High Rayleigh Number Research Articles

Fully compressible convection for planetary mantles

SUMMARY The numerical simulations of convection inside the mantle of the Earth or of terrestrial planets have been based on approximate equations of fluid dynamics. A common approximation is the neglect of the inertia term which is certainly reasonable as the Reynolds number of silicate mantles, or their inverse Prandtl number, are infinitesimally small. However various other simplifications are made which we discuss in this paper. The crudest approximation that can be done is the Boussinesq approximation (BA) where the various parameters are constant and the variations of density are only included in the buoyancy term and assumed to be proportional to temperature with a constant thermal expansivity. The variations of density with pressure and the related physical consequences (mostly the presence of an adiabatic temperature gradient and of dissipation) are usually accounted for by using an anelastic approximation (AA) initially developed for astrophysical and atmospheric situations. The BA and AA cases provide simplified but self-consistent systems of differential equations. Intermediate approximations are also common in the geophysical literature although they are invariably associated with theoretical inconsistencies (non-conservation of total energy, non-conservation of statistically steady state heat flow with depth, momentum and entropy equations implying inconsistent dissipations). We show that, in the infinite Prandtl number case, solving the fully compressible (FC) equations of convection with a realistic equation of state (EoS) is however not much more difficult or numerically challenging than solving the approximate cases. We compare various statistical properties of the Boussinesq, AA and FC simulations in 2-D simulations. We point to an inconsistency of the AA approximation when the two heat capacities are assumed constant. We suggest that at high Rayleigh number, the profile of dissipation in a convective mantle can be directly related to the surface heat flux. Our results are mostly discussed in the framework of mantle convection but the EoS we used is flexible enough to be applied for convection in icy planets or in the inner core.

Numerical investigation of 2D double-diffusive convection in rectangular cavities with different aspect ratios: Heat and mass transfer and flow characteristics

In this paper, the dynamical behavior of two-dimensional double-diffusive convection is numerically investigated using a high-accuracy numerical method. The process of flow transition in the presence of buoyancy is studied in detail, and the effects of the fluid properties and geometric parameters on the flow characteristics and heat and mass transfer are discussed. The results show that, as the buoyancy ratio increases from 0 to 2, the flow undergoes a complex series of transitions, from a steady, temperature-dominated state to periodic motion, then chaotic motion, back to periodic motion, and finally back to a steady, concentration-dominated state. At a fixed buoyancy ratio, when the Prandtl number Pr is less than 1, the flow changes from periodic or chaotic to steady with increasing Pr, and the heat and mass transfer efficiencies oscillate with an increasing trend. When Pr≥1, the flow is steady, and the heat and mass transfer remain nearly constant. For low Rayleigh numbers, the heat and mass transfer efficiencies increase monotonically with increasing Lewis number, but the flow is always in a steady state. For high Rayleigh numbers, the flow transitions from steady to periodic or chaotic via a supercritical Hopf bifurcation with increasing Lewis number, and the heat and mass transfer efficiencies oscillate with an increasing trend. In the range of aspect ratios considered in this study, the heat and mass transfer efficiencies exhibit an overall decay with increasing aspect ratio.

Flow and Heat Transfer Mechanisms in a Rotating Compressor Cavity Under Centrifugal Buoyancy-Driven Convection

Abstract This paper presents a systematic study of flow and heat transfer mechanisms in a compressor disk cavity with an axial throughflow under centrifugal buoyancy-driven convection, comparing with previously published experimental data. Wall-modeled large-eddy simulations (WMLES) are conducted for six operating conditions, covering a range of rotational Reynolds number (3.2×105−2.2×106), buoyancy parameter (0.11–0.26), and Rossby number (0.4–0.8). Numerical accuracy and computational efficiency of the simulations are considered. Wall heat transfer predictions are compared with measured data with a good level of agreement. A constant rothalpy core occurs at high Eckert number, appearing to reduce the driving buoyancy force. The flow in the cavity is turbulent with unsteady laminar Ekman layers observed on both disks except in the bore flow affected region on the downstream disk cob. The shroud heat transfer Nusselt number–Rayleigh number scaling agrees with that of natural convection under gravity for high Rayleigh numbers. Disk heat transfer is dominated by conduction across unsteady Ekman layers, except on the downstream disk cob. The disk bore heat transfer is close to a pipe flow forced convection correlation. The unsteady flow structure is investigated showing strong unsteadiness in the cavity that extends into the axial throughflow.

Mathematical modelling of mantle convection at a high Rayleigh number with variable viscosity and viscous dissipation

In this paper, the classical Rayleigh–Bénard convection model is considered and solved numerically for extremely large viscosity variations (i.e., up to 10^{30}) across the mantle at a high Rayleigh number. The Arrhenius form of viscosity is defined as a cut-off viscosity function. The effects of viscosity variation and viscous dissipation on convection with temperature-dependent viscosity and also temperature- and pressure-dependent viscosity are shown through the figures of temperature profiles and streamline contours. The values of Nusselt number and root mean square velocity indicate that the convection becomes significantly weak as viscosity variation and viscous dissipation are increased at a fixed pressure dependence parameter.

Recovery-Based Error Estimator for Natural Convection Equations Based on Defect-Correction Methods.

In this paper, we propose an adaptive defect-correction method for natural convection (NC) equations. A defect-correction method (DCM) is proposed for solving NC equations to overcome the convection dominance problem caused by a high Rayleigh number. To solve the large amount of computation and the discontinuity of the gradient of the numerical solution, we combine a new recovery-type posteriori estimator in view of the gradient recovery and superconvergent theory. The presented reliability and efficiency analysis shows that the true error can be effectively bounded by the recovery-based error estimator. Finally, the stability, accuracy and efficiency of the proposed method are confirmed by several numerical investigations.

Numerical simulation of buoyancy-induced heat transfer and entropy generation in 3D C-shaped cavity filled with CNT–Al2O3/water hybrid nanofluid

Abstract Three-dimensional investigation has been carried out to simulate buoyancy induced heat transfer and fluid flow as well as entropy creation inside C-shaped enclosure charged with based water CNT–Al2O3 (15–85%) hybrid nanofluid. Left side is isothermally heated while the vertical portions of the right wall are isothermally cooled. Effects of various parameters on the flow behavior and the produced irreversibilities, namely the cavity aspect ratio (0.1 ≤ Ar ≤ 0.4), Rayleigh number (103 ≤ Ra ≤ 106) and volumetric fraction of hybrid nanofluid (0 ≤ φ ≤ 0.06) have been examined. It was revealed that the aspect ratio is the main controlling parameter of thermal energy transfer and generated entropy. In addition, for specific Ra, adding hybrid nanoparticles leads to the increase of the average Nusselt number while the highest produced entropy is observed with higher Rayleigh number. Moreover, the maximum Bejan number occurred for a shape factor Ar = 0.1 and Ra = 104 disregarding the hybrid nanoparticles volume fraction showing the dominance of thermal irreversibility over the viscous dissipation irreversibility in such conditions.

Simulation of solid-liquid phase change at pore scale using lattice Boltzmann method with central moments in thermal energy storage

The solid-liquid phase change process is of significant importance to the thermal energy storage and electronics cooling using phase change material. In this paper, the central moments multiple-relaxation time (CM-MRT) collision model has been introduced into the solid-liquid phase change lattice Boltzmann model, in order to solve the solid-liquid phase change problem in porous medium at pore scale. To evaluate the influences of different collision functions, the problems of one-region phase change and natural convection with phase change at pore scale have been investigated. The results have showed that the CM-MRT model possessed higher accuracy in revealing temperature and liquid fraction distribution. Compared with mesh system of 256 × 256, the CM-MRT model with 64 × 64 possess the minimum error, 0.014%. Besides, in the case of high Rayleigh number (5 × 107) and low Prandtl number (0.005), the CM-MRT model presented extraordinary stability and the clear phase interface when investigating the heat transfer of porous medium composite phase change materials at the pore scale.

Rayleigh–Bénard convection in a cubic cell under the effects of gas radiation up to [formula omitted

This paper investigates radiative transfer effects on Rayleigh–Bénard convection in a cubic cell over a large range of Rayleigh numbers, from Ra=103 (below the onset of convection) to Ra=109 in the turbulent regime. Coupled direct numerical simulations are carried out for a radiating air/H2O/CO2 mixture at room temperature, using a Chebyshev spectral method for the flow and a ray-tracing method for the radiation field. For the highest Rayleigh numbers, a subgrid model is used to account for the radiation of the smallest, non-optically thin, turbulent scales. Symmetry and time-averaging (for unsteady solutions) are applied to compare coupled and uncoupled results, regardless of the multiple flow configurations that may be obtained. At low Rayleigh number, the potential energy decreases, and the onset of convection is delayed when radiation is taken into account. However, once convection settles, the potential energy increases with radiation, leading to a higher convective flux in the core and a higher kinetic energy. Specific contributions of radiative transfer to the potential energy balance and to the thermal energy balance are highlighted. It is also shown that the ratio of radiative and convective source terms in the energy balance roughly scales as Ra−1/2 and that radiative transfer effects weaken at high Rayleigh numbers. Finally, radiative transfer effects on turbulence budgets of mechanical and thermal fluctuations are analysed in the range 107≤Ra≤109. The magnitude of each term of these budgets is stronger when radiation is taken into account. However, radiative dissipation has little influence on the temperature fluctuation budget.

A coupled high-order implicit-explicit flux reconstruction lattice Boltzmann method for nearly incompressible thermal flows

In this paper, based on the double distribution function (DDF) model and the Boussinesq approximation, a high-order implicit-explicit flux reconstruction thermal lattice Boltzmann method (FRTLBM) is proposed for simulating nearly incompressible thermal flows. Two discrete velocity Boltzmann equations (DVBEs), one governing the flow field and the other governing the temperature field, are solved by using a high-order flux reconstruction scheme for spatial discretization and a second-order implicit-explicit Runge-Kutta scheme (IMEX RK) for time discretization in the generalized curvilinear coordinates with uniform and non-uniform grids. Numerical validations of the proposed method are implemented by simulating (a) porous plate problem, (b) natural convection in a square cavity, (c) Rayleigh-Bénard convection, (d) natural convection in a concentric annulus and (e) mixed heat transfer from a heated circular cylinder. Numerical results demonstrate that the present method can achieve the high-order accuracy and it is stable and accurate even at the relatively high Rayleigh number (Ra = 107 and 108). The present method is efficient due to the small amount of mesh, the simple algorithm and the time step unlimited by the relaxation time. Since the rescontruction is conducted in a single cell, the present method is compact for parallel computing. Moreover, the present method has a good adaptability of complicated geometries.

Analysis and reconstruction of the simplified thermal lattice Boltzmann method

The previous thermal lattice Boltzmann models are generally based on the lattice framework, which leads to some intrinsic drawbacks including the limitation of uniform mesh, coupled time step with mesh spacing, extra memory size, and complex boundary treatment. Aiming to decrease memory size and achieve good numerical stability for high Rayleigh number thermal flows, the simplified thermal lattice Boltzmann method (STLBM) was proposed. However, STLBM still has two fundamental problems. Firstly, as a weakly compressible model, its reason for the good numerical stability at high Rayleigh number thermal flows has not been revealed in the perspective of macroscopic scale yet. Secondly, it still depends on the uniform mesh, which makes the implementation of non-uniform meshes time-consuming and complicated. To tackle the two problems, the macroscopic equations of STLBM (MEs-STLBM) with actual numerical dissipative terms are derived firstly by approximating its actual computational process. By solving MEs-STLBM with the least-squares-based finite difference (LSFD) method, the limitation of the uniform mesh of STLBM can be easily overcome. Numerical investigation proves that the numerical dissipative terms in MEs-STLBM are the reason for the good numerical stability at high Rayleigh number thermal flows. By retaining these numerical dissipative terms, the discretized MEs-STLBM can recover the accuracy and numerical stability of STLBM well. Besides, they have significantly higher computational efficiency than STLBM.

A two-relaxation-time lattice Boltzmann study on the Soret and Dufour effects of double-diffusive convection over a rough surface

This study examines the Soret and Dufour effects of double-diffusive convection (DDC) over a rough surface by using a lattice Boltzmann (LB) model with two-relaxation-time (TRT) collision operators, where the cross-diffusion terms are modeled by introducing additional collision operators that can be used to avoid the need for special treatment of the gradient terms. The TRT model is applied to improve the stability of the LB method for flows at high Rayleigh numbers. We investigate how rough surfaces with different distributions and compactness of rough elements affect heat and mass transfer as well as the flow structure of the DDC system with the Soret and Dufour effects. We examined five rough models with different spatial distributions of the triangular rough elements as well as different values of the Rayleigh number (Ra=106 and 109), Prandtl number (Pr=0.7), Lewis number (Le=1 and 2), buoyancy ratio (−2≤Nc≤6.5), Soret factor (0≤STC≤1), Dufour factor (0≤DCT≤1), and the height of the roughness (1/96≤h≤1/2). Specifically, the influence of the buoyancy ratio on the DDC system was investigated, and the relationship of heat and mass transfer with the buoyancy ratio was divided into four stages: conduction-dominated, transition, steady convection-dominated, and oscillatory convection-dominated stages. The rough surfaces reduced heat and mass transfer at low Rayleigh numbers and low height of the roughness, and the third rough model (Model III) yielded the highest reduction. The flow showed periodic behavior after long-term reversals in some cases, which appear to have not been observed in previous research. Moreover, the effects of the Soret and Dufour factors were examined, and it was found that mass and heat transfer could be enhanced in most cases by increasing their values. To enhance heat and mass transfer, the height of the roughness should be increased as well. Model III delivered the best performance, with a scenario completely opposite to that in case of a low roughness height. Finally, approximate values of the critical height of the roughness with different rough models were obtained such that heat and mass transfer were enhanced only when the height of the roughness was greater than a critical value.

Numerical Study of Heat Transfer by Natural Convection in Concentric Hexagonal Cylinders Charged with a Nanofluid

In this document, a numerical study of the natural convection of steady-state laminar heat transfer in a horizontal ring between a heated hexagonal inner cylinder and a cold hexagonal outer cylinder. A Cu - water nanofluid traverses this annular space. The system of equations governing the problem was solved numerically by the fluent calculation code based on the finite volume method. Based on the Boussinesq approximation. The interior and exterior sides from the two cylinders are maintained at a fixed temperature. We investigated the impacts of various thermal Rayleigh numbers (103≤ Rat ≤2.5x105), and the volume fraction from the nanoparticles (0≤ Ø ≤0.12) on fluid flow and heat transfer performance. It is found that in high thermal Rayleigh numbers, a thin thermal boundary layer is illustrated at the flow that heavily strikes the ceiling and lower from the outer cylinder. In addition, the local and mean Nusselt number from a nanofluid are enhanced by enhancing the volume fraction of the nanoparticles.The results are shown within the figure of isocurrents, isotherms, and mean and local Nusselt numbers. Detailed results of the numerical has been compared with literature ones, and it gives a reliable agreement.

A Numerical Approach for Natural Convection With Curved Obstacles in an Enclosure Using Lattice Boltzmann Method

Abstract The impact of placing curved obstacles on natural convection in enclosures with differentially heated side walls is analyzed in the current study using the lattice Boltzmann method (LBM). A method to choose characteristic velocity based on Knudsen number is implemented which eradicates the need of arbitrarily guessing characteristic velocities to proceed with simulations. In addition, a less computationally intensive probability distribution function for equilibrium temperature is used. For validation, a standard natural convection problem with left wall at high temperature, right wall at low temperature, and top and bottom adiabatic walls is considered. A grid independence test is conducted and the code is validated with existing results for various Rayleigh numbers, which shows a good agreement. The problem is then modified by including circular and elliptical obstacles of adiabatic, hot, and cold nature. A boundary interpolation technique is used to implement the velocity and temperature boundary conditions at the inner boundaries. The streamline patterns and temperature contours show interesting observations such as dependence of location of vortices on the type of obstacle boundary used, and formation of low or high temperature zones around obstacle at high Rayleigh numbers. Results show that the change in the shape of the obstacle contributes to the Nusselt number variations at the high temperature boundary and low Rayleigh numbers.

ISPH simulations of thermosolutal convection in an annulus amongst an inner prismatic shape and outer cavity including three circular cylinders

During the transmission of heat and mass inside an annulus, the impacts of the thermal diffusion & diffusion-thermo should be considered. Then the target of this paper is solving the thermosolutal convection of a nanofluid inside an annulus amongst a square cavity and an inner prismatic shape with three circular cylinders. The ranges of the considered parameters are the solid volume fraction (0≤φ≤0.1), circular cylinder's radius (0.01≤Rc≤0.075), Hartmann number (0≤Ha≤40), Dufour number (0.03≤Du≤0.6), Rayleigh number (103≤Ra≤106), and Soret number (0.1≤Sr≤2). The results indicated that the radius of the circular cylinders is improving the nanofluid moments and strengths of convection flow in an annulus. The maximum of the streamlines is reducing according to an augmentation in Hartmann number or solid volume fraction. The extra buoyancy forces at higher Rayleigh numbers are improving the strengths of the temperature, concentration, and streamlines within an annulus. The mean Nusselt/Sherwood numbers are enhanced along with an expansion in the solid volume fraction or radius of the circular cylinders.

Use of 2-D and 3-D unsteady RANS in the computation of wall bounded buoyant flows

The present study numerically investigates the performance of a range of RANS turbulence closures with different near-wall treatments in the prediction of natural convection flows. Comparisons are performed of both 2-D and 3-D steady and time-dependent computations in differentially heated cavities, which involve very simple geometries, but give rise to complex flow physics of relevance to cooling applications, including safety features of nuclear reactors. The turbulence closures assessed include eddy-viscosity and second-moment closures and involve low-Reynolds-number versions (LRN) which fully resolve the viscous sublayer, as well as high-Reynolds-number versions (HRN) which adopt wall function treatments to prescribe boundary conditions for the wall shear stress and heat flux.In the 2-D computations of the tall rectangular cavity, there are only small deviations in the predictions of different models, and these are mainly confined to the local Nusselt number comparisons. Among the LRN models, the second-moment EBRSM is in good agreement with the data, while the LRN eddy-viscosity models under-estimate the Nusselt number levels. The HRN models, when used with the standard log-law-based wall function, over-estimate the Nusselt number. During the course of the present investigation, a new, more general, version of the Analytical Wall Function (AWF) has been developed and introduced to the open-source CFD code utilised. Here, this more general numerical wall treatment brings the HRN k-ε predictions of the Nusselt number to very close agreement with the experimental data.In the 2-D square cavity computations, the simulations focus on a high Rayleigh number (Ra) of 1011, for which DNS data has recently become available. At such high Ra value all the models are challenged due to the unsteadiness of the flow and the presence of a largely stationary and laminar core, and thin turbulent boundary layers. Assessment of different 3-D configurations of the same square cavity demonstrates that the effect of the turbulent mixing in the third (z) direction is significant, but can be taken into account by introducing a cavity depth of D=0.15H, matching that used in the DNS study. The deviations in the predictions of the different models are stronger than those observed in the corresponding rectangular cavity comparisons, especially for the local Nusselt number distribution. As is also the case in the rectangular cavity, the eddy-viscosity models under-estimate the Nusselt number, while the EBRSM with the more elaborate turbulent heat flux model once more is closest to the DNS data. All HRN models with the log-law wall function severely under-estimate the Nusselt number levels. Introduction of the buoyancy-adapted AWF leads to substantial predictive improvements. The HRN AWF approach is thus shown to be a reliable and cost-effective modelling strategy for natural convection flows.

Magnetohydrodynamic Effect on Thermal Transport by Silver Nanofluid Flow in Enclosure with Central and Lower Heat Sources

A numerical investigation into the magneto-convection heat transfer performance of Ag-based nanofluid (i.e., silver nanoparticles dispersed in fluid) filled square enclosure containing a thin central heater and a lower heated wall section is performed. The analysis focuses particularly on the effects of the magnetic field strength, central heater orientation and length, lower heated wall section length, Rayleigh number, and Ag nanoparticle volume fraction on the average Nusselt number along the cool, vertical sidewalls of the enclosure. It is found that the heat transfer performance improves as the lengths of the central heater and lower heated wall section increase. Also, the average Nusselt number increases given a vertical orientation of the central heater. Regardless of the heater orientation, the heat transfer performance decreases with increasing magnetic field strength. As Ag nanoparticle volume fraction increases, the average Nusselt number increases with increasing values of Rayleigh number. Finally, the heat transfer performance improves for increasing nanoparticle volume fraction (0.00, 0.03, 0.06, 0.09) at high Rayleigh numbers of 106 and 107.

Fully developed anelastic convection with no-slip boundaries

Anelastic convection at high Rayleigh number in a plane parallel layer with no slip boundaries is considered. Energy and entropy balance equations are derived, and they are used to develop scaling laws for the heat transport and the Reynolds number. The appearance of an entropy structure consisting of a well-mixed uniform interior, bounded by thin layers with entropy jumps across them, makes it possible to derive explicit forms for these scaling laws. These are given in terms of the Rayleigh number, the Prandtl number and the bottom to top temperature ratio, which also measures how much the density varies across the layer. The top and bottom boundary layers are examined and they are found to be very different, unlike in the Boussinesq case. Elucidating the structure of these boundary layers plays a crucial part in determining the scaling laws. Physical arguments governing these boundary layers are presented, concentrating on the case in which the boundary layers are so thin that temperature and density vary little across them, even though there may be substantial temperature and density variations across the whole layer. Different scaling laws are found, depending on whether the viscous dissipation is primarily in the boundary layers or in the bulk. The cases of both high and low Prandtl number are considered. Numerical simulations of no-slip anelastic convection up to a Rayleigh number of $10^7$ have been performed and our theoretical predictions are compared with the numerical results.

Heat transfer and entropy generation analysis of water-Fe3O4/CNT hybrid magnetic nanofluid flow in a trapezoidal wavy enclosure containing porous media with the Galerkin finite element method

The present study addresses theoretically and computationally the performance of electrically conducting water-Fe3O4/CNT hybrid nanofluid in three-dimensional free convection and entropy generation in a wavy-walled trapezoidal enclosure. The enclosure has two layers—a hybrid nanoliquid layer and a permeable medium layer. A transverse magnetic field is acting in the upward direction. Newtonian flow is considered, and the modified Navier–Stokes equations are employed with Lorentz hydromagnetic body force, Darcian and Forchheimer drag force terms. The wavy side walls are heated while the top and vertical walls are adiabatic. An elliptic cylindrical cooled fin is positioned at the center of the cavity, and several different tilting angles of the fin are considered. The transformed, non-dimensional systems of coupled nonlinear partial differential equations with their corresponding boundary conditions are solved numerically with the Galerkin Finite Element Method (FEM) using the COMSOL Multiphysics software platform. The impact of Darcy number, Hartmann number, volume fraction, undulation number of the wavy wall and Rayleigh number (thermal buoyancy parameter) on the streamlines, isotherms and Bejan number contours are investigated. Extensive visualization of the thermal flow characteristics is included. With increasing Hartmann and Rayleigh numbers, the average Bejan number is reduced strongly whereas the average Nusselt number is only depleted significantly at very high values of Rayleigh and high Hartmann numbers. With increasing undulation number, a slight elevation in average Bejan number at intermediate Rayleigh numbers is noticed, whereas the average Nusselt number is substantially boosted, and the effect is maximized at a very high Rayleigh number where the average Nusselt number was increased by 35%. An increment in Darcy number (i.e., reduction in permeability of the porous medium layer) is observed to considerably elevate the average Nusselt number at high values of the Rayleigh number up to 20%, whereas the contrary response is computed in average Bejan number, where it showed a reduction by 10 times. The simulations apply to hybrid magnetic nanofluid fuel cells and electromagnetic nanomaterials processing in cavities.

Heating a cold semi-annulus wall by MHD natural convetion with nanofluid

In the current research, the natural convection of water-Al2O3 nanofluid has been simulated inside a cold semi-annulus chamber with a hot block at the its bottom. Also, an oblique magnetic field (MHD) has been implemented to improve and control the flow. The unstructured triangular mesh and FVM with SIMPLE algorithm have been employed for discretization and coupling of pressure and velocity equations. In this simulation, the parameters of Hartmann, Rayleigh numbers and volume fraction of nanoparticles have been investigated on temperature contours, flow pattern, and hot wall Nusselt number. The observations show that, increasing the volume fraction increases the Nusselt number at low Rayleigh numbers. Moreover, the Nusselt number is inversely related to the Hartmann number for high Rayleigh numbers.

Convection Inside Nanofluid Cavity with Mixed Partially Boundary Conditions

In recent decades, research utilizing numerical schemes dealing with fluid and nanoparticle interaction has been relatively intensive. It is known that CuO nanofluid with a volume fraction of 0.1 and a special thermal boundary condition with heat supplied to part of the wall increases the average Nusselt number for different aspect ratios ranges and for high Rayleigh numbers. Due to its simplicity, stability, accuracy, efficiency, and ease of parallelization, we use the thermal single relaxation time Bhatnagar-Gross-Krook (SRT BGK) mesoscopic approach D2Q9 scheme lattice Boltzmann method in order to solve the coupled Navier–Stokes equations. Convection of CuO nanofluid in a square enclosure with a moderate Rayleigh number of 105 and with new boundary conditions is highlighted. After a successful validation with a simple partial Dirichlet boundary condition, this paper extends the study to deal with linear and sinusoidal thermal boundary conditions applied to part of the wall.