Terms Of Rayleigh Number Research Articles

A set of generic correlations for high-Rayleigh-number thermal convection in inclined rectangular enclosures

A detailed review of the high-Rayleigh-number thermal convection literature for inclined enclosures indicates that correlations proposed thus far for the response variable, Nusselt number, have been either for a particular angle of inclination or fail to include all control parameters for the problem. The present study proposes a set of empirical correlations to predict Nusselt number for turbulent thermal convection in differentially-heated, tilted, rectangular enclosures of different aspect ratios (1, 3, 6, and 10) and angles of inclination (0°–150°) for a given range of Rayleigh numbers (1.85×106≤Ra≤1.04×1011). This study utilizes previously published experimental data to devise a set of generic correlations for Nusselt number in terms of Rayleigh number (Ra), aspect ratio (AR), and angle of inclination (θ) of the rectangular enclosure for any given Prandtl number (Pr). Predicted Nusselt numbers obtained from these generic correlations yield a mean absolute percentage error of ∼5% when compared to the corresponding experimental results. Additionally, the predicted values are also compared with literature-reported values for studies pertaining to control parameters outside the scope of the present study and found to be in good agreement, with a maximum deviation of ∼10%.

Buoyancy induced convection in magnetite nanofluid filled in enclosure with thick fin under magnetic field produced by a magnetic source

Buoyancy-induced convection of the magnetite nanofluid-filled enclosure with a thick fin on the heated surface is investigated under the magnetic field generated by a magnetic source. Since the heat transfer characteristic is sensible to the thermo-physical properties of the fluid used, these properties are determined experimentally to reduce the error. Magnetite nanofluid of low particle concentration is prepared using two-step method experimentally. Thermal conductivity, dynamic viscosity, and density of the prepared fluid is measured and utilized in the numerical study. The buoyancy-induced convection is characterized in terms of Rayleigh number, the magnetic field strength, the fin material's thermal conductivity, and the magnetic source's position. The numerical investigation is performed for various dimensionless numbers, including Rayleigh number (103 ≤ Ra ≤ 105), Hartmann Number (0 ≤ Ha ≤ 75), and thermal conductivity ratio (10 ≤ Kr ≤ 1000). The thermal conductivity ratio is observed to affect the heat transfer rate significantly. With the increase in the thermal conductivity ratio, more heat is inducted inside the enclosure, causing a higher heat transfer rate. The magnetic field has an inverse relation with the convection current, whereas the Rayleigh number has positive relation. The position of the magnetic source significantly affects the heat transfer rate. The rate is found to be minimum when the source is below the center of the enclosure compared to when it is below one of the vertical surfaces.

Low Reynolds number MHD mixed convection of nanofluid in a corner heated grooved cavity

This study aims to explore mixed magnetohydrodynamic convective transport phenomena in a grooved channel geometry using CuO-H2O nano-fluid flow under low fluid velocity situation. Convective dynamics in such complex geometry have not been studied in detail considering multiphysical scenarios. The fluid enters through the enclosure in cold conditions having temperature Tc and all the walls of the cavity are insulated, except the corner heated with Th temperature. The numerical technique is adopted to solve two-dimensional continuity, momentum, and energy equations. A parametric study is carried out here in terms of Rayleigh number (Ra), Reynolds number (Re), Hartmann number (Ha), and nano-particle concentration (φ). The observations are highlighted in the form of isotherms, streamline plots, and average Nusselt number (Nu) to study the variation of Ra, Re, Ha, and φ on the thermo-fluid coupled process. The current study reveals that for the specified geometry, the change of Ra, Re, and Ha significantly affects the flow pattern along with related heat transfer features as compared to φ. The analysis implied that the optimum heat-transfer performance (Nu = 7.58) is obtained under conditions of Ra = 105, Re = 30, and Ha = 0. The flow separation process becomes more complex and is dictated by the magnetic field intensity.

Natural convection cooling of an infrared suppression device (IRS) with conical funnels- a computational approach

The present study involves the numerical computations of the free convection heat transfer from an Infrared suppression device with the conical funnels, which is used in the exhaust of the marine gas turbines and helicopters. The computations have been performed in the range of 1010 ≤ Ra ≤1012. The study also involves predicting the effect of the diameter ratio and the percentage overlap. Besides, our study proposes a correlation for the Nusselt number and the induced mass flow rate in terms of Rayleigh number, diameter ratio, and percentage overlap. The study also computes the cooling time of the IRS device. The Nusselt number initially increases with the diameter ratio, attains a maximum, and finally reduces to a constant value. Highest values of Nu are observed with the positive overlap of the funnels, whereas the lowest values are obtained for the negative overlap. Moreover, the present study also compares the cooling characteristics of the IRS having cylindrical and the conical funnels. The comparisons show that higher values of the Nu are obtained for the cylindrical funnels compared to the conical ones. The findings of the present study can be significant to both the engineers of the ship industries and the academicians.

Thermal Analysis of a Microhotplate - An Experimental Study

In the present work, experimental and numerical thermal analysis of a microhotplate were performed to evaluate the heat transfer mechanism at small Rayleigh number ( $Ra$ ). The convective and radiative heat transfer coefficient values were evaluated for microhotplate mounted over two different mounting positions (namely model-1 & model-2). At different heat generation ( $Q$ ) values, it was found that the average convective coefficient value was less than $10\frac {W}{m^{2}K}$ , irrespective of the microhotplate mounting position. Comparison of both models at a similar $Q$ ( $\simeq 0.69W$ ) value, reveals that the radiative heat transfer contribution was 33% & 68% for model-1 and model-2 respectively. Based on the results obtained in the present study, a correlation was developed using regression analysis for the convective Nusselt number in terms of Rayleigh number ( $8.84\times 10^{-4}\le \:Ra\:\le 4.94\times 10^{-3}$ ), and the convective Nusselt number obtained from the correlation and present study are within ±17%.

Linear instability of concentric annular flow: Effect of Prandtl number and gap between cylinders

The stability of non-isothermal Poiseuille flow in a coaxial annular domain is studied using normal mode analysis. The stably stratified flow (i.e., when buoyant force is in the direction of forced flow) is induced due to external pressure gradient and maintenance of linear variation of the temperature of the inner cylinder. We have emphasized the impact of the gap between cylinders in terms of curvature parameter (C) and Prandtl number (Pr) on the instability of the flow under axisymmetric as well as non-axisymmetric disturbances. In general, it has been found that the flow of low Pr fluids under axisymmetric disturbance is more stable in comparison with the flow under non-axisymmetric disturbance. When the gap between cylinders is relatively small (i.e. C is large), the flow under non-axisymmetric is most stable for the fluids having high Pr. It is known that the Newtonian pipe flow is linearly stable for all values of Reynolds number (Re). However, in the present study, we have seen the instability of the pipe flow with a thin rod placed at the center even for a very small value of heat source intensity (in terms of Rayleigh number) at Re=2000. Here the disturbance velocity is concentrated in the vicinity of the inner wall and instability is due to transfer of kinetic energy from the basic flow through Reynold’s stress. Depending on the value of controlling parameters, three types of instability: thermal-shear, interactive, thermal-buoyant have been observed. In general, for a fixed value of Pr, the type of instability is not affected by C and Re. The non-isothermal Poiseuille flow of low Pr (including mercury and gases) is governed by thermal-shear instability and the same of high Pr (including liquid and oil) is governed by thermal-buoyant instability.

Theoretical Modeling, Numerical Simulations and Experimental Study of Micro Thermal Convective Accelerometers

We present a one-dimensional (1D) theoretical model for the design analysis of a micro thermal convective accelerometer (MTCA). Systematical design analysis was conducted on the sensor performance covering the sensor output, sensitivity, and power consumption. The sensor output was further normalized as a function of normalized input acceleration in terms of Rayleigh number R $_{\mathrm {a}}$ (the product of Grashof number G $_{\mathrm {r}}$ and Prandtl number P $_{\mathrm {r}}$ ) for different fluids. A critical Rayleigh number ( R ac = 3,000) is founded, for the first time, to determine the boundary between the linear and nonlinear response regime of MTCA. Based on the proposed 1D model, key parameters, including the location of the detectors, sensor length, thin film thickness, cavity height, heater temperature, and fluid types, were optimized to improve sensor performance. Accordingly, a CMOS compatible MTCA was designed and fabricated based on the theoretical analysis, which showed a high sensitivity of 1,289 mV/g. Therefore, this efficient 1D model, one million times faster than CFD simulation, can be a promising tool for the system-level CMOS MEMS design.

Rayleigh-Bénard Convection for Nanofluids for More Realistic Boundary Conditions (Rigid-Free and Rigid-Rigid) Using Darcy Model

In this article, Rayleigh-Bénard convection for nanofluids for more realistic boundary conditions (rigid-free and rigid-rigid) under the influence of the magnetic field is investigated. Presence of nanoparticles in base fluid has introduced one additional conservation equation of nanoparticles that incorporates the effect of thermophoretic forces and Brownian motion and the inclusion of magnetic field has introduced Lorentz’s force term in the momentum equation along with Maxwell’s equations. The solution of the Eigen value problem is found in terms of Rayleigh number by implementing the technique of normal modes and weighted residual Galerkin approximation. It is found that the stationary as well as oscillatory motions come into existence and heat transfer takes place through oscillatory motions. The critical Rayleigh number for alumina water nanofluid has an appreciable increase in its value with the rise in Chandrasekhar number and it increases moderately as we move from rigid-free to both rigid boundaries. The effect of different nanofluid parameters on the onset of thermal convection for two types of boundaries is investigated.

Experimental investigation of the helium natural circulation heat transfer in two channels facility using varying riser channel heat fluxes

Natural circulation is considered an important passive safety aspect of the prismatic block gas cooled reactor during accident scenarios. Experimental investigations for helium natural circulation heat transfer in a scaled down separate-effects dual-channel facility have been performed at Multiphase Reactors Engineering and Applications Laboratory (mReal). The current facility consists of two channels (riser and downcomer) for coolant flow between upper and lower plena. In the present study, the riser channel is heated uniformly using an electric heater, and the downcomer channel is cooled uniformly using a heat exchanger with chilled water to initiate natural circulation. Intensity of natural circulation heat transfer along the riser and downcomer channels is investigated at different levels of constant heat fluxes ranging from 860 W/m2 to 2293 W/m2 at 413.7 kPa using sophisticated a noninvasive heat transfer probe. The heat transfer data in terms of the local heat transfer coefficient, the local wall surface, and helium temperatures are collected at different axial and radial locations. Also, the local Nusselt numbers are estimated along the two channels. Results confirm that the heat transfer coefficient and Nusselt number values increase as the heat fluxes increase due to increased convection currents. Average riser wall surface temperature increased by 84% when heat fluxes increase from 860 W/m2 to 2293 W/m2. Also, small variations in the temperatures of the wall surface and helium are observed along the downcomer channel due to the large volume of the upper plenum. A reversal in the direction of heat transfer close to the outlet of the riser channel (Z/L = 0.956) is observed, as well as a reduction in the wall surface temperature due to co-circulation. The heat transfer reversal being reported here is very significant and would have profound effects on the overall design of the natural circulation systems. The radial temperature distributions along the riser channel showed a unique peaking in the center close to the exit (Z/L = 0.956). Also, the local radial variation of density, dynamic viscosity, and thermal conductivity as dimensionless values with respect to bulk values are measured along the riser channel. Results showed that the deviation of local values from the bulk values increases with increasing the magnitude of heat flux to the riser channel. The average heat transfer results in terms of Rayleigh number and Nusselt number, when compared with previous literature correlations, showed a similar qualitative trend.

An experimental study on the natural convection heat transfer in rectangular enclosure using functionalized alumina-thermal oil-based nanofluids

The nanofluids are considered as an effective medium for thermal transport in various applications due to improved properties. Limited experimental studies are accomplished on the convective heat transfer of nanofluids. Natural convective heat transfer behavior in nanofluids is experimentally studied in a vertical rectangular enclosure (aspect ratio=4) with one heating and one cooling wall. The fluid under investigation is a novel and highly stable functionalized alumina-thermal oil-based nanofluid. The investigations are carried out for different concentrations of nanofluids ranging from 0 to 3wt%. The effectiveness of the natural convection heat transfer process is mainly dependent on the properties of cooling media. The measured thermophysical properties of nanofluids are used for the estimation of heat transfer characteristics with a Prandtl number range of 228–592. The heat transfer coefficient and Nusselt number are obtained at different nanoparticle concentrations. A heat flux is applied on the hot wall with a range of 1593.75–3150W/m2. An improvement in the cooling performance of nanofluids is observed. The high nanoparticle concentrations of nanofluids exhibit higher heat transfer coefficient as compared to the pure thermal oil. A correlation is developed for the Nusselt number in terms of Rayleigh number (4.43×105–2.59×106), nanoparticle concentration and effective thermophysical properties.

Experimental analysis of natural convection in vertical annuli filled with AlN and TiO2/mineral oil-based nanofluids

The thermal performance of mineral oil based nanofluids is experimentally investigated when they are used as a cooling fluid in a system that operates under natural convection. This system consists of a closed annular vertical cavity that is filled with two types of nanofluids made of different nanoparticles and concentrations. The inner cylinder works as a constant heat source while the outer cylinder removes the thermal energy with a constant temperature condition. High Prandtl number nanofluids (70–300) produced by dispersing AlN and TiO2 nanoparticles in mineral oil (0.01, 0.1 and 0.5 wt%) were previously characterized and then tested in this system to evaluate the effect in the free convective heat transfer coefficient under high Rayleigh numbers (>106). Additionally, oleic acid treated nanoparticles were also used to disperse nanofluids and compared to those without any treatment. Correlations for Nusselt number in terms of Rayleigh number are obtained for different nanoparticle concentrations. Under certain conditions, enhancements in heat transfer coefficients were found when using nanofluids while mainly deteriorations occurred when compared to base fluid.

Experimental investigation and general correlation of passive heat transfer in enclosures at different operating, orientations and venting configurations

Free convection heat transfer in enclosures was previously studied for specific operating, geometric and orientations conditions. A lot of correlations are presented in the literature for specific conditions. The current work aims to do inclusive experiments of heat transfer in heated enclosures for different inclination angles, venting configurations, venting opening ratios and Rayleigh numbers. Three various configurations of enclosure openings for air venting were examined: (i) top openings, (ii) side openings, and (iii) top and side openings. The experiments were conducted for wide ranges of venting opening ratios, inclination angles and Rayleigh numbers for each configuration of air venting. Developed correlation was presented for the studied venting configurations to expect the enclosure Nusselt number in terms of Rayleigh number, opening ratio, enclosure inclination angle and openings arrangements. It was found that the developed correlations can predicts the present experimental and previous results within ±8% error. The results showed that for all the studied venting configurations, the Nusselt number enhances with increasing the Rayleigh number, vents opening ratio and in range from 0° to 90° enclosure inclination angle. Furthermore, the top and side openings configuration showed the greatest Nusselt number.

The characteristic length on natural convection from a horizontal heated plate facing downwards

Natural convection from a downward facing horizontal heated plate was analyzed. An expression for the thickness of the thermal boundary layer was obtained in terms of Rayleigh number. Assuming this thickness as the characteristic length of the problem, the data published by other authors were modified and an equation for Nusselt number is presented. It was observed that this equation correlates the data more precisely than the commonly known equations in the literature that employ the ratio of the area to the perimeter or the shorter side of the plate as the characteristic length. It is concluded that taking the thermal boundary layer as the characteristic length of phenomenon is a proper approach and correlates all the data closely.

Convective heat transfer correlations for low-profile spherical cavities with planar bottom surfaces (1415-RP)

Domed cavities are found in many building applications, such as conventional skylights and tubular daylighting devices. Heat transfer through domed cavities is thus an important parameter for evaluating the energy performance rating of such skylight systems and in calculating the heating and cooling loads of buildings. Although there have been many studies on the convective heat transfer in related geometries, there is a limited information on natural convective heat transfer in domed cavities with planar inner surfaces. In a previous study, numerical modeling was conducted on natural laminar convective heat transfer in horizontal high-profile domed cavities with planar inner surfaces. In this article, the previous study is extended to investigate the natural convective heat transfer in horizontal low-profile spherical cavities with planar inner surfaces. The bounding surfaces are subject to uniform temperature conditions. The numerical model is based on the finite-element method. The results show that for different boundary temperature conditions, the airflow in the cavities is mono-cellular and reaches steady-state conditions for both cold and hot weather conditions. The numerical results are used to develop practical correlations for the Nusselt number in terms of Rayleigh number.

Natural Convection in a Series of Thermally Interacting Cavities with Wall Mounted Heaters

Laminar natural convection in a series of thermally interacting cavities is numerically studied. Each cavity consists of a conducting bottom wall with a surface mounted heater. The side walls of the cavities are isothermally cooled. Each cavity thermally interacts with its adjacent cavities through the conducting walls. Flow and heat transfer characteristics are studied in detail for various Rayleigh numbers. The convection characteristics in multiple cavities are compared with those in single independent cavity. The thermal interaction between the cavities results in lower temperatures compared with those in independent cavities. While heat is rejected into the adjacent upper cavity through some portion of the conducting wall, heat is received from the adjacent cavity through the remaining portion of the wall. The influence of substrate conductivity on heat exchange between adjacent cavities are examined. Substrate conductivity shows strong effect on temperature distribution. When cooling at both vertical sides is changed to one side cooling, the heat transfer characteristics are changed drastically and many interesting flow features are observed. Effects of cavity aspect ratio is studied and higher heat transfer rates are observed at higher aspect ratios. Correlations for dimensionless temperature maximum and average Nusselt number are presented in terms of Rayleigh number.

Computational fluid dynamic investigations and experimental validation of frozen seal sodium valve assembly of a fast reactor

Frozen seal sodium valves are used in fast reactors. To achieve sodium freezing, horizontal fins are attached to the outer surface of valve sheath. Adjacent fins form open-ended cavities and natural convection of air in these cavities is investigated using the PHOENICS code for various values of fin length, spacing and root temperature. It is seen that convective air does not penetrate deep into shallow cavities leading to poor heat transfer coefficient, offsetting the enhancement in surface area. Penetration depth of air is a function of aspect ratio and Rayleigh number based on fin spacing and is independent of fin length. Generalized correlations are derived for Nusselt number in terms of Rayleigh number and aspect ratio. Using these correlations, temperature distribution in entire valve assembly is predicted using the HEATING5 code, to select an optimum design. Experiments have been conducted on a model valve of selected design in the SILVERINA facility available at this centre. Measured stem temperature distribution is found to compare satisfactorily with HEATING5 predictions, validating the correlations derived from computational fluid dynamic studies and integrated thermal analysis methodology.

Numerical Investigation on the Steady State Natural Convection in a Horizontal Open-Ended Cavity with a Heated Upper Wall

In this article, the investigation is focused on a configuration made of two horizontal parallel plates with the upper plate heated at uniform heat flux and the lower one adiabatic. Results are presented in terms of velocity and temperature fields, and both the temperature and the velocity profiles at different sections are shown. They are reported at two Rayleigh numbers, 103 and 105, and for two aspect ratio values, 1 and 10. Results are also shown in terms of the upper and lower wall temperature profiles. Correlations for average Nusselt numbers and maximum dimensionless wall temperature, in terms of Rayleigh number and aspect ratio, are given for 103 ≤ Ra ≤ 105 and 1 ≤ L/b ≤ 10.

Experimental Investigation of Radiation Effects on Natural Convection in Horizontal Channels Heated From Above

Radiation heat transfer affects natural convection of air inside an open-ended cavity with a heated horizontal upper plate and an unheated lower parallel plate. Its effect is the heating of the lower plate, which heats the adjacent fluid layer and could determine secondary motions. In this paper, an experimental study is carried out to describe the effect of high value of surface emissivity on air flow in an open-ended cavity. The investigation is performed by means of wall temperature profiles, smoke visualization, and air temperature measurements. Results are obtained for an emissivity of the horizontal plates equal to 0.8, for aspect ratios between 10.0 and 20.0. By means of flow visualization and local air temperature measurements in the cavity as a function of time, remarkable secondary motions in the cavity are observed for the highest considered surface heat flux (Ra=8.91×103, 6.45×104, and 1.92×105). Measurement of the air temperature in the cavity also shows that radiation causes and damps secondary motions at the same time. Mean air temperature profiles as a function of the vertical coordinate, at different locations along the longitudinal axis, confirm both the main flow path inside the cavity and radiation effect on convective heat transfer. Finally, correlations for average Nusselt numbers and dimensionless maximum wall temperatures, in terms of Rayleigh number and channel aspect ratio, are proposed for natural convection with or without radiative heat transfer contribution for 2.26×103≤Ra≤1.92×105 and 10≤2L/b≤20.

Free convection in a vertical cylindrical annulus filled with anisotropic porous medium

A numerical study has been carried out for free convection in a vertical cylindrical annulus filled with a porous medium and whose inner wall is isothermally heated and the outer wall is isothermally cooled, the horizontal walls being insulated. The porous medium is assumed to be both hydrodynamically and thermally anisotropic. Numerical results are reported for 0.1 ? K*? 10, 0.1 ? ? ? 10,1 ? A ? 20,2 ? Rr ? 20, and Ra*? 10000. Anisotropy of the porous medium is found to affect fluid flow, temperature distribution and heat transfer significantly. Higher permeability in the vertical direction enhances convective flow intensity and heat transfer inside the annulus. Average Nusselt number on the inner hot wall increases with increase in Rayleigh number or radius ratio, while it decreases with increase in aspect ratio or permeability ratio. The influence of thermal anisotropy is not so significant as that of hydrodynamic anisotropy. The numerically predicted temperature distribution at various locations inside the annulus shows reasonable agreement with experimental results available for isotropic porous medium. Based on a parametric study, correlation for heat transfer is presented in terms of Rayleigh number, aspect ratio, radius ratio, and permeability ratio.

Numerical studies on laminar natural convection inside inclined cylinders of unity aspect ratio

The effect of cylinder inclination on thermal buoyancy induced flows and internal natural convective heat transfer is explored using CFD simulations. The cylinder’s top and bottom surfaces were maintained at different temperatures while the curved surface was adiabatic. The aspect ratio (length/diameter) of the cylinder was unity and the Prandtl number of the fluid was fixed at 0.71. The Rayleigh number of the confined fluid was varied from 10 3 to 3.1 × 10 4 by changing the specified end wall temperatures. The critical Rayleigh number was estimated to be 3800 for the vertical cylinder. Relaxing the convergence criterion caused false hysteresis in the converged results for the vertical cylinder. Typical natural convective fluid flow and temperature patterns obtained under laminar flow conditions are illustrated for various inclinations ranging from 0° to 180°. Flow visualization studies revealed complex three-dimensional patterns. Different thermal–hydrodynamic regimes were identified and were classified in terms of Rayleigh number and angle of inclination. Empirical correlations for the Nusselt number and maximum velocities in the domain as a function of the inclination angle and Rayleigh number are developed.