in the angle of inclination also goes with a systematic rise in the average temperature. However, increasing the ratio of the solid–fluid thermal conductivities decreases the average temperature of the component, given the respective contributions of the conductive and natural convective phenomena occurring through the nanofluid saturated porous media. The values of this ratio vary in this work between 0 (interstice between the two hemispheres without porous medium) and 70.

The correlation proposed in this work allows to calculate the temperature of the active electronic component for all the combinations of the four influence parameters which vary in wide ranges.

Nusselt-Rayleigh-Fourier type correlations are proposed to quantify the temporal evolution of convective heat transfer occurring within air-filled hemispherical enclosures whose disk, initially at ambient temperature, is suddenly maintained at a higher temperature. The temperature difference imposed between this hot wall and the isothermal cold dome involves Rayleigh number varying between 104 and 2.55×1012. Depending on the application, the disk can be inclined with respect to the horizontal plane by an angle varying between 0° (horizontal disk) and 90° (vertical disk) in steps of 15°. The paper aims to discuss these issues.

The results are obtained by means of a numerical approach based on the finite volume method. The proposed correlations linked to the steady state Nusselt-Rayleigh internships recently published, concerning the same inclination angle and Rayleigh ranges.

The statistical analysis of a large number of calculations leads to reliable results covering laminar, transitional and turbulent natural convection heat transfer zones.

The proposed relationships can be applied in several engineering fields such as nuclear technology, solar energy, security and safety electronics, building, domotics or aeronautics.

The new relationships proposed in this paper provide important information on the evolution of convective heat transfer during the transient regime.

The main purpose of this work is to quantify the convective heat transfer occurring between two inclined and concentric hemispheres.

The inner one is an electronic assembly generating a constant heat flux during operation. The outer hemisphere is maintained isothermal at cold temperature. The interstitial space is air-filled. The base of the equipment can be inclined with respect to the horizontal plane by an angle ranging from 0° (horizontal position with dome faced upwards) to 180° (horizontal position with dome faced downwards).

Nusselt–Rayleigh correlations are proposed for several configurations obtained by varying the generated power and the base inclination. The large resulting Rayleigh number ranging between 2.4 × 10⁵ and 1.7 × 10⁷ allows using these new and original correlations in various engineering fields, such as electronics in the present work. The calculations are realized by means of a 3D numerical approach based on the finite volume method.

The geometry and the thermal boundary conditions considered in the present survey are suitable for applications in many engineering areas.

The purpose of this study is to theoretically analyze the laminar free convection heat transfer of nanofluids in a square cavity. The sidewalls of the cavity are subject to temperature difference, whereas the bottom and top are insulated. Based on the available experimental results in the literature, two new non-dimensional parameters, namely, the thermal conductivity parameter (Nc) and dynamic viscosity parameter (Nv) are introduced. These parameters indicate the augmentation of the thermal conductivity and dynamic viscosity of the nanofluid by dispersing nanoparticles.

The governing equations are transformed into non-dimensional form using the thermo-physical properties of the base fluid. The obtained governing equations are solved numerically using the finite element method. The results are reported for the general non-dimensional form of the problem as well as case studies in the form of isotherms, streamlines and the graphs of the average Nusselt number. Using the concept of Nc and Nv, some criteria for convective enhancement of nanofluids are proposed. As practical cases, the effect of the size of nanoparticles, the shape of nanoparticles, the type of nanoparticles, the type of base fluids and working temperature on the enhancement of heat transfer are analyzed.

The results show that the increase of the magnitude of the Rayleigh number increases of the efficiency of using nanofluids. The type of nanoparticles and the type of the base fluid significantly affects the enhancement of using nanofluids. Some practical cases are found, in which utilizing nanoparticles in the base fluid results in deterioration of the heat transfer. The working temperature of the nanofluid is very crucial issue. The increase of the working temperature of the nanofluid decreases the convective heat transfer, which limits the capability of nanofluids in decreasing the size of the thermal systems.

In the present study, a separation line based on two non-dimensional parameters (i.e. Nc and Nv) are introduced. The separation line demonstrates a boundary between augmentation and deterioration of heat transfer by using nanoparticles. Indeed, by utilizing the separation lines, the convective enhancement of using nanofluid with a specified Nc and Nv can be simply estimated.

The purpose of this paper is to make a numerical analysis on unsteady analysis of natural convection heat and mass transfer to obtain flow field, temperature distribution, and concentration distribution.

A finite element method is applied to solve governing equations of natural convection in curvilinear-shaped system for different parameters as thermal Rayleigh numbers (103=Ra_T=106), inclination angle (0°=φ=60°) and Hartmann numbers (0=Ha=100).

Both magnetic field and inclination angle can be used as control parameter on heat and mass transfer. Flow strength decreases almost 100 percent between Ha=0 and Ha=100 on behalf of the higher values of thermal Rayleigh number.

The originality of this work is to application of magnetic field on time-dependent natural convection flow, heat and mass transfer for curvilinear geometry.

This work deals with the case of the quad flat non-lead 64 (QFN64) electronic package generating a low power range ranging from 0.01 to 0.1W. It is installed on one side of a printed circuit board (PCB) that can be inclined relative to the horizontal plane with an angle varying between 0° and 90° (horizontal and vertical positions, respectively). The surface temperature of the electronic assembly is subjected to air natural convection.

Calculations are done by means of the finite volume method for many configurations obtained by varying the generated power and the inclination angle.

The distribution of the surface temperature is determined on all the assembly areas (QFN and PCB). The study shows that the thermal behaviour of the electronic device is influenced by the generated power and the inclination angle. The 3D numerical survey leads to correlations allowing calculation of the average surface temperature in any part of the assembly, according to the power generated by the QFN64 and the inclination angle.

The proposed accurate correlations are original and unpublished. They optimize the thermal design of the electronic QFN64 package, which is increasingly used in many engineering fields.

The wire-bonded version of the quad flat non-lead with 64 leads (QFN64b) is increasingly integrated in modern arrangements, given its thermal and electrical characteristics suited for specific applications. Temperature control is thus essential for its proper operation, particularly when the heat exchange with the environment is done by natural convection. This work aims to consider a conventional assembly consisting of a large printed circuit board (PCB) on which is welded a QFN64b generating a power in the range 0.01-0.1 W. The PCB could be inclined at an angle varying between 0° and 90° (horizontal and vertical positions, respectively) according to the intended application.

The 3D numerical approach done by means of the finite volume method is complemented by thermal and electrical measurements for all the configurations numerically processed. The low deviations obtained between the calculations and the measurements validate the adopted model. These results complement recent work that considers the same assembly equipped with a tilted and low-powered QFN64 basic model subjected to free convection.

The surface temperature in any part of the assembly has been determined. The influence of the power generated by the device and the PCB’s inclination angle relative to the gravity field have been quantified. The work shows that the radiative heat transfer is negligible given the temperatures reached and that the thermal state of the considered assembly is different from the one equipped with the QFN64 basic model. The QFN’s temperature is lowered, while that of the PCB is increased. The temperature distribution is also different from that of assemblies equipped with other QFN models with and without wire-bonding.

The correlations proposed in this survey help optimize the thermal design of the QFN64b electronic package used in many engineering fields.

This paper aims to present the numerical models and experimental outcomes pertain to the performance of the parabolic dish concentrator system with a modified cavity-type receiver (hemispherical-shaped).

The numerical models were evolved based on two types of boundary conditions; isothermal receiver surface and non-isothermal receiver surface. For validation of the numerical models with experimental results, three statistical terms were used: mean of absolute deviation, R² and root mean square error.

The thermal efficiency of the receiver values obtained using the numerical model with a non-isothermal receiver surface found agreeing well with experimental results. The numerical model with non-isothermal surface boundary condition exhibited more accurate results as compared to that with isothermal surface boundary condition. The receiver heat loss analysis based on the experimental outcomes is also carried out to estimate the contributions of various modes of heat transfer. The losses by radiation, convection and conduction contribute about 27.47%, 70.89% and 1.83%, in the total receiver loss, respectively.

An empirical correlation based on experimental data is also presented to anticipate the effect of studied parameters on the receiver collection efficiency. The anticipations may help to adopt the technology for practical use.

The developed models would help to design and anticipating the performance of the dish concentrator system with a modified cavity receiver that may be used for applications e.g. power generation, water heating, air-conditioning, solar cooking, solar drying, energy storage, etc.

The originality of this manuscript comprising presenting a differential-mathematical analysis/modeling of hemispherical shaped modified cavity receiver with non-uniform surface temperature boundary condition. It can estimate the variation of temperature of heat transfer fluid (water) along with the receiver height, by taking into account the receiver cavity losses by means of radiation and convection modes. The model also considers the radiative heat exchange among the internal ring-surface elements of the cavity.

This paper aims to present experimental work examining the effect of opening size on the collection efficiency of cavity-type receiver geometries, e.g. modified cavity and spherical cavity with single- as well as dual-stage water heating. The correlations, obtained using the experimentally obtained data, are helpful in designing of cavity receivers (modified and spherical geometry type) to be used in solar-power harnessing assignments/projects, for yielding better system performance.

The parameters of study encompass receiver opening or aperture ratios (d/D, ratio of diameter of opening to the maximum diameter of spherical cavity) of 0.4, 0.47, 0.533 and 0.6; flow Reynolds numbers of 938, 1,175, 1,525 and 1,880 with water as a coolant; and receiver inclination angles of 90, 60, 45 and 30° (with 90° as receiver-opening facing downward and 30° as receiver-aperture facing closer to sideway). A modified cavity receiver was examined for opening ratios of 0.46, 0.6, 0.7 and 0.93. The glass covers, with thickness 2, 4 and 6 mm, were positioned at the opening of cavity to mitigate the energy losses.

The experiments have been conducted at a lesser incoming radiative heat flux, for receiver cavity wall surface temperatures ranging from 90°C to 180°C. The collection efficiency values of both the receivers, modified cavity and spherical cavity types, are seen increasing with coolant flow rate and receiver tilt (inclination) angles, i.e. 30° → 90°. The collection efficiency exhibits maxima at an opening ratio of 0.533 in case of both single- and double-stage spherical cavity receiver. This value was observed as 0.6 for modified cavity receiver. The mathematical correlations developed for obtaining the collection efficiency values of modified cavity-type receiver, spherical cavity receiver with single stage and spherical cavity receiver with dual-stage water heating are given as ɳ=0.4667 Re0.0798dD0.1651 δ0.0281θ̇−0.011, ɳ=0.2317 Re0.124 dD1.265δ0.0192θ̇0.2914 and ɳ=0.1137 Re0.1715dD0.8702θ̇0.2757, respectively.

The findings of the paper may be helpful in erecting concentrating solar collector systems for household water heating, concentrating solar-based power generation as well as for various agricultural applications.

The experimental investigations are fewer in the literature examining the combined geometrical influence on the efficiency of cavity receivers with single- and double-stage water heating provisions.