This paper presents the results of a numerical simulation for the natural convection inside an enclosure that has an inner open square at its center. The inner square is open at the top and connected to the ceiling of the enclosure. The open inner square distorts the convection patterns, slows down the flow, and provides a compartment to confine the fluid at the core of the enclosure. Ultimately, this lowers the local Nusselt number, Nu, along the hot wall, and reduces the heat flux through the enclosure. The analysis shows the effects of changing the dimensions of the inner square on the heat flux through the enclosure for a range of Rayleigh numbers- from 10 3 to 10 6 . Short-sided inner squares work as flow deflectors while long-sided inner squares provide compartments to accommodate new flow circulation at the core of the enclosure. The inner square is most effective when the length of its sides equals the width of the stagnant core inside the empty enclosure at the same Rayleigh number, and the heat flux at this condition is the lowest. Inner squares made of thermally conducting materials can reduce the heat flux through the enclosure by 70%, while adiabatic inner squares can reduce the heat flux by 90%. Inner squares reduce the external heat load on buildings when fitted inside the holes of hollow bricks used in building facades. The external heat flux can be lowered by 30%–55% depending on the material of the inner square and outer side temperature.

Conjugate pure mixed convection in a differentially heated square cavity with two vertically placed heat conductive revolving cylinders has been analyzed in a computational approach applying the finite element method. This analysis has been implemented considering the upper and lower wall as insulated simultaneously and the left vertical wall as heated maintaining constant temperature (i.e., isothermally heated) and the right vertical wall as isothermally cooled. The outcomes of this study have been examined concerning streamlines, isotherms, average Nusselt number (Nu) which unveils a noteworthy fact that both the rotating cylinders' inclination patterns and Reynolds number (Re) have a vital role upon the average Nusselt number (Nu), flow pattern, and isotherms. From that perspective, best heat transfer phenomena have been observed for counterclockwise circulation of both cylinders so that the condition for these cases has been assessed from a distance variation between the two cylinders maintaining a constant speed ratio ( Ω ). Moreover, the best result from this assessment has been trialed changing the type of materials of the rotating cylinders and ultimately, the best one has been specified as well as tested for various speed ratios. In the end, the results have been compared with the stationary cylinders where a similar type of results have been observed, but for rotating ones, Nusselt number (Nu) has been observed higher than stationary ones.

Two-dimensional (2D) numerical experiments are performed to investigate the flow instabilities and mixing of different nonisothermal counterflowing jets in a passive-mixer. The fluid is modeled as a binary mixture with thermal and solutal buoyancy effects considered through the Boussinesq approximation. The streams are arranged in a thermal and solutal buoyancy aiding configuration. Computations are carried out for three different ratios of the upper jet bulk velocity to the lower jet bulk velocity (VR), namely, VR = 0.5, 1.0, and 2. Within the parametric domain of Ri T and Ri C defined by region (Ri T + Ri C ) ≤ 3, the instability causing transition from steady to unsteady flow regime is observed for VR = 1 and 2, while no transition is found to occur at VR = 0.5. Using Landau theory, it is established that the transition from steady to unsteady flow regime is a supercritical Hopf bifurcation. A complete regime map identifying the steady and unsteady flow regimes, within the parametric space of this study, is obtained by plotting the neutral curves of Ri C and Ri T (obtained using Landau theory) for different values of VR. Proper orthogonal decomposition (POD) analysis of the unsteady flows at VR = 1 establishes the presence of standing waves. However, for VR = 2, the presence of degenerate pairs in the POD eigenspectrum ascertains the presence of traveling waves in the unsteady flows. The standing wave unsteady flow mode is found to yield the highest rate of mixing.

The thermoconvective instability of the parallel vertical flow in a fluid saturated porous layer bounded by parallel open boundaries is studied. The open boundaries are assumed to be kept at constant uniform pressure while their temperatures are uniform and different, thus forcing a horizontal temperature gradient across the layer. The anisotropic permeability of the porous layer is accounted for by assuming the principal axes to be oriented along the directions perpendicular and parallel to the layer boundaries. A linear stability analysis based on the Fourier normal modes of perturbation is carried out by testing the effect of the inclination of the normal mode wavevector to the vertical. The neutral stability curves and the critical Rayleigh number for the onset of the instability are evaluated by solving numerically the stability eigenvalue problem.

The influence of real gas radiation on the thermal and hydrodynamic stability of a two-dimensional layer of radiatively participating H 2 O and/or CO 2 heated from below is investigated. The nongray radiation effects of the two species are treated rigorously using a global spectral approach, the Spectral Line Weighted-sum-of-gray-gases model. The phenomena are explored by solving the full coupled laminar equations of motion, energy, and radiative transfer from the low-Rayleigh number, pure conduction-radiation regime through the onset of buoyancy-induced flow to the developed Bénard convection regime. The evolution of the thermal, hydrodynamic, and radiative heating fields is studied, and the critical Rayleigh number is characterized as a function of participating gas species mole fraction, average layer gas temperature, layer thickness, wall emissivity, and total pressure. It is found that participating radiation in the medium has the effect of stabilizing the layer, delaying transition from a stable conduction regime to buoyancy-induced flow. The development of convective flow and temperature, along with the radiative heating are presented. It is found that the critical Rayleigh number in the radiatively participating gas layer can be more than an order of magnitude higher than the classical convection-only scenario. The onset of instability is found to depend on the species mole fractions, average gas temperature in the layer, wall emissivity, layer thickness, and total pressure. Generally, all other variables being the same, H 2 O has a greater stabilizing influence on the layer than CO 2 .

For the very first time, this study attempts to address the heat dissipation from an isothermal ribbed sphere under the action of pure natural convection. Semicircular ribs of different radii are superimposed azimuthally on the outer surface of a sphere. The addition of ribs on the sphere serves a dual purpose in its practical applications: beautification of electronic devices such as spherical light sources as well as an increase in heat dissipation from the hot surface, which prevents the electronic component from getting overheated. Finite volume method-based axisymmetric numerical simulations are performed in the laminar flow regime for the following ranges of nondimensional parameters: Rayleigh number (10 2 ≤ Ra ≤ 10 8 ), inter-rib-spacing to sphere diameter (0.191 ≤ P/D ≤ 0.785), and rib-radius to sphere diameter (0.03 ≤ R/D ≤ 0.083). The main target of this study is to identify the critical parameters for heat transfer enhancement from the ribbed sphere compared to a conventional plane sphere. The results obtained from this work show that the average Nusselt number increases with an increase in Ra and P/D, whereas it decreases as R/D increases. Effectiveness of the ribs ( ε rib ) and critical Rayleigh numbers (Ra cr ), corresponding to ε rib = 1, are also calculated. Ribs are more effective in heat dissipation at low Ra and P/D and high R/D. A correlation for the average Nusselt number is also developed in this work, which would help design a better thermal management system.

In this study, a numerical investigation on mixed convection inside a trapezoidal cavity with a pair of rotating cylinders has been conducted. Three different power-law fluid indexes (n = 1.4, 1.0, and 0.6) have been considered to model different sets of non-Newtonian fluids. Four separate cases are considered based on the rotational orientation of the cylinders within the cavity. In the first two cases, the cylinders rotate in the same direction, i.e., both counterclockwise (CCW), and both clockwise (CW), whereas, in the other two cases, cylinders rotate in opposite directions (CW–CCW and CCW–CW). Simulations have been carried out over a broad range of Reynolds number (from 0.5 to 500) and angular speeds (a dimensionless value from 0 to 10). The average Nusselt number values at the isothermal hot inclined cavity surface are determined to evaluate heat transfer performance in various circumstances. Streamlines and isotherm contours are also plotted for a better understanding of the effects of different cases for various parameters on thermal and fluid flow fields. It is found that the Nusselt number varies nonlinearly with different angular speeds of the cylinders. The combined effect of the mixing induced by cylinder rotation and viscosity characteristics of the fluid dictates the heat transfer in the system. Predictions from the numerical investigation provide insights into the sets of key parametric configurations that have a dominant influence on the thermal performance of the lid-driven cavity with double rotating cylinders.

Single-phase natural circulation thermosiphon loops have been attracting increased interest as they represent the prototype of passive safety systems. However, the stability properties of thermosiphon loops, which can affect and compromise their functionality, are still actively investigated. Traditionally, the stability analysis of thermosiphon loops has been simplified to one-dimensional (1D) calculations, on the argument that the flow would be monodimensional when the diameter of the pipe D is orders of magnitude smaller than the length of the loop L t . However, at lower L t /D ratios, rectangular thermosiphon loops show that the flow presents three-dimensional (3D) effect, which also has been confirmed by stability analyses in toroidal loops. In this paper, we performed a series of high-fidelity simulations using the spectral-element code nek 5000 to investigate the stability behavior of the flow in rectangular thermosiphon loops. A wide range of L t /D ratio from 10 to 200 has been considered, and the results show many different outcomes compared to previous 1D analytical calculations or stability theory. Moreover, we analyzed the flow in rectangular thermosiphon loops using proper orthogonal decomposition (POD), and we observed that the cases without flow reversal are characterized by swirl modes typical of bent pipes and high-frequency oscillation of the related time coefficients obtained by Galerkin projection. However, the swirl mode was not observed in cases with flow reversals, and these cases are characterized by symmetric flow field at second POD mode and the similarity of low-frequency oscillation in the projection of POD modes.

The mixed convection in a thin liquid film flow over a horizontal plate is investigated under finite Prandtl numbers. The gas–liquid interface is considered free, nondeformable and subject to surface tension gradients and convection, while gravity is assumed negligible. Therefore, thermocapillary instead of buoyancy effects appears due to the unstable temperature stratification induced by the internal heating generated by viscous dissipation. A linear and modal stability analysis of this model is then performed to identify its convective/absolute nature. This is achieved by solving the resulting differential eigenvalue problem with a shooting method. Longitudinal rolls are the most unstable at the onset of instability for most parametric conditions. Otherwise, transverse rolls are the first to become convectively unstable. Finally, longitudinal rolls are absolutely stable. A transition to absolute instability occurs through transverse rolls, but only within a limited region in parametric space.

An experimental and numerical smoothed particle hydrodynamics (SPH) analysis was performed for the convective flow arising from a horizontal, thin cylindrical heat source enclosed in a glycerin-filled, slender enclosure at low Rayleigh numbers ( 1.18 ≤ Ra ≤ 242 ). Both the experiments and the SPH calculations were performed for positive ( 0.1 ≤ Δ T ≤ 10 K) and negative ( − 10 ≤ Δ T ≤ − 0.1 K) temperature differences between the source and the surrounding fluid. In all cases, a pair of steady, counter-rotating vortices is formed, accompanied by a plume of vertically ascending flow just above the source for Δ T > 0 and a vertically descending flow just below the source for Δ T < 0 . The maximum flow velocities always occur within the ascending/descending plumes. The SPH predictions are found to match the experimental observations acceptably well with root-mean-square errors (RMSE) in the velocity profiles of the order of ∼ 10 − 5 m s −1 . The fact that the SPH method is able to reveal the detailed features of the flow phenomenon demonstrates the correctness of the approach.

Three-dimensional continuity, momentum, and energy equations have been solved around a perforated vertical hollow cylinder to predict the buoyancy-induced flow field and the temperature distribution around it. Finite volume method (FVM) has been implemented for the discretization of the underlying governing equations. Second-order upwind scheme has been adopted to discretize the convective terms in the momentum and energy equation. Results have been obtained by varying the input parameters like hole diameter to cylinder length ratio (d/L), pitch to length ratio (P/L), angular pitch ( θ ), cylinder length to diameter ratio (L/D), and Rayleigh number (Ra) spanning from 0.005 to 0.08, 0.1 to 0.3333, 30 deg to 180 deg, 2 to 20, and 10 4 to 10 8 , respectively. It has been found that the average surface Nusselt number (Nu) for the outer surface increases with the diameter of the hole for Ra of 10 6 , however for Ra of 10 8 , it marginally decreases up to d/L of 0.01 and then increases. Nu for the inner surface increases when d/L is more than 0.04 for all Ra. The cylinder with the staggered holes shows a slightly higher Nu compared to the inline holes. Nu for the inner and outer surface at a lower pitch is less than that of the higher pitch when d/L is less than 0.02 for all Ra. The heat transfer rate of the perforated cylinder is more than the nonperforated cylinder for all the cases when L/D is less than 10 and Ra less than 10 6 . However, for Ra more than 10 6, the perforated cylinder always loses more heat compared to the nonperforated one for all L/D. Finally, the correlation for Nu has been proposed as a function of the pertinent input parameters for future reference in the academic as well as industrial practices.

This paper reports the numerical investigations for steady-state natural convection in power-law fluids inside a square enclosure embedded with bottom discrete heaters. The lattice Boltzmann method (LBM) is employed to model the flow and heat transfer phenomenon at different combinations of power-law index, Rayleigh number, and heat source length for a constant Prandtl number. The buoyancy force is incorporated in the collision term of the LBM through Boussinesq approximation. Simulation outcomes are furnished using streamlines, temperature contours, velocity profiles, and variation of heat transfer on the nonadiabatic walls to probe natural convection phenomena. The results indicate that the temperature and the flow fields in the enclosure are symmetric about the vertical centerline. The detailed physical interpretations have been provided for the reported results. Further, the increase in the power-law index means a rise in viscosity and a decrease in thermal energy transport for other constant parameters. The outcomes also specify that the intensity of circulation and heat transfer enhances with the increase of Rayleigh number and size of the localized heater. Finally, though, a rise in the size of the confined heat source enhances the rate of total thermal transport, it does not change the trend of fluid flow and local heat transfer rate.

Numerical investigations are performed on natural and mixed convection around stationary and rotating vertical heated hollow cylinder with negligible wall thickness suspended in the air. The fluid flow and heat transfer characterization around the hollow cylinder are obtained by varying the following parameters, namely, Rayleigh number (Ra), Reynolds number (Re D ), and cylindrical aspect ratio (L/D). The heat transfer quantities are estimated by varying the Rayleigh number (Ra) from 10 4 to 10 8 and aspect ratio (L/D) ranging from 1 to 20. Steady mixed convection with active rotation of hollow vertical cylinder is further studied by varying the Reynolds number (Re D ) from 0 to 2100. The velocity vectors and temperature contours are shown in order to understand the fluid flow and heat transfer around the vertical hollow cylinder for both rotating and nonrotating cases. The surface average Nusselt number trends are presented for various instances of Ra, Re D, and L/D and found out that the higher rate of heat loss from the cylinder wall occurs at high Ra, low L/D (short cylinder) and high Re D .

The effect of high frequency vibration in the gravity field on the double-diffusive convection in a two-layer system with a viscoelastic fluid-saturated porous layer is studied. The averaging method is employed to split the unknown functions into a periodic rapidly varying part and a slower mean part. Then, the governing equation of perturbations is numerically solved by the Chebyshev tau method and QZ decomposition method. The influence of physical parameters on the stability of system is investigated. It is shown that the neutral stability curves are bimodal under high frequency vibration. The parameter of the high frequency vibration mainly stabilizes the pure fluid layer for greater wave numbers and has a weak impact on the whole system for smaller wave numbers.

Mixed convection heat transfer in a vertically oriented air-cooled square enclosure is simulated numerically using the finite volume method. The vertical left wall being heated and all others are considered insulated. The effects of six opposite and staggered inlet/outlet openings' locations over the top and bottom walls are investigated, with different sizes of the opening height (0.05 ≤ d / H ≤ 0.3). The objective is to figure out the better size and location of inlet and outlet to acquire more efficient cooling system in the enclosure by maximizing the heat removal rate. This is conducted over ranges of the governing parameters, which are the Richardson number (0 ≤ Ri ≤ 30) and the Reynolds number (50 ≤ Re ≤ 250). The results show that the level of heat transfer enhancement increases with increasing the opening height, with an optimal size of d/H = 0.25 for obtaining maximum heat removal, for all Richardson and Reynolds numbers. The results also indicate that the higher heat dissipation occurs when the cold air is injected vertically near the hot wall and exits the enclosure from the opposite or staggered outlet, for all Richardson and Reynolds numbers.

The influence of the thermophysical variable properties on the buoyancy-driven flows of liquid sodium and gallium established in a cylindrical cavity is numerically investigated, for the entire range of Rayleigh number corresponding to practical applications. Axisymmetric turbulent simulations (initially steady) are obtained, considering appropriate boundary and reference conditions for simulating the emergency cooling of a nuclear reactor. The results obtained for different heating intensities are analyzed and compared. In the case of sodium, the expected decay in the heat transfer coefficients is less relevant than that previously obtained for airflows. In turn, strong differences in the gallium thermal behavior are encountered. In fact, a trend opposite to that of sodium is detected for wide ranges of Rayleigh number and heating parameter. Additional transient simulations are carried out to complete a comparative assessment of the performance of both liquid sodium and gallium as cooling agents.

This report presents an investigation of the characteristics for transitional natural-convection flow in an open-ended inclined channel heated from below in the air under uniform heat flux intensity and non-Boussinesq condition. The investigated range of modified Rayleigh number and inclination is from 5.93 × 10 6 to 1.45 × 10 9 and 30 – 90 deg to the horizontal, respectively. Fine-resolution implicit large Eddy simulation is performed to solve the compressible governing equations using the modified preconditioned all-speed Roe scheme, hybrid boundary condition, and dual-time-stepping technique. The Nusselt number based on the maximum wall-temperature differs significantly while based on averaged wall-temperature is closer to the previously proposed laminar correlations. Transition is found to be pronounced at a lower angle of inclination ( 30 deg ) for the considered heat flux intensity. The absolute magnitude of the critical length for the start and end of the transition when converted to nondimensional parameters is found to be higher compared to similar data for natural convection flow over a flat plate in water but the ratio of the end to start of the transition is found to be comparable. Single-roll longitudinal vortices periodically placed in spanwise direction exists in the transition region whose wavelength is found to be higher than those reported for channel flow under the isothermal condition and flow over a flat plate in water. Correlations for Nusselt number, critical aspect ratio, and vortex wavelength to the modified Rayleigh number are presented.

The use of approximate boundary conditions at the opening of the cavities leads to restriction of the computational domain and, hence, the reduction in computational effort. However, the accuracy of the restricted domain approach (RDA) had been evaluated only for the natural convection inside open cavities and that too only for one aspect ratio (AR). The validity of the approach had not been evaluated for inclined, as well as, shallow cavities. This study focuses on the analysis of the accuracy of RDA against extended domain approach (EDA) in open cavities of different ARs, at different inclinations and different Rayleigh numbers (Ra). The results show that the difference between the approaches is only significant in very shallow cavities (AR is defined as the height of the hot wall divided by the depth of the cavity) at low Ra. For Ra higher than 10 6 and an AR greater than 0.2, the maximum difference between the two approaches is around 5% and hence RDA can be recommended in these ranges, resulting in increased computational efficiency without significant loss in the accuracy. Moreover, the maximum difference in the results for the two methods is for intermediate inclinations. Even there, an increase in the difference is more pronounced at lower Ra. Furthermore, distribution of the exit velocity and temperature at the opening as well as the distribution of the Nusselt number at the hot wall is compared for RDA and EDA to explain the behavior of error at different ARs and inclinations.

Experimental analysis of the onset of buoyancy-driven convection in a top facing high aspect ratio cavity is reported. Bottom surface of the cavity is heated, with its two vertical side walls being insulated. Thermal field in the cavity has been non-intrusively mapped using a Mach–Zehnder interferometer. The cavity has been subjected to two different temperature differences, ΔT = 3 °C (Ra ≃ 300) and ΔT = 15 °C (Ra ≃ 1400). Sudden change in the heat transfer coefficient as well as the formation of thermally stratified layers at the bottom part of the cavity was not observed for the applied cavity temperature differences, which in turn, indicates that there is no such phenomenon of onset of buoyancy-driven convection in high aspect ratio cavities. Corner flow, induced due to the temperature difference between the atmosphere and the cavity, is the dominant flow inside the cavity. Almost identical profiles of flow in both the cases of the applied temperature potentially signify that the flow profile is independent of the Rayleigh number or the temperature differences. These observations have been supported by whole field temperature distribution profiles, spatial distributions of local Nusselt number, and nondimensional temperature at different position of the cavity.

The simultaneous effect of a time-dependent velocity term in the momentum equation and a maximum density property on the stability of natural convection in a vertical layer of Darcy porous medium is investigated. The density is assumed to vary quadratically with temperature and as a result, the basic velocity distribution becomes asymmetric. The problem has been analyzed separately with (case 1) and without (case 2) time-dependent velocity term. It is established that Gill's proof of linear stability effective for case 2 but found to be ineffective for case 1. Due to the lack of Gill's proof for case1, the stability eigenvalue problem is solved numerically and observed that the instability sets in always via traveling-wave mode when the Darcy–Prandtl number is not larger than 7.08. The neutral stability curves and isolines are presented for different governing parameters. The critical values of Darcy–Rayleigh number corresponding to quadratic density variation with respect to temperature, critical wave number, and the critical wave speed are computed for different values of governing parameters. It is found that the system becomes more stable with increasing Darcy–Rayleigh number corresponding to linear density variation with respect to temperature and the Darcy–Prandtl number.