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This study aims to carry out the analysis of Rayleigh-Bénard convection within enclosures with curved isothermal walls, with the special implication on the heat flow visualization via the heatline approach.

The Galerkin finite element method has been used to obtain the numerical solutions in terms of the streamlines (ψ ), heatlines (Π), isotherms (θ), local and average Nusselt number ( Nut¯) for various Rayleigh numbers (10³ ≤ Ra ≥ 10⁵), Prandtl numbers (Pr = 0.015 and 7.2) and wall curvatures (concavity/convexity).

The presence of the larger fluid velocity within the curved cavities resulted in the larger heat transfer rates and thermal mixing compared to the square cavity. Case 3 (high concavity) exhibits the largest Nut¯ at the low Ra for all Pr. At the high Ra, Nut¯ is the largest for Case 3 (high concavity) at Pr = 0.015, whereas at Pr = 7.2, Nut¯ is the largest for Case 1 (high concavity and convexity).

The results may be useful for the material processing applications.

The study of Rayleigh-Bénard convection in cavities with the curved isothermal walls is not carried out till date. The heatline approach is used for the heat flow visualization during Rayleigh-Benard convection within the curved walled enclosures for the first time. Also, the existence of the enhanced fluid and heat circulation cells within the curved walled cavities during Rayleigh-Benard heating is illustrated for the first time.

Sinusoidal gravity modulation fields imposed on two‐dimensional Rayleigh‐Benard convection flow are studied to understand the effects of periodic source (g‐jitter) on fluids system and heat transfer mechanism. The transient Navier‐Stokes and energy equations are solved by semi‐implicit operator splitting finite element method. Results include two sets. One is considered at normal terrestrial condition and the other one is related to low‐gravity condition. Under low‐gravity condition the research focuses on the effects of modulation frequency and direction in order to find out the critical frequency for heat transfer mechanism transferring from conduction to convection.

The post-critical convective state for Rayleigh-Benard (RB) convection is studied using a nonlinear spectral-amplitude-perturbation approach in a fluid layer heated from below. The paper aims to discuss these issues.

In the spectral method the flow and temperature fields are expanded periodically along the layer and orthonormal shape functions are used in the transverse direction. A combined amplitude-perturbation approach is developed to solve the nonlinear spectral system in the post-critical range, even far from the linear stability threshold. Also, to leading order, the Lorenz model is recovered.

It is found that very small Prandtl numbers (Pr < 0.1) can change the Nusselt number, when terms to O(ε5/2) and higher are considered. However, to lower orders the Prandtl number does not affect the results. Variation of the Nusselt number to different orders is found to be highly consistent. Comparison with experimental results is made and a very good qualitative agreement is observed, even far from the linear threshold.

Unlike existing nonlinear formulations for RB thermal convection, the present combined spectral-perturbation approach provides a systematic method for mode selection. The number and type of modes to be included are directly related to the post-critical Rayleigh number. The method is not limited to the weakly nonlinear range.

Being extensively used in metallurgy, rotating magnetic fields are also becoming increasingly interesting for application in crystal growth, where they are intended to act by stabilizing the melt flow. For this purpose, it is important to understand the basic interactions of the magnetically induced flow and other flow components like time‐dependent buoyant convection. So a three‐dimensional finite volume method was developed in order to numerically study the effect of a rotating magnetic field on convection in a cylindrical melt volume. The equations of mass, momentum, and heat transport are solved together with the potential equations describing the electromagnetic field. The numerical computation of the Lorenz force distribution is validated by comparison with an analytical solution. The effects of magnetic field parameters on the temperature distributions and the flow patterns in the considered configurations are analysed.

The purpose of this paper is to present a fast and bare bones implementation of a numerical method for quickly simulating turbulent thermal flows on GPUs. The work also validates earlier research showing that the lattice Boltzmann method (LBM) method is suitable for complex thermal flows.

A dual lattice hydrodynamic (D3Q27) thermal (D3Q7) multiple-relaxation time LBM model capable of thermal DNS calculations is implemented in CUDA.

The model has the same computational performance compared to earlier publications of similar LBM solvers. The solver is validated against three benchmark cases for turbulent thermal flow with available data and is shown to be in excellent agreement.

The combination of a D3Q27 and D3Q7 stencil for a multiple relaxation time -LBM has, to the authors’ knowledge, not been used for simulations of thermal flows. The code is made available in a public repository under a free license.

This paper aims to conduct numerical simulations to investigate steady-state laminar Rayleigh–Bénard convection of yield stress fluids obeying Bingham model in rectangular cross-sectional cylindrical annular enclosures. In this investigation, axisymmetric simulations have been carried out for nominal Rayleigh number range Ra = 10³ to 10⁵, aspect ratio range AR = 0.25 to 4 (i.e. AR = H/L where H is the enclosure height and L is the difference between outer and inner radii) and normalised inner radius range r_i/L = 0 to 16 (where r_i is internal cylinder radius) for a nominal representative Prandtl number Pr = 500. Both constant wall temperature (CWT) and constant wall heat flux (CWHF) boundary conditions have been considered for differentially heated horizontal walls to analyse the effects of wall boundary condition.

The bi-viscosity Bingham model is used to mimic Bingham fluids for Rayleigh–Bénard convection of Bingham fluids in vertical cylindrical annuli. The conservation equations of mass, momentum and energy have been solved in a coupled manner using the finite volume method where a second-order central differencing scheme is used for the diffusive terms and a second-order up-wind scheme is used for the convective terms. The well-known semi-implicit method for pressure-linked equations algorithm is used for the coupling of the pressure and velocity.

It is found that the convective transport strengthens (weakens) with an increase in Ra (AR) for both Newtonian (i.e. Bn = 0) and Bingham fluids, regardless of the boundary conditions. Moreover, the strength of convection is stronger in the CWT configuration than that is for CWHF boundary condition due to higher temperature difference between horizontal walls for both Newtonian (i.e. Bn = 0) and Bingham fluids. The mean Nusselt number Nūcy does not show a monotonic increase with increasing Ra for AR = 1 and r_i/L = 4 because of the change in flow pattern (i.e. number of convection rolls/cells) in the CWT boundary condition, whereas a monotonic increase of Nūcy with increasing Ra is obtained for the CWHF configuration. In addition, Nūcy increases with increasing r_i/L and asymptotically approaches the corresponding value obtained for rectangular enclosures (r_i/L → ∞) for both CWT and CWHF boundary conditions for large values of r_i/L. It is also found that both the flow pattern and the mean Nusselt number Nūcy are dependent on the initial conditions for Bingham fluid cases, as hysteresis is evident for AR = 1 for both CWT and CWHF boundary conditions.

Finally, the numerical findings have been used to propose a correlation for Nūcy in the range of 0.25 ≤ r_i/L ≤ 16, 0.25 ≤ AR ≤ 2 and 5 × 10⁴ ≤ Ra ≤ 10⁵ for the CWHF configuration.

The purpose of this paper is to analyze two-dimensional steady-state Rayleigh–Bénard convection within rectangular enclosures in different aspect ratios filled with yield stress fluids obeying the Herschel–Bulkley model.

In this study, a numerical method based on the finite element has been developed for analyzing two-dimensional natural convection of a Herschel–Bulkley fluid. The effects of Bingham number Bn and power law index n on heat and momentum transport have been investigated for a nominal Rayleigh number range (5 × 10³ < Ra < 10⁵), three different aspect ratios (ratio of enclosure length:height AR = 1, 2, 3) and a single representative value of nominal Prandtl number (Pr = 10).

Results show that the mean Nusselt number Nu¯ increases with increasing Rayleigh number due to strengthening of convective transport. However, with the same nominal value of Ra, the values of Nu¯ for shear thinning fluids n < 1 are greater than shear thickening fluids n > 1. The values of Nu¯ decrease with Bingham number and for large values of Bn, Nu¯ rapidly approaches unity, which indicates that heat transfer takes place principally by thermal conduction. The effects of aspect ratios have also been investigated and results show that Nu¯ increases with increasing AR due to stronger convection effects.

This paper presents a numerical study of Rayleigh–Bérnard flows involving Herschel–Bulkley fluids for a wide range of Rayleigh numbers, Bingham numbers and power law index based on finite element method. The effects of aspect ratio on flow and heat transfer of Herschel–Bulkley fluids are also studied.

The study of instability due to the effects of Maxwell–Cattaneo law and internal heat source/sink on Casson dielectric fluid horizontal layer is an open question. Therefore, in this paper, the impact of internal heat generation/absorption on Rayleigh–Bénard convection in a non-Newtonian dielectric fluid with Maxwell–Cattaneo heat flux is investigated. The horizontal layer of the fluid is cooled from the upper boundary, while an isothermal boundary condition is utilized at the lower boundary.

The Casson fluid model is utilized to characterize the non-Newtonian fluid behavior. The horizontal layer of the fluid is cooled from the upper boundary, while an isothermal boundary condition is utilized at the lower boundary. The governing equations are non-dimensionalized using appropriate dimensionless variables and the subsequent equations are solved for the critical Rayleigh number using the normal mode technique (NMT).

Results are presented for two different cases namely dielectric Newtonian fluid (DNF) and dielectric non-Newtonian Casson fluid (DNCF). The effects of Cattaneo number, Casson fluid parameter, heat source/sink parameter on critical Rayleigh number and wavenumber are analyzed in detail. It is found that the value Rayleigh number for non-Newtonian fluid is higher than that of Newtonian fluid; also the heat source aspect decreases the magnitude of the Rayleigh number.

The effect of Maxwell–Cattaneo heat flux and internal heat source/sink on Rayleigh-Bénard convection in Casson dielectric fluid is investigated for the first time.

This paper aims to investigate the aspect ratio (AR; ratio of enclosure height:length) dependence of steady-state Rayleigh–Bénard convection of Bingham fluids within rectangular enclosures for both constant wall temperature and constant wall heat flux boundary conditions. A nominal Rayleigh number range 103 ≤ Ra ≤ 10⁵ (Ra defined based on the height) for a single representative value of nominal Prandtl number (i.e. Pr = 500) has been considered for 1/4 ≤ AR ≤ 4.

The bi-viscosity Bingham model is used to mimic Bingham fluids for Rayleigh–Bénard convection of Bingham fluids in rectangular enclosures. The conservation equations of mass, momentum and energy have been solved in a coupled manner using the finite volume method where a second-order central differencing scheme is used for the diffusive terms and a second-order up-wind scheme is used for the convective terms. The well-known semi-implicit method for pressure-linked equations algorithm is used for the coupling of the pressure and velocity.

It has been found that buoyancy-driven flow strengthens with increasing nominal Rayleigh number Ra, but the convective transport weakens with increasing Bingham number Bn, because of additional flow resistance arising from yield stress in Bingham fluids. The relative contribution of thermal conduction (advection) to the total thermal transport strengthens (diminishes) with increasing AR for a given set of values of Ra and Pr for both Newtonian and Bingham fluids for both boundary conditions, and the thermal transport takes place purely because of conduction for tall enclosures.

Correlations for the mean Nusselt number Nu ¯ have been proposed for both boundary conditions for both Newtonian and Bingham fluids using scaling arguments, and the correlations have been demonstrated to predict Nu ¯ obtained from simulation data for 1/4 ≤ AR ≤ 4, 10³ ≤ Ra ≤ 10⁵ and Pr = 500.

According to the research, viscoplastic fluids are sensitive to slipping. The purpose of this study is to determine whether slip affects the Rayleigh–Bénard convection of viscoplastic fluids in cavities and, if so, under what conditions.

The wall slip was evaluated using a model created for viscoplastic (Bingham) fluids. The coupled conservation equations were solved numerically using the finite element method. Simulations were performed for various parameters: the Rayleigh number, yield number, slip yield number and friction number.

Wall slip determines two essential yield stresses: a specific yield stress value beyond which wall slippage is impossible (S_Yc); and a maximum yield stress beyond which convective flow is impossible (Y_c). At low Rayleigh numbers, Y_c is smaller than S_Yc. Hence, the flow attained a stable (conduction) condition before achieving the no-slip condition. However, for more significant Rayleigh numbers Y_c exceeded S_Yc. Thus, the flow will slip at low yield numbers while remaining no-slip at high yield numbers. The possibility of slipping on the wall increases the buoyancy force, facilitating the onset of Rayleigh–Bénard convection.

An essential aspect of this study lies in its comprehensive examination of the effect of slippage on the natural convection flow of viscoplastic materials within a cavity, which has not been previously investigated. This research contributes to a new understanding of the viscoplastic fluid behavior resulting from slipping.