Search results
1 – 10 of 144Pratibha Biswal and Tanmay Basak
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…
Abstract
Purpose
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.
Design/methodology/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 (
Findings
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
Practical implications
The results may be useful for the material processing applications.
Originality/value
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.
Details
Keywords
The effect of throughflow and Coriolis force on convective instabilities in micropolar fluid layer heated from below for free‐free, isothermal and micro‐rotation free boundaries…
Abstract
The effect of throughflow and Coriolis force on convective instabilities in micropolar fluid layer heated from below for free‐free, isothermal and micro‐rotation free boundaries is investigated. Calculations are made using a lower order Galerkin approximation to solve the eigenvalue problem for stationary instability. It is observed that both stabilizing and destabilizing factors due to constant vertical throughflow can be enhanced by rotation.
Details
Keywords
T.O.M. Forslund, I.A.S. Larsson, J.G.I. Hellström and T.S. Lundström
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…
Abstract
Purpose
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.
Design/methodology/approach
A dual lattice hydrodynamic (D3Q27) thermal (D3Q7) multiple-relaxation time LBM model capable of thermal DNS calculations is implemented in CUDA.
Findings
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.
Originality/value
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.
Details
Keywords
Keerthi R, B. Mahanthesh and Smita Saklesh Nagouda
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…
Abstract
Purpose
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.
Design/methodology/approach
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).
Findings
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.
Originality/value
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.
Details
Keywords
Mohammad Saeid Aghighi and Amine Ammar
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…
Abstract
Purpose
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.
Design/methodology/approach
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).
Findings
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.
Originality/value
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.
Details
Keywords
Sahin Yigit and Nilanjan Chakraborty
This paper aims to conduct numerical simulations to investigate steady-state laminar Rayleigh–Bénard convection of yield stress fluids obeying Bingham model in rectangular…
Abstract
Purpose
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 ri/L = 0 to 16 (where ri 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.
Design/methodology/approach
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.
Findings
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
Originality value
Finally, the numerical findings have been used to propose a correlation for
Details
Keywords
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…
Abstract
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.
Details
Keywords
Mohammad Saeid Aghighi, Christel Metivier and Sajad Fakhri
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…
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
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.
Originality/value
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.
Details
Keywords
Saeid Aghighi, Amine Ammar, Christelle Metivier and Francisco Chinesta
The purpose of this paper is to focus on the advanced solution of the parametric non-linear model related to the Rayleigh-Benard laminar flow involved in the modeling of natural…
Abstract
Purpose
The purpose of this paper is to focus on the advanced solution of the parametric non-linear model related to the Rayleigh-Benard laminar flow involved in the modeling of natural thermal convection. This flow is fully determined by the dimensionless Prandtl and Rayleigh numbers. Thus, if one could precompute (off-line) the model solution for any possible choice of these two parameters the analysis of many possible scenarios could be performed on-line and in real time.
Design/methodology/approach
In this paper both parameters are introduced as model extra-coordinates, and then the resulting multidimensional problem solved thanks to the space-parameters separated representation involved in the proper generalized decomposition (PGD) that allows circumventing the curse of dimensionality. Thus the parametric solution will be available fast and easily.
Findings
Such parametric solution could be viewed as a sort of abacus, but despite its inherent interest such calculation is at present unaffordable for nowadays computing availabilities because one must solve too many problems and of course store all the solutions related to each choice of both parameters.
Originality/value
Parametric solution of coupled models by using the PGD. Model reduction of complex coupled flow models. Analysis of Rayleigh-Bernard flows involving nanofluids.
Details
Keywords
Sahin Yigit and Nilanjan Chakraborty
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…
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
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.
Originality/value
Correlations for the mean Nusselt number
Details