Convective Nusselt Number Research Articles

Limiting regimes of turbulent horizontal convection. Part 2. Large Prandtl numbers

Horizontal convection at large Rayleigh and Prandtl numbers is studied experimentally in a regime up to seven orders of magnitude larger in terms of Rayleigh numbers than previously achieved. To reach Rayleigh numbers up to $10^{17}$ , the horizontal density gradient is generated using differential solutal convection by a differential input of salt and fresh water controlled by diffusion in a novel experiment in which the zero-net mass flux of water is ensured through permeable membranes. This set-up allows us to accurately measure the Nusselt number in solutal convection by carefully controlling the amount of salt water exchanged through the membranes. Combined measurements of density and velocity across more than five orders of magnitude in Rayleigh numbers show that the flow transitions from the Beardsley & Festa (J. Phys. Oceanogr., vol. 2, issue 4, 1972, pp. 444–455), Shishkina & Wagner (Phys. Rev. Lett., vol. 116, issue 2, 2016, 024302) regime to the Chiu-Webster et al. (J. Fluid Mech., vol. 611, 2008, pp. 395–426) regime and frames the present results within the scope of Shishkina et al. (Geophys. Res. Lett., vol. 43, issue 3, 2016, pp. 1219–1225), and the theory of Part 1 (Passaggia & Scotti, vol. 997, 2024, J. Fluid Mech., A5). In particular, we show that, even for large Prandtl numbers, the circulation eventually clusters underneath the forcing horizontal boundary, leaving a stratified core without motion. Finally, the previous regime diagrams (Hughes & Griffiths, Annu. Rev. Fluid Mech., vol. 40, 2008, pp. 185–208; Shishkina et al., Geophys. Res. Lett., vol. 43, issue 3, 2016, pp. 1219–1225) are extended by combining the present results at high Prandtl numbers, the results at low Prandtl numbers of Part 1, together with previous results from the literature. This work sets a new picture of the transition landscape of horizontal convection over six orders of magnitude in Prandtl number and sixteen orders of magnitude in Rayleigh number.

Analysis of magneto-natural convection and second law of thermodynamics of Cu-Al2O3-hybrid nanofluid in a vertical wavy cabinet having a localized non-uniform heat source

Improvements in thermal transference rate and minimization of entropy generation are critical issues in many industrial and engineering applications where heat transfer coefficient is essential to achieve optimal performance and minimal energy consumption. In the present investigation, a computational analysis has been conducted to analyze the impact of magnetic field on magneto-free convection and entropy generation inside a vertical wavy cabinet filled by Cu-Al2O3/H2O hybrid nanosuspension. In the geometry of this model, vertical boundaries of the chamber are designed as wavy and kept as cooled temperature (Tc), whereas the horizontal boundaries are modeled as square and are designed to be thermally adiabatic, except the centrally heated portion on the bottom wall. The centered bottom heated section is supposed to be isothermal with linearly changing temperature, and it changes linearly from Th1 to Th2, whereas it is modelled as a non-isothermal condition. The main focus, in this investigation, is on the entire chamber filled with the combination of hybrid nanoparticles regarded the volumetric concentration of copper and alumina nanoparticles (Cu-50 %+Al2O3-50 %) along with base liquid (H2O). The transformed dimensionless partial differential equations were solved by using finite volume method (FVM) with power law differencing scheme. The simulated flow and temperature fields are scrutinized by streamlines, isotherms, entropy formations, total entropy generation and average convective Nusselt number associated with varying number of undulations (0 ≤ N≤3) volume fraction of hybrid nano liquid (0 ≤ φ ≤ 0.04) magnetic orientation angles (0° ≤ ς ≤ 135°), Hartmann number (Ha = 0 and 50), and dimensionless temperature drop (Ω = 0.001–0.1). From this study, it is found that the average Nusselt number and entropy generation increase as the solid volume fraction of hybrid nanoadditives increases, while opposite trend is observed when the values of Hartmann number rises. The findings show that growth of undulation number (N) causes the reduction of convective heat transfer rate as well as average entropy production intensity. The obtained outcomes concluded that hybrid nano liquid is more effective and finest choice for the improvement of cooling of heat transfer process and minimal energy loss than single nanoliquid. According to the new proposed criterion (TPC), the results show that square-shaped enclosure (N=0) manifests the better cooling performance among the considered governing parameters. The novelty of this study is to scrutinize the flat/ vertical wavy boundaries of the cabinet which can be represented as a model of heat transfer controller, in which it manages the thermal and flow field characteristics. Predominantly, the isothermal line source is used to boost the overall convective heat transfer which is applied in buildings and fluid-mounted heaters. Additionally, many investigators have focused only on the enhancement of heat transfer. As it is known, to increase the thermodynamic efficiency of a system, optimization of entropy generation is an excellent tool which reduces the loss of energy. Hence, it recently does a good engineering sense to highlight an entropy irreversibility.

Modeling of thermal radiation in a participating media with conjugate heat transfer

AbstractModeling a combination of thermal radiation and conjugate heat transfer in a three‐dimensional rectangular domain which has a participating media CO2 flowing through is done numerically in OpenFOAM. The rectangular duct has a vertical step (facing forward to the inlet) which is located at a distance from the inlet (the distance is same as the height of the inlet section). The domain is divided into two regions (namely solid and fluid). Carbon dioxide, a highly absorbing fluid with extinction, is used here as the participating medium. The ability of the code is verified to analyze the thermal radiation in a participating media with conjugate heat transfer. The study was carried out for a constant Reynolds number 250 and a contraction ratio of 0.5. The study focused primarily on the importance of adding thermal radiation on to thermal analysis and the reason behind the Nusselt number variation on different regions of solid–fluid interface. It also discussed the effect of radiative properties, such as optical thickness and linear scattering albedo, on the average convective Nusselt Number.

Optical and thermal investigation of hyperbolic cavity receiver with secondary reflector for solar parabolic dish collector

A hyperbolic-shaped cavity-type receiver with a second stage reflection for a 40 m2 solar parabolic dish concentrator (PDC) is presented in this paper,along with optical and thermal modeling. The receiver geometry and the secondary reflector complete the hyperbolic geometrical shape of the present receiver. This study aims to estimate heat losses owing to natural convection and radiation under influential parameters associated with solar parabolic dish system. Optical modeling has been performed with verified model using ASAP® 2013 V1R1. The optical simulations have been carried out for varying receiver height (h1), height of the secondary (h2) and diameter-to-total height ratios (d/h) of 0.5, 1, and 1.5 while keeping the diameter of the plane aperture of the receiver (d) constant. The optimum receiver geometry has been selected based on the performance in terms of optical efficiency. The maximum efficiency found is 91.72% for h1 = 0.75 m and d/h = 0.5 for the mounting distance of 4.21 m. The optimized shape is further studied to determine how the receiver absorptivity and the secondary reflector's reflectivity affect the optical performance. The absorptivity and reflectivity range from 0.86 to 0.94. Obtained optimum receiver geometry from the optical investigation is further analyzed to estimate the heat transfer rate. The thermal modeling is performed for 0°, 30°, 60°, and 90° orientations of the receiver in ANSYS Fluent 2020 R1. A comprehensive comparison among the available models has been reported and validated with well-established experimental data. This work has developed free convective Nusselt number correlation. It can be a valuable addition to the existing literature.

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%.

Natural convection–thermal radiation interaction in a non-Newtonian nanofluid-filled square cavity with a conductive baffle

This research aims to investigate the combination of natural convection and surface and volumetric radiation in water-aluminum oxide nanofluid with non-Newtonian effects in a square cavity with a conductive baffle on its hot wall. The left wall is hot while the right one is cold. Moreover, the horizontal walls are insulated, and the internal walls are radiatively active. The mass, momentum, and energy conservation equations are solved numerically using the control-volume-based finite difference method and the SIMPLE algorithm considering the surface radiation for the interior surfaces of the cavity and volumetric radiation for the non-Newtonian nanofluid. The volumetric radiation term in the energy equation is approximated using the Rosseland method. The effect of the Rayleigh number (Ra), the power-law index, and the volumetric radiation parameter on the flow field and the heat transfer rate are investigated using the numerical analysis results. Based on the results, an increase in Ra and a decrease in the power-law index lead to a rise in the heat transfer rate at a constant radiation parameter. As the Ra rises in the range, the average Nusselt number increases to 10 times at n = 0.8. Moreover, a rise in the volumetric radiation parameter increases the radiative Nusselt number and decreases the convective Nusselt number in both shear thickening and shear thinning fluids, although it increases the overall Nu. Increasing the volumetric radiation parameter from 0 to 2 enhances the average Nusselt number by more than 2.5 times at Ra = 103 and less than 2 times at Ra = 105.

Convective heat transfer in a thermal chimney for freshwater production in geothermal total flow systems

The convective heat transfer of air in a laboratory-scale thermal chimney with rectangular cross-section of constant area and two row electrical heaters simulating two heat exchangers was studied experimentally and numerically at 60–200 ℃ nominal temperatures of the top row heaters, 100 ℃ of the low row heaters and 20 ℃ ambient temperature to verify our design concept on freshwater production in geothermal total flow systems. Computational fluid dynamics simulations of air convective heat transfer were performed in ANSYS 2019R CFX based on the three-dimensional, steady Reynolds-averaged Navier-Stokes equations, Boussinesq buoyancy model, k-ω turbulence model, and energy equation. The thermal radiation between heater surfaces and chimney walls was considered. The overall thermal and heat transfer characteristics, temperature and flow fields in the chimney were obtained. Effects of boundary condition of heater surface and thermal radiation between two row heaters on heat transfer were discussed. The thermal characteristics of the chimney with two row heaters are better than that with single row heaters. The predicted thermal power and convective Nusselt number agree with the experimental data, and the convective Nusselt number of the low row heaters is enhanced by (11.6–29.8) % compared with the single row heaters. The optimal operating nominal temperature of top row heaters should be higher than 140 ℃, and the optimal centre-to-centre row gap ratio is 5. Multiple jets in the gaps among the heaters and temperature jump crossing each row were observed. The maximum velocity and temperature jump rise with increasing heater nominal temperature.

Effect of humidity level and aspect ratio on convective heat transfer coefficient and water productivity of a solar still: Experimental and theoretical analysis

This article proposes a new correlation to estimate the convective heat transfer coefficient inside the evaporation chamber (enclosed space over the basin) of a single slope solar still with a low humidity level. The Rayleigh number, aspect ratio (width to the average height of chamber) and the relative humidity of the chamber are the main variables in proposed correlation. Existing models use only Rayleigh number to characterise the convection and neglect the effect of vapour pressure. Therefore, they fail to accurately predict the convection in higher water temperatures or in unsaturated humidity levels. In this work, the natural convection Nusselt number is generated based on a theoretical approach and the constant values in the correlation are calculated using the multiple linear regression analysis on experimental data obtained in this work. The transient thermal model of solar still using the new correlation predicts daily water yield within 7.6% of experiments under different humidity levels and aspect ratios. Higher performance is obtained in larger aspect ratio and lower humidity inside solar still. The modified solar still with a relative humidity of 62% generated 3.49 kg m−2 d−1 of water during summer in Melbourne, demonstrating an 18% increase in water yield.

Natural convection of large Prandtl number fluids: A controversy answered by a new thermal lattice Boltzmann model

The purpose of this work is to deepen our understanding of natural convection with large Prandtl number fluids and to resolve some controversies in the previous publications. To achieve this purpose, a new thermal multiple-relaxation-time lattice Boltzmann model is proposed. Natural convection in a square cavity, a benchmark test case, is investigated numerically using the new model. The Prandtl number is up to 100. For the first time, it is numerically observed that there are two critical Prandtl numbers in the natural convection, which will affect the correlation between the Nusselt number and Prandtl number critically. Three heat transfer characteristic ranges of natural convection are defined in this work, according to the two critical Prandtl numbers. In each range, the dominant heat transfer mechanism is different, which can solve a long-standing issue in the discipline of heat and mass transfer: completely opposing statements on the correlation between the Nusselt number and Prandtl number for natural convection, were published in the open literature. For the first time, this work reveals cause behind the controversial reports and provides the guidance for the future research.

Simultaneous development of the hydrodynamic and thermal boundary layers of mixed convective laminar flow through a horizontal tube with a constant heat flux

The thermal and hydrodynamic features of developing mixed convective laminar flow in a long horizontal tube were numerically and experimentally investigated. The tube was heated at different constant heat fluxes and had an inner diameter of 11.52 mm and a total length of 9.5 m. Numerical simulations were conducted using ANSYS-Fluent 19.3 with a highly structured mesh and accurate temperature-dependant thermophysical properties for water. The studied parameters consisted of the wall temperatures, Nusselt numbers, vorticity, velocity and temperature gradients, hydrodynamic and thermal boundary layer development, secondary flow, as well as significant momentum terms. By analysing the vorticity characteristics, it was found that our conventional understanding of the merging boundary layer in internal tube flows had to be modified. Subsequently, methods were proposed to determine the development of the hydrodynamic and thermal boundary layers, as well as the momentum terms. The experimental and numerical results indicated that the local mixed convective Nusselt numbers decreased near the tube inlet but then increased along the tube length as secondary flow increased significantly. Furthermore, an increase in secondary flow led to a decreased thermal entrance length but increased hydrodynamic entrance length. By analysing the simultaneous development of the hydrodynamic and thermal boundary layers, it was revealed that the entrance region of a mixed convective laminar flow could be divided into six regions: (1) hydrodynamic inlet region, (2) buoyancy development region, (3) buoyancy dominating region, (4) buoyancy settling region, (5) hydrodynamically stabilising region, and (6) fully developed region.

Heat transfer by natural convection and radiation in three dimensional differentially heated tall cavities

Natural convection coupled with radiation is numerically studied in a tall rectangular parallelepiped cavity filled with air and constant differentially heated opposite vertical walls. This type of tall cavity is found in walls built with hollow blocks. Three dimensional steady state numerical simulations are performed. Numerical models for pure natural convection and natural convection coupled with radiation are validated with experimental results. In this work, the tall cavity studied has a 0.06 m width, 0.155 m depth and a 2.56 m height, giving a vertical aspect ratio of A=42.7 and a horizontal aspect ratio of A′=2.6. The cold wall temperature, Tc, is fixed. The hot wall temperature, Th, is varied, obtaining the Rayleigh numbers: RaW, 1.01×104, 1.07×105 and 7.20×105. The emissivity, ϵ, varies from 0.0 to 1.0. The results show that with a given Th, the convective Nusselt number, Nuc, depends on ϵ. For the emissivity value of hollow block materials (ϵ=0.8) the radiative heat transfer represents 83% for the lowest Th. For pure natural convection, a Nuc correlation as a function of RaW is obtained. A simplified calculation of the total heat transfer, Nut, is proposed.

Heat Transfer Characteristics of an Aeroengine Turbine Casing Based on CFD and the Surrogate Model

A good turbine casing cooling design should control the thermal stress and maintain a reasonable tip clearance between the turbine blade and the casing. Since the turbine inlet temperature has been increased yearly, the influence of thermal radiation on the temperature of a turbine casing has become more significant. Therefore, the heat transfer characteristics of a turbine casing considering the radiation effect need to be precisely predicted. In this study, a theoretical model is established for describing the heat transfer characteristics of a turbofan casing, and the model’s effectiveness is verified by comparing the numerical and experimental results. Based on the validated model, the effects of single changes of the wall temperature, cooling air temperature, Reynolds number, and surface emissivity on the heat transfer of the casing are discussed. The results show that the increment of cooling air temperature and surface emissivity leads to the enhancement of the average radiative Nusselt number, and the average convective Nusselt number increases as the Reynolds number increases. The emissivity can improve the temperature distribution uniformity of the turbine casing. Finally, a Kriging surrogate model is fitted with 20 sample points to predict the joint effect of multiple parameters on the casing surface Nusselt number. It is found that the Reynolds number has a more significant influence on the average Nusselt number compared with the emissivity and the temperature ratio.

Buoyancy-Driven Mixed Convection and Radiation Heat Transfer in a Tilted Vented Cavity

Abstract Experimental and numerical studies have been carried out to determine the impact of tilt angle on buoyancy-driven mixed convection coupled to surface radiation heat transfer inside a vented cavity. The present investigation might be rationalized in the thermal design of the electronic equipment housing, solar collector receiver, regenerative heating/cooling system, etc. Keeping the constant ventilation size and its location, the tilt angle measured from horizontal is varied from 0 deg to 90 deg with the increment of 15 deg. The experimental investigation comprising planner symmetry is complemented with the two-dimensional numerical study incorporating the range of Rayleigh number from 7.21 × 108 to 1.75 × 109, Reynolds number from 665 to 9931, Richardson number from 20.1 to 2283.4, and the surface emissivity from 0.05 to 0.85. The results signify that the convective Nusselt number enhances significantly at the optimum tilt angle of 90 deg, whereas the moderate increment in radiative Nusselt number is found at the optimum tilt angle of 0 deg. Based on the obtained experimental data, the empirical correlations of the average convective Nusselt number and dimensionless temperature are developed in terms of Reynolds number, Richardson number, and tilt angle.

Investigation of convective heat transfer from a high temperature prolate spheroid to moving fluid

Most of the currently used fluid-solid heat transfer models assume that solid particles are perfect spheres. Heat transfer between non-spherical particles and flowing fluids acquires great importance in many engineering appliances. A numerical study is performed on airflow past a stationary confined prolate spheroid under the forced convective heat transfer regime, and the influence of non-sphericity of the particle on their heating rate is examined. The prolate spheroid is assumed to be maintained at a constant wall temperature. The effect of Reynolds number (Re) and Aspect Ratio (AR) on convective heat transfer rate and Nusselt number was investigated by solving steady-state Navier-Stokes and energy equations. The influence of the flow in terms of Reynolds number and the prolate spheroid aspect ratio was investigated. The spheroid’s surface temperature (Ts) was varied between 294 K and 1500 K. The simulations show that the mean Nusselt number has a positive dependence on Ts, AR, and Re. A new correlation was developed to predict the mean Nusselt number for a wide range of temperature differences. The new correlation consolidates the influence of aspect ratio, surface temperature, and Reynolds number, in contrast to the existing correlations that assume merely isothermal conditions to calculate the mean Nusselt number for spheroid particles.

Heat and Mass Transfer Correlations for Staggered Nanoporous Membrane Tubes in Flue Gas Crossflow

Abstract The use of transport membrane condenser (TMC) technology to recover heat and mass from the flue gas has been increasing recently. The heat and mass transfer from the TMC tube bundle have been studied experimentally and numerically, and several numerical models have been proposed. Although many heat transfer and pressure drop correlations are available for single-phase flows over tube bundles of solid walls, to the best of our knowledge, there is a lack of heat and mass transfer and pressure drop correlations for the porous membrane tubes with condensing flue gas that cover a wide range of parameters. In this study, the heat transfer, mass transfer, and pressure drop imposed by the crossflow ceramic nanoporous tubes in TMC have been studied numerically within wide ranges of tube diameters (4.57–7.62 mm), number of rows (2–24 rows), and Reynolds number (170–8900), under flue gas condensation. The turbulent flow of the flue gas mixture was modeled by the shear stress transport SST k−ω turbulence model. A hybrid/mixed condensation model written in user defined functions was employed to calculate the water vapor condensation rate. Numerical results with condensing flue gas are compared to available correlations for single-phase Nusselt number and pressure drops in the literature. It was found that except for selected conditions, the single-phase correlations noticeably differed from the TMC numerical results. Empirical TMC correlations for heat transfer and pressure drops with respect to condensation rate, number of rows, and the nanoporous membrane geometrical properties were derived thereby. The derived correlations for TMC show a good agreement with numerical data for all investigated parameters and can predict the 96% of the convective Nusselt number, overall Nusselt number, and friction factor inside the TMC within ±10%, ±10%, and ±15%, respectively. The effects of key parameters on the heat transfer, mass transfer, and pressure drops are illustrated and discussed in detail.

Predictions of Reynolds and Nusselt numbers in turbulent convection using machine-learning models

In this paper, we develop a multivariate regression model and a neural network model to predict the Reynolds number (Re) and Nusselt number in turbulent thermal convection. We compare their predictions with those of earlier models of convection: Grossmann–Lohse [Phys. Rev. Lett. 86, 3316 (2001)], revised Grossmann–Lohse [Phys. Fluids 33, 015113 (2021)], and Pandey–Verma [Phys. Rev. E 94, 053106 (2016)] models. We observe that although the predictions of all the models are quite close to each other, the machine-learning models developed in this work provide the best match with the experimental and numerical results.

Numerical assessment of thermal characteristics of metal foams of orderly varied pore density and porosity under different convection regimes

The present study is done to analyze heat transfer and fluid flow in a channel with orderly varied pore density and porosity combination of foam samples. Darcy Forchheimer flow and LTNE thermal models are considered to estimate heat transfer characteristics. Considering the effect of orderly varied combinations of the dual structural properties, forced convection over a range of flow velocities and natural convection phenomenon are studied numerically in the channel housing porous samples. Two limiting solutions for Nusselt number (Nu) i.e., Nun (for natural convection) and Nuf (for forced convection) for Ri→∞ and Ri→0 respectively, as a function of independent variable Richardson number (Ri) with structural properties pore density and porosity are obtained with the help of local thermal non-equilibrium (LTNE) thermal model and Darcy-Forchheimer flow model. Further these asymptotic solutions are blended using technique illustrated in the literature in order to obtain solution for Nusselt number for mixed convection (Num). Correlations for Nusselt number as a function of combination of porosity and pore density are obtained emphasizing on the varied significance of these parameters in different convection regime. The present study not only emphasizes on effect of combination of structural properties of metal foams on heat transfer characteristics, but also illustrates a technique that enables to arrive at suitable correlation for an intermediate phenomenon existing between two other extremes, with zero computational cost. Effect of pore density on heat transfer characteristics at a given porosity, is found to be not much influencing in natural convection dominant regime. However, in mixed and forced convection dominant scenario it is illustrated that, effect of variation in pore density and porosity plays a significant role in expressing distinguishable heat transfer characteristics, along with other well-known independent parameters such as porosity and Reynolds number.

Heat transfer and performance analysis of SAH having new transverse finned absorber of lateral gaps and central holes

An experimental work is presented on the performance of solar air heater (SAH) has new designed absorber of finned transverse plate of lateral gaps and central holes. Moreover, a complete heat transfer analysis of the radiation and convection and SAH thermal performance are presented and discussed. The performance of this transverse SAH (TR_SAH) is compared with identical conventional flat plate SAH (FP_SAH) for single (SP) and double-pass (DP) airflow and air mass flow rates (AMFR) of 0.025, 0.05, and 0.075 kg/s. The experimental study is performed under hot climate conditions of Upper Egypt. The findings show that for all studied cases, TR_SAH has higher energy gain, output air temperature, thermal efficiency, and Nusselt number on the absorber plate, thermal-hydraulic performance parameter, and pressure drop compared to FP_SAH. The energy loss and radiation and convection Nusselt number on the TR_SAH glass plate is lower than that of FP_SAH. The maximum TR_SAH energy efficiency of value of about 89% is achieved in the case of DP airflow and high AMFR of 0.075 kg/s, with an enhancement of 24.2% compared to FP_SAH. The higher TR_SAH efficiency at these conditions reflects the optimal TR_SAH absorber design especially at high AMFR and using DP airflow. Despite TR_SAH air pumping power is greater than FP_SAH but it has a negligible effect on net energy gain.

Poiseuille-Rayleigh-Bénard mixed convection flow in a channel: Heat transfer and fluid flow patterns

In the present work, a numerical and experimental study of mixed convection of water flow in a horizontal channel subjected to a constant heat flux is presented. An experimental setup was constructed to delineate the fluid flow patterns inside the channel, while a numerical simulation was performed to study the heat transfer characteristics of the flow. This study is performed for Rayleigh and Reynolds numbers in the range of 104 ≤ Ra≤ 106 and 25≤ Re≤ 100, respectively. The present predicted results are in good agreement with the experimental ones. The longitudinal evolution rolls revealed the existence of four zones corresponding to the entry zone, establishment zone, destabilization zone, and turbulent zone. Moreover, numerical simulations showed that the Nusselt number for the mixed convection gives higher heat transfer coefficient compared to forced convection. In addition, new correlations for the Nusselt number have been developed for the first time for the establishment length, onset and established zones as a function of Rayleigh and Reynolds numbers.

Studies on Nusselt and Sherwood number for diffusion-advective convection during physical vapor transport of Hg 2 Br 2

Studies on Nusselt and Sherwood number for diffusion-advective convection during physical vapor transport of Hg 2 Br 2