Function Of Rayleigh Number Research Articles

Critical transitions on a route to chaos of natural convection on a heated horizontal circular surface

The transition route and bifurcations of the buoyant flows developing on a heated horizontal circular surface are elaborated using direct numerical simulations and direct stability analysis. A series of bifurcations, as a function of Rayleigh numbers ( $Ra$ ) ranging from $10^6$ to $6.0\times 10^7$ , are found on the route to chaos of the flows at $Pr=7$ . When $Ra<1.0\times 10^3$ , the buoyant flows above the heated horizontal surface are dominated by conduction, because of which the distinct thermal boundary layer and plume are not present. At $Ra=1.1\times 10^6$ , a Hopf bifurcation occurs, resulting in the flow transition from a steady state to a periodic puffing state. As $Ra$ increases further, the flow enters a periodic rotating state at $Ra=1.9\times 10^6$ , which is a unique state that was rarely discussed in the literature. These critical transitions, leaving from a steady state and subsequently entering a series of periodic states (puffing, rotating, flapping and period-doubling) and finally leading to chaos, are diagnosed using two-dimensional Fourier transforms. Moreover, direct stability analysis is conducted by introducing random numerical perturbations into the boundary condition of the surface heating. We find that when the state of a flow is in the vicinity of critical values (e.g. $Ra=2.0\times 10^6$ ), the flow is conditionally unstable to perturbations, and it can bifurcate from the rotating state to the flapping state in advance. However, for relatively stable flow states, such as at $Ra=1.5\times 10^6$ , the flow remains in its periodic puffing state even though it is being perturbed.

Measurements of natural convective heat transfer of the inclined torus

Experiments were conducted to investigate the natural convective heat transfer characteristics of an inclined torus. The Rayleigh numbers ranged from 4.54 × 106 to 1.23 × 108 and the inclination angle was varied from 0° to 80° Mass transfer experiments were performed based on the analogy between heat and mass transfer using the CuSO4H2SO4 copper electroplating system. The heat transfer of the inclined torus exhibited a trend similar to that of an inclined cylinder, with a gradual decrease in heat transfer with the inclination angle due to the variation of vertical cross-sectional shape. However, the inclined torus demonstrated better heat transfer performance than an inclined cylinder as the curved structure interrupts the formation of the stable boundary layer underneath the torus. The flows were visualized by Particle Image Velocimetry (PIV) and the heat transfers, by the electric plating patterns. New correlations were proposed to predict the heat transfer coefficient of the inclined torus as a function of Rayleigh number, inclination angle, and toroidal ratio.

Analysis of multiple steady states for natural convection of Newtonian fluids in a square enclosure

Multiple steady states are investigated for natural convection of fluids in a square enclosure with non-isothermally hot bottom wall, isothermally cold side walls, and thermally insulated top wall. A robust computation scheme involving steady-state governing equations has been developed to compute the steady states as a function of Rayleigh number (102 ⩽ Ra ⩽ 106) for two different Prandtl numbers (Pr = 0.026 and 0.1). Penalty Galerkin finite element method with Newton–Raphson solver is employed for the solution of the governing equations, while the solution branches are initiated by varying initial guess to the Newton–Raphson solver. In this context, a dual-perturbation scheme involving perturbations of the boundary conditions and various process parameters has been designed leading to the rich spectrum of the symmetric and asymmetric solution branches for the current symmetric problem. It is found that multiple steady states occur beyond a critical value of Ra, which depends on the magnitude of Pr. In addition to the basic solution branch (corresponding to the solutions obtained via uniform initial guesses), nineteen additional solution branches (six symmetric and thirteen asymmetric) are obtained for Pr = 0.026, while four additional solution branches (two symmetric and two asymmetric) are obtained for Pr = 0.1. The solution branches are associated with a wide spectrum of flow structures (24 distinct types for Pr = 0.026 excluding the reflection symmetric mirror images of the asymmetric solutions), which are reported for the first time. The flow structures lead to various heating scenarios within the enclosure resulting in a significant variation of heat transfer rates (more than 50%). The current results are important for the practical applications. The spectrum of the possible scenarios revealed in this work can be pivotal to design the optimal processes based on the process requirement (targeted heating or enhanced heating rates).

Optimization of Horizontal Annular Finned Tube Under Natural Convection Heat Transfer

Free convection heat transfer over annular finned tubes was studied numerically for more than 60 different cases and verified against two experimental works. In addition, the effect of fin spacing on heat transfer was investigated. As a result, a correlation was proposed to estimate Nusselt number as a function of Rayleigh number. Moreover, it was shown that there was an optimum fin spacing for which the total heat transfer was maximized. Based on the proposed equation, an expression for optimum fin spacing was derived, which proved that the optimum Nusselt number was 0.9035. The presented equation for optimum fin spacing was a general equation in so far that it could also be used to find the optimum spacing between a series of circular disks by letting the tube diameter in the equation be zero. Moreover, a good agreement was observed between the derived equation for optimum fin spacing and the results of the scale analysis method.

Conjugate natural convection in a vertically divided square enclosure by a corrugated solid partition into air and water regions

The purpose of this study is to investigate conjugate natural convection inside a partitioned differentially heated square enclosure. A corrugated heat-conducting solid partition of three different values of thickness and three different materials is selected. The partition divides the empty spaces of the enclosure into two fluid zones and those zones are filled with air and water, respectively. The governing Navier-Stokes and energy equations are numerically solved by means of the finite element method. The effects of corrugation amplitude, corrugation frequency, thermal conductivity, position and thickness of the corrugated solid partition along with the variation of Rayleigh numbers based on the properties of air on thermal and flow fields have been depicted through contour plots of temperature and stream function, respectively. The average Nusselt number along the hot wall and the average temperatures of both air and water in their respective domains have also been examined to observe the influence of the above variations. The change of corrugation amplitude, thermal conductivity, position and thickness of the corrugated solid partition has considerable effects on heat transfer performance with increasing Rayleigh number. Out of those controlling parameters, it is found that increasing partition thermal conductivity enhances thermal performance by up to 25%. However, the variation of corrugation frequency of the partition as a function of Rayleigh number does not seem to be significant for heat transfer enhancement.

Thermal energy storage in a confined cylindrical heat source filled with phase change materials

Thermal energy storage in the phase change materials (PCMs) around a confined heated cylindrical heat source has been investigated numerically. This work aims to explore three major objectives namely; evolution of melting front around the cylindrical heat source, quantification of overall rate of heat transfer and identifying the factors to maximize the energy storage. The enthalpy-porosity formulation is utilized to model melting of PCMs. The flow and energy equations with relevant boundary conditions have been solved using finite element method for range of parameters as Rayleigh number (102≤Ra≤106), Prandtl number (102≤Pr≤103), Stefan number (0.01≤Ste≤0.5) and aspect ratio (0.1≤AR≤0.5). The evolution of melting front and melt fraction, streamlines, isotherms, Nusselt number and thermal energy storage are reported as a function of Rayleigh number (Ra), Prandtl number (Pr), Stefan number (Ste), and aspect ratio (AR). Stefan number and the aspect ratio have shown to be a positive influence on the amount of thermal energy absorbed during the melting of PCMs. At low Rayleigh and Stefan number, melting kinetics is shown to be sluggish. All else being equal, the energy storage exhibits three distinct regimes depending upon the Fourier number namely, the lag phase, the exponential phase and stationary phase. For process design calculations, the gross engineering parameters like Nusselt number and steady-state melt fraction are often required, and therefore a predictive correlation for the value of the average Nusselt number is proposed to facilitate the estimation of average Nusselt number at intermediate values of dimensionless numbers for a given practical application.

Silicon as high-temperature phase change medium for latent heat storage: A thermo-hydraulic study

Latent heat storage (LHS) using high-temperature phase change medium (PCM) can provide cost-competitive solutions for dispatchable solar power and accumulate surplus Photo-voltaic (PV) and wind power. Moreover, at a sufficiently high temperature, the round trip efficiency of LHS system may approach that of electrochemical storage system. A conceptual LHS system utilizing high-temperature silicon as the phase change medium (PCM) is presented in the article. Silicon is chosen due to its high melting point (1414 °C), latent heat (1.8 × 106 J/kg), and thermal conductivity (25–50 W/mK). The thermo-hydraulic behavior during melting of silicon is modeled using a combined numerical methodology in COMSOL Multiphysics. The thermal performance of proposed system is compared against high-temperature salt-based system for different aspect ratios (AR). Results indicate that silicon systems are significantly superior to high-temperature salts under the same operating conditions. The anomalous behavior of silicon melting is established by demonstrating natural convection pattern in molten silicon. A generalized correlation is developed to predict the melting fraction as a function of Rayleigh number, Stefan number, and Fourier number for various domain sizes.

Natural Convection Air cooling of Electronic Components in Partially top vented Enclosures.(Dept.M)

The study of natural convection from a heat source located at the bottom of partially top vented enclosure is presented. Air cooling for electronic component situated at the bottom of a top vented enclosure is studied theoretically. The flow is assumed to be laminar, steady and of constant physical properties. The process is described by continuity, momentum and energy partial differential equations, which are be expressed in Cartesian coordinates system. Due to the nature of the studied problem and with proper transformation of the problem dependent and independent variables, these governing equations are transformed to a set of dimensionless partial differential equations. This set of differential equations is transformed to set of difference equations by the implantation of finite difference technique. Accordingly, one can obtain the solutions for this problem, which are obtained by application of the well known Gauss Siedel iteration method. A computer program is developed to solve the present proposed mathematical model. According to this solution, the values of Nusselt number, for different values of Rayleigh number are obtained. Comparisons between the present obtained results and those results obtained in previous theoretical results are performed for parametric variations of the vent opening size and shape. Also a correlation for Nusselt number as a function of Rayleigh number and equivalent diameter of the vent is proposed.

A hybrid scheme of single relaxation time lattice Boltzmann and finite volume methods coupled with discrete ordinates method for combined natural convection and volumetric radiation in an enclosure

This paper is focused on the application of hybrid Single relaxation time lattice Boltzmann and finite volume methods in conjunction with discrete ordinates method to simulate coupled natural convection and volumetric radiation in differentially heated enclosure, filled with an absorbing, emitting and non-scattering gray medium. In this work, the velocity and temperature fields are calculated using lattice Boltzmann and finite volume methods respectively, whereas the radiative term is computed by the discrete ordinates method. This study is carried out for Pr = 0.71, a Rayleigh number range of 103 ≤ Ra ≤ 106, an optical thickness with values 0 ≤ τ ≤ 100, a Planck number ranging in 0.001≤ Pl ≤ 100 and an aspect ratio varying between 0.5 ≤ Ar ≤ 2. Results are presented in terms of streamlines, isotherms, velocity profiles and average Nusselt number. Based on the obtained results, it can be concluded that the presence of volumetric radiation is noteworthy. Its effect, as a function of Rayleigh number and the radiative properties, yields significant changes on the behavior of streamlines and isotherms. In the taller enclosure, the increase of average total Nusselt number with increasing Rayleigh number is less significant than that in the case of the shallow enclosure.

Natural convection heat transfer in corrugated annuli with H2O-Al2O3 nanofluid

The present work includes a numerical study of natural convection heat transfer in symmetrical and unsymmetrical corrugated annuli filled with H2O-Al2O3 nanofluid. In this study, higher and lower temperatures were kept constant at inner and outer cylinders of the annulus; respectively. Eight mathematical models with an aspect ratio of 1.5 were developed to find the best model giving the highest heat transfer rates. The stream-vorticity formulation in curvilinear coordinates was used to solve the governing equations of heat transfer and fluid motion. The influences of Rayleigh number. ((103≤ Ra ≤106) and volume fraction of nanoparticles. (0≤ϕ≤0.25) on isotherms, streamlines, local and average Nusselt numbers on the inner and outer cylinder were investigated. The results show that the heat transfer rate is significantly increased with an increase in nanoparticles volume fraction and Rayleigh number. The activity of the heated surface is increased with an increase in the undulation number, but the flow motion tends to be most difficult in the spaces between active undulation walls. Moreover, the heat transfer rates in unsymmetrical annuli are relatively higher than the rates in the symmetrical annuli. There are no evident changes in isotherms with an increase in the nanofluid volume fraction. Correlations for the mean Nusselt number on the inner and outer walls of annulus were deduced as a function of Rayleigh number and nanoparticles volume fraction for eight models with an accuracy range of 8–15 %.

Natural convection solar air heater: Bell-mouth integrated converging channel for high flow applications

The bulk movement of fluid in natural convection solar air heater (SAH) is generated due to density variation and hence suffers from lower mass flow rates. Mounting additional surfaces/fins in SAH duct enhances the thermal characteristics, however, it comes at the cost of hydraulic performance. This limits the device usage in buildings and other high flow rate applications. In the present study, two new designs of SAH were numerically analyzed are: (a) taper flow passage for better thermal performance; (b) tapered designs incorporated with bell-mouth inlet opening for improved hydraulic performance. Parametric design analysis was conducted for large range of taper ratio and bell-mouth ratio. The results show that the tapered design is about 70% thermally more effective and about 6% higher Nusselt number per unit pressure drop than conventional SAH. A significant enhancement in hydraulic performance of more than 300% was observed when bell-shaped inlet design was integrated with the tapered designs. An independent correlation for Nusselt number variation has been developed as a function of Rayleigh number and tapper ratio. Predictions from the developed correlation is in excellent following with the numerical data.

Experimental analysis of free convection heat loss in a bicylindrical cavity receiver

Convection heat loss from solar cavity receivers in parabolic dish concentrators significantly reduces the performance of the system. In this paper, steady-state experiments were conducted to investigate heat losses from an electrically heated bicylindrical cavity receiver, which consists of two coaxial cylinders of diameters 0.06 and 0.09 m with an aspect ratio (length to diameter) of one. The cavity surface was exposed to constant heat fluxes from 785 W/m2 to 1770 W/m2 at different inclination angles from −90° (vertically upward-facing) to +90° (vertically downward-facing). The temperature distribution of the cavity surface depicts that due to the presence of a sharp corner between the two cylinders, the flow instability intensifies, and the temperature of the top surface rises. The results showed that the maximum convective loss occurs approximately at −30° that corresponds to 63% of the total heat loss while the minimum convective loss occurs at +90°, which accounts for about 19% of the total heat loss. A convective heat loss relation was developed for cavity surface temperatures up to 300 °C and used to estimate convective losses at higher temperatures. Flow visualization experiments were also performed to investigate heat losses from the cavity receiver. It was observed that increasing the inclination angle from 45° to 60° results in a decrease in the induced buoyant force. Empirical correlations were also developed for Nusselt number as a function of Rayleigh number, inclination angle, and the ratio of cavity surface temperature to the ambient temperature for both upward and downward-facing situations. Comparing correlated Nusselt numbers with experimental results for upward-facing positions shows ±5% deviation, while for downward-facing inclinations, the correlation predicts the experimental data by a deviation within ±12%. Moreover, a comparison of experimentally measured convective losses with literature shows discrepancy at lower inclinations but depicts good agreement when the inclination angle increases. For the vertically downward-facing situation, the experimental data shows a close fit where the effect of aperture size becomes negligible. The analyses also revealed that the relative combined standard uncertainty of convective Nusselt number varies between 2% and 14%, depending upon the cavity inclination and the heat flux applied.

Numerical analysis of 2-D laminar natural convection heat transfer from solid horizontal cylinders with longitudinal fins

Proper thermal management through an effective cooling mechanism is essential for improving the reliability of operation of various electronic devices. A number of cooling methods are available among which passive cooling by natural convection has been deemed appropriate since it has distinctive advantages over active cooling or forced convection like high reliability, low maintenance cost, energy efficiency and noise-free nature. In the present study, natural convection from solid horizontal cylindrical heat sources of the geometry and dimensions of heat sinks of LED bulbs with external longitudinal plate fins have been modelled. Numerical computations of continuity, momentum and energy equations to solve the two dimensional incompressible natural convection conjugate heat transfer from such cylinders has been studied in the laminar regime (4.5×105<RaD<5.2×105). The diameter of the cylinder is kept at 60 mm whereas the length is kept at 50 mm. The number of fins has been varied from three to 36, the height of fins kept at 10, 20 and 30 mm and thickness at one mm. The effect of fin geometry parameters and Rayleigh number on total heat transfer, heat transfer exclusively from fin surface and from bare cylinder surface, heat transfer per fin and Nusselt number based on cylinder diameter have been studied in detail. Finally, optimum fin spacing for a particular fin height has been evaluated. Contour plots to capture temperature and velocity vectors around the heat source have also been developed. Numerical correlations of Nusselt number as a function of Rayleigh number, non-dimensional fin spacing and non-dimensional fin height reveal that the scaling laws of RaD1∕3 and RaD1∕4 are valid both for the computational data of our present analysis and experimental data even though the experiments are for a slightly different boundary condition.

Fluid-structure interaction of a hot flexible thin plate inside an enclosure

This study aims to assess the natural convection heat transfer in a square cavity wherein the buoyancy-induced flow is generated by a thin flexible heater-plate inside the cavity. The vertical walls of the cavity are cold and the horizontal walls are adiabatic. The thin hot plate is assumed to be isothermal and fixed at an alterable point in the middle of the cavity with different inclination angles. To analysis the fluid-structure interaction (FSI), the finite element method along with the Arbitrary Lagrangian-Eulerian (ALE) technique is employed. Isotherms and streamlines, as well as the average Nusselt number, the dimensionless temperature in the cavity, and the maximum applied stress on the flexible plate, are studied. The results are presented as a function of Rayleigh number, Prandtl number, inclination angle, and different positions of the fixed point. The outcomes indicate the importance of the inclination angle and the position of the fixed point of the hot plate. The plate experiences significantly large values of stress when it is mounted horizontally. In the case of a plate fixed at its top, the highest stress occurs with an inclination angle of 40°. In contrast, the lowest stress is associated with the plate when it is positioned vertically.

Convective Heat Transfer and Entropy Generation Around a Sphere Within Cuboidal Enclosure

The intricate three-dimensional natural convection and entropy generation of a flow between cuboidal enclosure and a spherical surface is numerically examined in this study. The sphere is maintained hot and centrally located in cubical enclosure with four cooled walls, whereas top and bottom walls are perfectly insulated. The effects of inner shape, Rayleigh numbers, and inclination angles on fluid flow and heat transfer characteristics are analyzed in detail for Rayleigh numbers ranging from to and a tilted angle of the enclosure varying from 0 to 90°. The working fluid is air so that the Prandtl number equates to 0.71. The developed mathematical model is governed by the coupled equations of continuity, momentum, and energy and is solved by a finite volume method. Based on numerical results, two correlation expressions for predicting average Nusselt number of lateral walls of the cubical enclosure and the inner sphere are proposed as a function of Rayleigh number and inclination angle under different wake parameters. By comparing inner spherical shape results with that of cylindrical shape, it can be inferred that using a spherical shape provides the highest thermal performance for heat transfer. Moreover, this comparison reveals that the inner spherical shape decelerates the unsteadiness for the considered inclinations. Results indicate also that the optimal average heat transfer rate is obtained for extreme Rayleigh number, , and an inclination of 90° for both cases of the inner sphere and lateral walls of the cuboidal enclosure. The Bejan number and total entropy generation are found to be increased by increasing the inclination angle for the considered Rayleigh numbers. Maximum local entropy generation due to heat transfer and that due to fluid friction decrease gradually by increasing the inclination angle. The results of this investigation find extensive array of applications in several engineering devices, which will be mentioned in the paper content.

Investigation of entropy generation in a square inclined cavity using control volume finite element method with aided quadratic Lagrange interpolation functions

One of the most concerned subjective in Mechanical science is natural convection study in a cavity. Furthermore, the investigation of entropy generation can be useful for better designing of the thermal systems. In the present study, natural convection flow and entropy generation are numerically investigated in the presence of a magnetic field in a square inclined cavity which known as the effect of magneto-hydrodynamic (MHD). Firstly, governing equations, including mass, momentum, and energy balance equations are applied to the problem. Then, governing equations are rewritten in dimensionless form using non-dimensional parameters, vorticity, and stream function. Furthermore, the entropy generation equation is written as a non-dimensional equation. Then, the contribution of the heat transfer entropy generation into the total entropy generation rate is determined using the Bejan number. A new measure for evaluation of the thermal performance of the cavity is presented that is the so-called ecological coefficient of performance (ECOP) based on the second law of thermodynamics. Flow and heat transfer characteristics are investigated for different values of the Rayleigh number, inclination angle, and Hartmann number. The new correlations of entropy generation as a function of Rayleigh number are obtained using the two-dimensional version of quadratic Lagrange interpolation functions (QLIFs). The obtained values for the average Nusselt number and the entropy generation number are compared with those of the literature and excellent agreement is observed. The results show that the entropy generation number rises with increasing of Hartmann number and whereas it has a maximum value for a specified inclination angle. Also, ECOP increases with increasing of Hartmann number for low values of Rayleigh number. The results discover that the optimum values of the inclination angle are 20°, 35° and 48°for Hartmann number 0, 25 and 75 at Ra = 105, respectively. Also, with increasing Ha from 25 to 75, the contribution of the Ngen due to magnetic field decreases from 23% to 9% for β = 0° and it decreases from 24% to 6% for β = 45°.

Transitions and scaling in horizontal convection driven by different temperature profiles

Horizontal convection has been used as an idealised model of the ocean overturning circulation, where some non-uniform buoyancy forcing profile is imposed along a horizontal boundary. Several different driving temperature profiles have been chosen for past numerical and laboratory studies, likely for convenience, yet the effect of the shape of the chosen profile on the resulting horizontal convection flow remains unexplored. Here high order numerical simulation is used to investigate this problem. Time independent, periodic and chaotic regimes are identified as functions of Rayleigh number (Ra) and profile shape, with a step temperature profile being found to be more unstable than a linear temperature profile. Using a nonlinear Stuart–Landau analysis, the primary instability is consistently found to occur through a supercritical (non-hysteretic) bifurcation. This research highlights the importance of the horizontal buoyancy forcing profile in determining the thermal forcing required to produce instability in horizontal convection. In addition, Nusselt number scales to Ra1/5 in the fully convective regime, with scaling exponents elevating beyond Ra≈1010. This elevated scaling was more pronounced for the linear thermal boundary profile than for the step profile over the computed Rayleigh numbers range.

Thermal analysis of high-pressure hydrogen during the discharging process

The transient temperature and pressure of hydrogen are measured during the hydrogen discharging process through an orifice in a high-pressure vessel. The initial pressures of hydrogen in the vessel are set to approximately 30, 60, and 100 MPa. The mass flow rate and heat flux between hydrogen and the inner wall of the vessel are theoretically estimated using fundamental equations and experimental results with accurate thermophysical properties of hydrogen. The generation of temperature distribution and flow due to heat transfer in the vessel during discharge is verified by numerical analysis. Further, the relationship between reference gas temperature and heat flux in the vessel during the release of high-pressure hydrogen is studied. The average heat flux in the vessel is calculated using experimental and numerical analysis. The appropriate reference temperature is obtained using the comparison of the average heat flux in the vessel. In addition, the dominant heat transfer mode during hydrogen discharge is investigated. Numerical analysis shows that natural convection is formed inside the vessel due to a decrease in temperature. The Nusselt numbers in this process are presented as a function of Rayleigh numbers which are obtained by the experimental results and mass and energy conservations. The relationship between the Nusselt and Rayleigh numbers agrees with the heat transfer correlations of natural convections.

Solar Still Efficiency Enhancement by Using Graphene Oxide/Paraffin Nano-PCM

Solar-driven water desalination technologies are rapidly developing with various links to other renewable sources. However, the efficiency of such systems severely depends on the design parameters. The present study focused on using graphene oxide (GO) with the Φ = 0.2, 0.4 and 0.6 wt.% dispersed in paraffin, as phase-change materials (PCMs), to improve the productivity of a solar still for desalination applications. The outcomes showed that by adding more graphene oxide to paraffin, the melting temperature got reduced. Solar still with GO/paraffin showed 25% productivity improvement in comparison with the solar still with only PCM. The obtained Nusselt number during the melting time also represented that free convection heat transfer into the melted region of the solar still has been enhanced by adding dispersed GO to the PCM, compared to the base paraffin. Also, increasing the hot wall temperature augments the Nusselt number. Finally, an empirical equation was derived to correlate the average Nusselt number as a function of Rayleigh number (Ra), the Stefan number (Ste), the subcooling factor (Sb), and the Fourier number (Fo). The obtained correlation depicted that Nusselt number enhancement has a reverse relation with Fourier number.

Conjugate natural heat transfer scrutiny in differentially heated cavity partitioned with a conducting solid using the lattice Boltzmann method

In the present paper, we numerically investigated the two-dimensional conjugate heat transfer problems in a unitary computational domain containing both the solid and fluid regions. The physical problem configuration consists of two adiabatic horizontal walls of finite thickness and two vertical walls; the left one is maintained at hot temperature Th and the right one is maintained at cold temperature Tc. The lattice Boltzmann method (LBM) based on the BGK model has been used to simulate laminar natural convection in the partitioned air-filled cavity with a heat-conducting solid. In the interface boundaries of the heat-conducting solid, the continuity of temperature and heat transfer is considered. A series of numerical simulation is carried out over a wide range of the Rayleigh number (Ra = 103–106), the thermal conductivity ratio kr and the solid partition thickness (δ = 1–95℅) and its horizontal position. The results show that the partition reduces the heat transfer rate in the cavity. For a centered partition (Xs = 0.5), the average Nusselt number decreases almost linearly with partition thickness for δ ≤ 0.45; however, it increases for δ ≥ 0.45 due to the confinement in the thin fluid regions. For Ra = 105, the heat transfer rate decreases with the partition position until a critical value close to 0.325 and rises slightly until Xs = 0.5. The critical position value decreases with the Ra number increase and it is close to 0.2 for Ra = 106 where Nu = 3.766. The heat transfer rate is enhanced with the increase in thermal conductivity. Correlations of the average Nusselt numbers are obtained as a function of Rayleigh number.