Prandtl number dependence of laminar natural convection heat transfer in a horizontal cylindrical enclosure with an inner coaxial triangular cylinder

A numerical study of laminar convection heat transfer from a horizontal triangular cylinder to its concentric cylindrical enclosure is performed to investigate the Prandtl number effect on flow and heat transfer characteristics. The Prandtl number over several orders of magnitude (10^?2 < Pr < 10³) as well as different aspect ratios (AR = 1.2 and 2.0) and different Rayleigh numbers (Ra = 10³, 10⁴, 10⁵, and 10⁶) are considered. The finite volume approach is used to solve the governing equations, in which buoyancy is modeled via the Boussinesq approximation. The computed flow patterns and temperature fields are shown by means of streamlines and isotherms, respectively, and the local and average heat transfer coefficients are also presented. It is found that the flow and heat transfer characteristics for a low Prandtl number fluid (Pr = 0.03) are unique and they are almost independent of Prandtl number when Pr ? 0.7. The entire spectrum of Prandtl number investigated can be divided into three sections based on the variations of average heat transfer coefficients. In each section, correlating equations of the average Nusselt number to the Rayleigh number are proposed with the maximum deviation less than 3%.     

Turbulent large-scale structures in natural convection vertical channel flow

We analyzed a database of a direct numerical simulation of natural convection in a vertical channel. The flow is driven by a constant temperature difference imposed at the walls (Ra = 5.4 × 10⁵, Pr = 0.7). The averaged flow and turbulent statistics are in good agreement with previous direct numerical simulations reported in the literature. Contrary to forced convection flows, the fluctuations of the heat transfer rate are uncorrelated with the fluctuations of the wall shear stress, which exhibit a symmetric probability density function. At the low Rayleigh number considered, the large-scale structures, which consist mainly in two counter-rotating vortices, with sizes comparable to the separation of the walls, are responsible for the extreme fluctuations of the wall heat transfer rate. The occurrence and the averaged topology of these structures have been determined using a conditional sampling technique.     

Finite element based heatline approach to study mixed convection in a porous square cavity with various wall thermal boundary conditions

A penalty finite element method based simulation is performed to analyze the influence of various walls thermal boundary conditions on mixed convection lid driven flows in a square cavity filled with porous medium. The relevant parameters in the present study are Darcy number (Da = 10^?5 ? 10^?3), Grashof number (Gr = 10³ ? 10⁵), Prandtl number (Pr = 0.7–7.2), and Reynolds number (Re = 1–10²). Heatline approach of visualizing heat flow is implemented to gain a complete understanding of complex heat flow patterns. Patterns of heatlines and streamlines are qualitatively similar near the core for convection dominant flow for Da = 10^?3. Symmetric distribution in heatlines, similar to streamlines is observed irrespective of Da at higher Gr in natural convection dominant regime corresponding to smaller values of Re. A single circulation cell in heatlines, similar to streamlines is observed at Da = 10^?3 for forced convection dominance and heatlines are found to emanate from a large portion on the bottom wall illustrating enhanced heat flow for Re = 100. Multiple circulation cells in heatlines are observed at higher Da and Gr for Pr = 0.7 and 7.2. The heat transfer rates along the walls are illustrated by the local Nusselt number distribution based on gradients of heatfunctions. Wavy distribution in heat transfer rates is observed with Da ? 10^?4 for non-uniformly heated walls primarily in natural convection dominant regime. In general, exponential variation of average Nusselt numbers with Grashof number is found except the cases where the side walls are linearly heated. Overall, heatlines are found to be a powerful tool to analyze heat transport within the cavity and also a suitable guideline on explaining the Nusselt number variations.     

Effect of a magnetic field on natural convection in an open cavity subjugated to water/alumina nanofluid using Lattice Boltzmann method

In this paper, the effect of a magnetic field on natural convection in an open enclosure which subjugated to water/alumina nanofluid using Lattice Boltzmann method has been investigated. The cavity is filled with water and nanoparticles of Al₂O₃ at the presence of a magnetic field. Calculations were performed for Rayleigh numbers (Ra = 10⁴–10⁶), volume fractions of nanoparticles (φ = 0,0.02,0.04 and .0.06) and Hartmann number (0 ≤ Ha ≤ 90) with interval 30 while the magnetic field is considered horizontally. Results show that the heat transfer decreases by the increment of Hartmann number for various Rayleigh numbers and volume fractions. The magnetic field augments the effect of nanoparticles at Rayleigh number of Ra = 10⁶ regularly. Just as the most effect of nanoparticles for Ra = 10⁴ is observed at Ha = 30, so the most influence of nanoparticles occurs at Ha = 60 for Ra = 10⁵.     

Effect of solid volume fraction and tilt angle in a quarter circular solar thermal collectors filled with CNT–water nanofluid

Solar thermal collectors have significant importance due to its wide use in solar thermal technology. Augmentation of heat transfer is a key challenge for solar thermal technology. A quarter circular solar thermal collectors is investigated throughout the paper introducing carbon nanotube (CNT)–water nanofluid in the cavity. Tilt angle of this type of collector plays a vital role and heat transfer can be maximized for a particular tilt angle and solid volume fraction of the nanofluid. Galerkin weighted residual of FEM has been applied for the numerical solution of the problem. Grid independency test and code validation have been assessed for the accuracy of numerical solution. In this paper a wide range of solid volume fraction (δ = 0 to δ = 0.12) and tilt angle (ϕ = 0 to ϕ = 60°) has been investigated for Rayleigh number (Ra = 10⁵–10⁸) with varying dimensionless times. It has been found that both solid volume fraction and tilt angle play vital roles for the augmentation of heat transfer and a good heat transfer characteristic can be obtained by compromising between these two parameters. The results are shown using streamline, isotherm contour and related graph and chart.     

Mixed convection from an open cavity in a horizontal channel

Heat transfer results for mixed convection from a bottom heated open cavity subjected to an external flow are reported in this study for a wide range of the governing parameters (i.e., 1 ≤ Re ≤ 2000, 0 ≤ Gr ≤ 10⁶) over cavities with various aspect ratios (A = 0.5, 1, 2 and 4). It has been found that the Reynolds number and Garshof number control the flow pattern and the occurrence of recirculating cells while the aspect ratio has a significant influence on the orientation of these cells. Heat transfer from the cavity base approaches that of natural convection at a low Reynolds number (i.e., the asymptotic natural convection regime) and approaches that of forced convection at a high Reynolds number (i.e., the asymptotic forced convection regime). In the mixed convection regime, the heat transfer rate is reduced and the flow may become unstable. A unique heat transfer correlation which covers all three convection regimes is also presented.     

Experimental investigation of the turbulent heavy liquid metal heat transfer in the thermal entry region of a vertical annulus with constant heat flux on the inner surface

The thermally developing turbulent lead bismuth (Pb⁴⁵Bi⁵⁵) flow within a vertical annulus with the inner surface uniformly heated is experimentally investigated. The ratio between internal and external diameter is 0.136. The investigated Reynolds numbers vary between 1.48 × 10⁴ and 2.37 × 10⁵ and the applied heat flux from 135 kW/m² to 905 kW/m², covering both the forced and mixed convection regime. For forced convection, the local heat transfer convective coefficient is evaluated and compared with literature correlations for low Prandtl number fluids. Additionally, a new empirical relation for the local Nusselt number in the thermal entry region is proposed. The applicability of criteria addressing the forced to mixed convection transition in medium to high Prandtl number fluids is reviewed and extended to account also for low Prandtl number fluids such as heavy liquid metals. Here, the transition from turbulent-diffusion to molecular-diffusion dominated mixed convection is clearly shown.     

Lattice Boltzmann simulation of natural convection heat transfer in eccentric annulus

In this article, the natural convection flow in eccentric annulus is simulated numerically by Lattice Boltzmann Model (LBM) based on double-population approach. A numerical strategy presents for dealing with curved boundaries of second order accuracy for both velocity and temperature fields. The effect of vertical, horizontal, and diagonal eccentricity at various locations is examined at Ra = 10⁴ and σ = 2. Velocity and temperature distributions as well as Nusselt number are obtained. The results show that the average Nusselt number increases when the inner cylinder moves downward regardless of the radial position. The validation with previous studies shows that double-population approach can evaluate the velocity and temperature fields in curved boundaries with a good accuracy.     

Experimental investigation of mixed convection heat transfer from longitudinal fins in a horizontal rectangular channel

Mixed convection heat transfer from longitudinal fins inside a horizontal channel has been investigated for a wide range of modified Rayleigh numbers and different fin heights and spacings. An experimental parametric study was made to investigate effects of fin spacing, fin height and magnitude of heat flux on mixed convection heat transfer from rectangular fin arrays heated from below in a horizontal channel. The optimum fin spacing to obtain maximum heat transfer has also been investigated. During the experiments constant heat flux boundary condition was realized and air was used as the working fluid. The velocity of fluid entering channel was kept nearly constant (0.15 ? w_in ? 0.16 m/s) using a flow rate control valve so that Reynolds number was always about Re = 1500. Experiments were conducted for modified Rayleigh numbers 3 × 10⁷ < Ra¹ < 8 × 10⁸ and Richardson number 0.4 < Ri < 5. Dimensionless fin spacing was varied from S/H = 0.04 to S/H = 0.018 and fin height was varied from H_f/H = 0.25 to H_f/H = 0.80. For mixed convection heat transfer, the results obtained from experimental study show that the optimum fin spacing which yields the maximum heat transfer is S = 8–9 mm and optimum fin spacing depends on the value of Ra¹.     

Analysis of entropy generation for distributed heating in processing of materials by thermal convection

Analysis of entropy generation has been carried out for square cavities with distributed heated sources filled with various materials involving wide range of Pr(=0.015, 0.7, 10, 1000) during the conduction and convection regime within Ra(=10³ ? 10⁵). Entropy generation terms involving thermal and velocity gradients are evaluated accurately based on elemental basis set via Galerkin finite element method. Local entropy maps are analyzed in detail for various cases and the dominance of thermal and frictional irreversibilities is studied via average Bejan number. The heat transfer irreversibility is found to dominate during conduction regime while the fluid friction irreversibility dominates the entropy generation in the convection regime, except for the low Pr fluid based on the heating configuration of the cavity. Further, the variation of total entropy generation has been observed to be similar for different heating configurations for higher Pr fluids (=10, 1000) whereas, the configuration of cavity has been found to have little effect on total entropy generation for fluids with Pr = 0.7 during both conduction and convection regimes. Thermal mixing and degree of temperature uniformity due to distributed heating in various cases are also reported and optimum cases for processing of various fluids are presented based on minimum entropy generation.     

Natural convection in a square cavity filled with a porous medium: Effects of various thermal boundary conditions

Natural convection flows in a square cavity filled with a porous matrix has been studied numerically using penalty finite element method for uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls. Darcy–Forchheimer model is used to simulate the momentum transfer in the porous medium. The numerical procedure is adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number Ra, 10³ ⩽ Ra ⩽ 10⁶, Darcy number Da, 10⁻⁵ ⩽ Da ⩽ 10⁻³, and Prandtl number Pr, 0.71 ⩽ Pr ⩽ 10) with respect to continuous and discontinuous thermal boundary conditions. Numerical results are presented in terms of stream functions, temperature profiles and Nusselt numbers. Non-uniform heating of the bottom wall produces greater heat transfer rate at the center of the bottom wall than uniform heating case for all Rayleigh numbers but average Nusselt number shows overall lower heat transfer rate for non-uniform heating case. It has been found that the heat transfer is primarily due to conduction for Da ⩽ 10⁻⁵ irrespective of Ra and Pr. The conductive heat transfer regime as a function of Ra has also been reported for Da ⩾ 10⁻⁴. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominated regimes the power law correlations between average Nusselt number and Rayleigh numbers are presented.     

Oscillatory double-diffusive mixed convection in a two-dimensional ventilated enclosure

By starting from a steady flow configuration based on the work of Deng et al. [Qi-Hong Deng, Jiemin Zhou, Chi Mei, Yong-Ming Shen, Fluid, heat and contaminant transport structures of laminar double-diffusive mixed convection in a two-dimensional ventilated enclosure, Int. J. Heat Mass Transfer 47 (2004) 5257–5269], a numerical investigation was conducted to analyse the unsteady double-diffusive mixed convection in two-dimensional ventilated room due to heat and contaminant sources. Owing to the large number of parameters, the results are reported only for a constant buoyancy ratio N equal to 1. The flow is found to be oscillatory for a fixed Reynolds number (700 ⩽ Re ⩽ 1000) when the Grashof number is varied in a wide range (10³ ⩽ Gr ⩽ 10⁶). Results of the simulations show that the onset of the oscillatory indoor airflow occurs for couples (Re, Gr) values that can be correlated as Re = aGr^b.     

Effect of nanofluid variable properties on natural convection in enclosures filled with a CuO–EG–Water nanofluid

This work focuses on the study of natural convection heat transfer characteristics in a differentially-heated enclosure filled with a CuO–EG–Water nanofluid for different published variable thermal conductivity and variable viscosity models. The problem is given in terms of the vorticity–stream function formulation and the resulting governing equations are solved numerically using an efficient finite-volume method. Comparisons with previously published work are performed and the results are found to be in good agreement. Various results for the streamline and isotherm contours as well as the local and average Nusselt numbers are presented for a wide range of Rayleigh numbers (Ra = 10³–10⁵), volume fractions of nanoparticles (0 ≤ φ ≤ 6%), and enclosure aspect ratios (½ ≤ A ≤ 2). Different behaviors (enhancement or deterioration) are predicted in the average Nusselt number as the volume fraction of nanoparticles increases depending on the combination of CuO–EG–Water variable thermal conductivity and viscosity models employed. In general, the effects the viscosity models are predicted to be more predominant on the behavior of the average Nusselt number than the influence of the thermal conductivity models. The enclosure aspect ratio is predicted to have significant effects on the behavior of the average Nusselt number which decreases as the enclosure aspect ratio increases.     

Unsteady conjugate mixed convection phase change of a power law non-Newtonian fluid in a square cavity

Transient phase change of a power law non-Newtonian fluid inside an inner thin walled container caused by external mixed convection in a square cavity has been analyzed numerically. Air was chosen as external cooling fluid and modified non-Newtonian water as the phase change fluid. Fluid mechanics and conjugate convective heat transfer, described in terms of continuity, linear momentum and energy equations, were predicted by using the finite volume method. Solidification was treated in terms of a phase change function varying linearly with temperature. The effect of the external Reynolds number, for Re = 200 and 1000 on solidification was studied along the influence of the non-Newtonian power law index (n = 0.5, n = 1.0). Results for the time evolution of streamlines, isotherms and freezing curves are analyzed. The effect of the Reynolds number on streamlines of the external fluid is remarkable, principally near the region close to the internal water filled container. Differences between cooling and freezing times are found for Newtonian (n = 1.0) and non-Newtonian modified (n = 0.5) water.     

Effects of moving lid direction on MHD mixed convection in a linearly heated cavity

Effects of moving lid-direction on MHD mixed convection in a cavity with the bottom wall being linearly heated are analyzed using a numerical technique. Vertical walls of the enclosure are adiabatic and the sliding wall at the top has constant temperature. The lid moves in the negative and positive x-direction. Finite volume method has been used to solve the governing equations. Results are presented for different values of Hartmann number (0 ? Ha ? 30), Reynolds number (100 ? Re ? 1000) and Grashof number (10⁴ ? Gr ? 10⁶). It is found that direction of lid is more effective on heat transfer and fluid flow in the case of mixed convection than it is the case in forced convection. Heat transfer is also decreased with increasing of magnetic field for all studied parameters.     

Laminar free convection inside an inclined L-shaped enclosure

We have numerically reported the buoyancy induced flow and heat transfer characteristics inside an inclined L-shaped enclosure. A control volume based Finite-Volume method is applied to discretize the governing equations with collocated variable arrangement. SIMPLE algorithm is used and the system of equations is solved by Stone's SIP solver with full multigrid acceleration. Results are presented in the form of the average Nusselt number for a range of inclination angle, θ = 0°–360°; Rayleigh number, Ra = 1–10⁵; and aspect ratio, A = 0.1–0.5.     

Effects of thermal boundary conditions on natural convection flows within a square cavity

A numerical study to investigate the steady laminar natural convection flow in a square cavity with uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls has been performed. A penalty finite element method with bi-quadratic rectangular elements has been used to solve the governing mass, momentum and energy equations. The numerical procedure adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number Ra, 10³ ⩽ Ra ⩽ 10⁵ and Prandtl number Pr, 0.7 ⩽ Pr ⩽ 10) with respect to continuous and discontinuous Dirichlet boundary conditions. Non-uniform heating of the bottom wall produces greater heat transfer rates at the center of the bottom wall than the uniform heating case for all Rayleigh numbers; however, average Nusselt numbers show overall lower heat transfer rates for the non-uniform heating case. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominated regimes, power law correlations between average Nusselt number and Rayleigh numbers are presented.     

Experimental investigation of opposing mixed convection hear transfer in the vertical flat channel in a laminar–turbulent transition region

In this paper we present the results on experimental investigation of the local opposing mixed convection heat transfer in the vertical flat channel with symmetrical heating in a laminar–turbulent transition region. The experiments were performed in airflow (p = 0.1–1.0 MPa) in the range of Re from 1.5 × 10³ to 6.6 × 10⁴ and Gr_q up to 1 × 10¹¹ at the limiting condition q_w1 = q_w2 = const. The analysis of the results revealed significant increase in the heat transfer with increasing of air pressure (Gr number). Also sharp increase in heat transfer was noticed in the region with vortex flow in comparison with the turbulent flow region.     

Turbulent Rayleigh–Bénard convection of water in cubical cavities: A numerical and experimental study

Experimental measurements and numerical simulations of natural convection in a cubical cavity heated from below and cooled from above are reported at turbulent Rayleigh numbers using water as a convective fluid (Pr = 6.0). Direct numerical simulations were carried out considering the Boussinesq approximation with a second-order finite volume code (10⁷ ⩽ Ra ⩽ 10⁸). The particle image velocimetry technique was used to measure the velocity field at Ra = 10⁷, Ra = 7 × 10⁷ and Ra = 10⁸ and there was general agreement between the predicted time averaged local velocities and those experimentally measured if the heat conduction through the sidewalls was considered in the simulations.     

Unsteady conjugate natural convection in a square enclosure filled with a porous medium

Mathematical simulation of unsteady natural convection modes in a square cavity filled with a porous medium having finite thickness heat-conducting walls with local heat source in conditions of heterogeneous heat exchange with an environment at one of the external boundaries has been carried out. Numerical analysis was based on Darcy–Forchheimer model in dimensionless variables such as a stream function, a vorticity vector and a temperature. The special attention was given to analysis of Rayleigh number effect Ra = 10⁴, 10⁵, 10⁶, of Darcy number effect Da = 10^?5, 10^?4, 10^?3, ∞, of the transient factor effect 0 < τ < 1000 and of the heat conductivity ratio k_2,1 = 3.7 × 10^?2, 5.7 × 10^?4, 6.8 × 10^?5 on the velocity and temperature fields. The influence scales of the defining parameters on the average Nusselt number have been detected.