Onset of Rayleigh–Bénard MHD convection in a micropolar fluid

The present work is concerned with the effect of a uniform magnetic field on the onset of convection in an electrically conducting micropolar fluid. A flat fluid layer bounded by horizontal rigid boundaries, subjected to thermal boundary conditions of the Neumann type, is considered. The parallel flow approximation is used to predict analytically the critical Rayleigh number for the onset of convection. The onset of motion is found to depend on the Hartmann number Ha, materials parameters K, B, $\lambda$, and the micro-rotation boundary condition n. A linear stability analysis is carried out to study numerically the onset of convection. The predictions of the analytical model are found to be in good agreement with the numerical solution. The above results are also compared with those obtained numerically for the case of a system subject to Dirichlet thermal boundary conditions.     

Probing the Rayleigh–Benard convection phase change mechanism of low-melting-point metal via lattice Boltzmann method

A double distribution function lattice Boltzmann method (LBM) with multirelaxation time is implemented to simulate the Rayleigh–Benard convection melting of a typical low-melting-point metal in a rectangular cavity. Typical cases frequently encountered in practice with constant heat flux/constant temperature boundary conditions are parametrically investigated, with corresponding dimensionless results outlined; the influence of inclination angle of the cavity is also clarified. The computational speed of the current LBM would reach about 40 times faster than that of conventional finite volume method as performed by commercial software Fluent. The obtained results would be valuable for guiding practical thermal design.     

The Rayleigh–Bénard convection in near-critical fluids: Influences of the specific heat ratio

This article studies the natural convection in near-critical fluids under the Rayleigh–Bénard configuration. The governing equations are non-dimensionalized by using modified scaling factors and five dimensionless parameters are determined, out of which the specific heat ratio γ is investigated thoroughly in terms of its influences on the convection. The governing equations are solved by the finite volume method along with the low Mach number approximation technique. It is revealed that the strength of the piston effect increases with γ. Since the piston effect is more efficient than the convection in terms of heat transfer, as γ is reduced, the relaxation of temperature field is weakened, while the development of convection is enhanced. By comparing the temperature and velocity fields in different cases and analyzing the heat transfer characteristic, we conclude that the final quasi-steady state is almost unaffected.     

Effect of heat source on Rayleigh–Bénard convection in rotating viscoelastic liquids

The influence of heat sources on instability in rotating viscoelastic liquids is studied. Linear stability analysis is done using normal modes. Computations are done for 10 boundary combinations and the results reveal that convection manifests via the oscillatory mode in this case. The critical values of the oscillatory and stationary instability have been studied. The results indicate individual stabilizing influences of rotation and strain retardation along with heat source in the case of free isothermal boundary conditions. It has quite unpredictable influences on the system stability in all the other boundary conditions for the chosen parameters. By suitable limiting processes, results pertaining to Oldroyd liquid B will lead to those of Maxwell, Newtonian, and Rivlin–Ericksen liquids. The problem finds applications in a working media consisting of viscoelastic liquids with nonisothermal systems.     

Rayleigh–Bénard and Bénard–Marangoni magnetoconvection in variable viscosity finitely conducting liquids

The thermorheological effect on magneto-Bénard-convection is studied numerically in fluids with finite electrical conductivity. A nonlinear thermorheological equation is considered in the problem. The results are compared with the classical approach of constant viscosity, which depicts the fact that the effect of increasing the strength of the magnetic field is to delay the onset of convection. The magnetic field is shown to have a rheostatic influence on convective instabilities. The results obtained by the study have possible applications in the field of astrophysics, sunspots, and in space applications under microgravity.     

Rayleigh–Bénard convection in a supercritical fluid along its critical isochore in a shallow cavity

We perform a numerical investigation of the Rayleigh–Bénard convection in supercritical nitrogen in a shallow enclosure with an aspect ratio of 4. The transient and steady-state fluid behaviors over a wide range of initial distances to the critical point along the critical isochore are obtained and analyzed in response to modest homogeneous bottom heating. On account of the fluid layer being extremely thin, density stratification is notably excluded from consideration herein, which leads to the dominating role of the Rayleigh criterion in the onset of convection. Following the Boussinesq approximation, we find the power law scaling relationships over five decades of the Rayleigh number (Ra) for various transient quantities including the exponential growth rate of the mean enstrophy in the cavity and the characteristic times of the development of convective motion. The correlation of the Nusselt number versus the Rayleigh number shows asymptotic features at the two ends of the Ra spectrum, which incidentally correspond to different convection patterns. Under the regime of high Ra, the heat transfer through the fluid cavity is enhanced by the turbulent bursts of thermal plumes from the boundary layers. On the other hand, under the regime of low Ra, it is the orderly multicellular flow that moves heat from the bottom of the layer to the top, which includes a transition from a four-cell structure to a six-cell structure with decreasing Ra.     

Natural convection flow of Cu–Water nanofluid in horizontal cylindrical annuli with inner triangular cylinder using lattice Boltzmann method

In this paper the lattice Boltzmann method is used to investigate the effect of nanoparticles on natural convection heat transfer in two-dimensional horizontal annulus. The study consists of an annular-shape enclosure, which is created between a heated triangular inner cylinder and a circular outer cylinder. The inner and outer surface temperatures were set as hot (T_h) and cold temperatures (T_c), respectively and assumed to be isotherms. The effect of nanoparticle volume fraction to the enhancement of heat transfer was examined at different Rayleigh numbers. Furthermore, the effect of vertical, horizontal, and diagonal eccentricities at various locations is examined at Ra = 10⁴. The result is presented in the form of streamlines, isotherms, and local and average Nusselt number. Results show that the Nusselt number and the maximum stream functions increase by augmentation of solid volume fraction. Average Nusselt number increases when the inner cylinder moves downward, but it decreases, when the location of inner cylinder changes horizontally.     

Rayleigh–Bénard convection in a Boussinesq–Stokes ferromagnetic fluid under sinusoidal and non-sinusoidal internal heat modulation

Internal heat modulation has several applications in nuclear reactor design and safety, as well as meteorology. In this paper, the influence of internal heat modulation on Rayleigh–Bénard convection in a Boussinesq–Stokes ferromagnetic fluid is explored using linear and nonlinear analyses. The impact of the square, sine, triangular, and sawtooth wave type of internal heat modulation on the onset of convection and heat transport is considered. Using a Venezian method, linear stability analysis is performed to derive the correction Rayleigh number and the critical Rayleigh number for all four waveforms. A nonautonomous Lorenz model is derived and solved for the amplitude to obtain the Nusselt number, which quantifies the heat transport. The impact of the nondimensional parameter on the convective onset and heat transfer under heat source/sink modulation is analyzed. The study shows that all four types of internal heat modulation destabilize the system. It is also found that the presence of a heat source/sink modulation affects the impact of all four types of internal heat modulation on heat transport.     

The onset of Rayleigh–Bénard convection and heat transfer under two-frequency rotation modulation

The impact of 16 combinations of sinusoidal (sine) and nonsinusoidal (square, triangular, and sawtooth) time-periodic Coriolis force (rotation modulation) on Rayleigh–Bénard convection in a Newtonian liquid is studied in this paper. This consideration is made to capture the possible effects of two-frequency rotation modulation on stability, that is, the onset of convection and the simultaneous amount of heat transfer in the system. The Venezian approach has been asserted on the linearized Lorenz model to derive the correction Rayleigh number as a function of the two frequencies. The Lorenz model with nonlinearities is evaluated numerically to assess the quantity of heat transfer in the system. The present study states that in comparison with existing studies of no-modulation and single-frequency rotation modulation, two-frequency rotation modulation yields higher stability bounds and thus diminishes the heat transfer. Heat transfer is found to be enhanced by a pair of coprime integers associated with the harmonics in the system.     

Lattice Boltzmann simulations of a radiatively participating fluid in Rayleigh–Benard convection

Thermal radiation is an integral part of the heat transfer process but it is often neglected due to the complexity involved in the analysis of radiative transfer. We use the lattice Boltzmann method as a common computational tool to solve all three modes of heat transfer: conduction, convection, and radiation. This tool is then used to analyze the effect of radiatively participating medium on Rayleigh–Benard convection. We find that increasing the effects of radiation (i) increases the critical Rayleigh number required for the onset of Rayleigh–Benard convection and (ii) affects the temperature and flow patterns of convection rolls significantly changing the net heat transfer between the hot and cold plates. Both these effects are due to the presence of radiation available as an additional mode of heat transfer. Thus, we establish that the unified lattice Boltzmann framework is an effective computational tool for heat transfer and propose to use this method for a large range of problems in science and engineering involving radiative heat transfer.     

Effect of horizontal pressure gradient on Rayleigh–Bénard convection of a Newtonian nanoliquid in a high porosity medium using a local thermal non-equilibrium model

A study of linear and weakly nonlinear stability analyses of Darcy–Brinkman convection in a water–alumina, nanoliquid-saturated porous layer for stress-free isothermal boundaries, when the solid and nanoliquid phases are in local thermal nonequilibrium, is conducted. The critical eigenvalue is found using the Galerkin approach. The effect of the pressure gradient, thermal conductivity ratio, interphase heat transfer coefficient, inverse Darcy number, and Brinkman number on the heat transport and onset of convection is examined and represented graphically. The critical values of wavenumber and nanoliquid Rayleigh number are found for different problem parameter values. The effect of increasing the porosity-modified ratio of thermal conductivity advances the onset of convection and increases the amount of heat transport, whereas the remaining parameters have the opposite impact on the onset of convection and amount of heat transport. The classical results of the local thermal equilibrium case and Darcy–Bénard convection in the presence of pressure gradient are obtained as a limiting case of the present problem.     

Individual effects of four types of rotation modulation on Rayleigh–Bénard convection in a ferromagnetic fluid with couple stress

The effect of trigonometric sine, square, triangular, and sawtooth wave types of rotation modulation on Rayleigh–Bénard convection in a ferromagnetic fluid with couple stress is investigated in this paper using linear and nonlinear analyses. The expression for the critical Rayleigh number and the correction Rayleigh number is deduced from the three-mode linearized Lorenz model using the Venezian approach. The effect of rotation modulation on heat transport is studied using the generalized fifth-order Lorenz model. The study reveals that the Taylor number stabilizes the no-modulation system and decreases the heat transport, and this situation remains so in the presence of rotation modulation. It is found that the effect of all four types of modulation is to stabilize the system and diminish heat transport. It is also observed that the sawtooth wave type of modulation has the least diminishing effect on heat transport and the square wave type of modulation diminishes the most.     

Bénard convection from a circular cylinder in a packed bed

Bénard convection around a circular heated cylinder embedded in a packed bed of spheres is studied numerically. The Forchheimer–Brinkman–extended Darcy momentum model with the Local Thermal Non-Equilibrium energy model is used in the mathematical formulation for the porous layer. The governing parameters considered are the Rayleigh number (10³ ≤ Ra ≤ 5 × 10⁷) and the thermal conductivity ratio (0.1 ≤ k_r ≤ 10,000). The structural properties of the packed bed are kept constant as: cylinder-to-particle diameter ratio D/d = 20 and porosity ε = 0.5, while the Prandtl number is fixed at Pr = 0.71. It is found that the presence of the porous medium suppresses significantly the strong free convection produced in the empty enclosure, and reduces considerably the high intensity of the pair of vortices generated behind the cylinder. Also, the results show that the porous medium can play the role of insulator or enhancer of heat transfer from the heat source, depending mainly on their thermal conductivities regardless of the Rayleigh number.     

Investigation of natural convection via heatlines for Rayleigh–Bénard heating in porous enclosures with a curved top and bottom walls

The current study deals with the heatline-based analysis of natural convection in porous cavities with the curved top and bottom walls involving the Rayleigh–Bénard heating. The streamline cells are weak, and the wall-to-wall heatlines are observed for all the cases at the low Da_m involving two test cases, Pr_m?=?0.015 and 7.2. At the high Da_m, the convective force takes the command, and multiple heatline cells are observed for all the concave (except for high wall concavity) and convex cases. The directions of the streamlines (for all Da_m) and heatlines (at the high Da_m) are exactly opposite for the concave and convex cases. The case 3 (concave) is the efficient case based on the largest heat transfer rate for Pr_m?=?0.015 involving all Da_m and for Pr_m?=?7.2 involving the low Da_m. At Pr_m?=?7.2 and high Da_m, the case 1 (concave or convex) may be the efficient cases compared with the cases involving high wall curvatures.     

Analysis of exergy loss vs heat transfer rate for Rayleigh–Bénard convection of various fluids in enclosures with curved walls

The investigation of entropy generation is highly desirable for the optimization of the thermal systems to avoid larger energy wastage and ensure higher heat transfer rate. The numerical investigation of natural convection within enclosures with the concave and convex horizontal walls involving the Rayleigh–Bénard heating is performed via entropy generation approach. The spatial distributions of the temperature (θ), fluid flow (ψ), entropy generation due to heat transfer and fluid friction (S_θ and S_ψ) are discussed extensively for various Rayleigh numbers and Prandtl numbers involving various wall curvatures. A number of complex patterns of spatial distributions of fluid flow and temperature for cavities with concave or convex isothermal walls (top and bottom) have been obtained. The zones of high entropy generation for temperature and fluid flow are detected within cavities with concave and convex horizontal walls. The optimal situation involves the high heat transfer rate with moderate or low entropy generation. Overall, case 3 (highly concave) is found to be optimal over cases 1 and 2 (concave) and cases 1–3 (convex) for all Pr and Ra.     

A three-dimensional enthalpic lattice Boltzmann formulation for convection–diffusion heat transfer problems in heterogeneous media

In this paper, an enthalpic lattice Boltzmann method formulation for 3D unsteady convection–diffusion heat transfer problems is used to overcome discontinuity issues in heterogeneous media. The new formulation is based on the appearance of a source term added to the collision step. The major achievement of the proposed enthalpic LB formulation is avoiding any interface treatments or geometry considerations even when dealing with complex geometries. The performance of the present method is tested for several three-dimensional convection–diffusion problems. Comparisons are made with the control volume method, and numerical results show excellent agreements.