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Article
Publication date: 4 September 2017

Pratibha 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 ( Nut¯) for various Rayleigh numbers (103Ra ≥ 105), Prandtl numbers (Pr = 0.015 and 7.2) and wall curvatures (concavity/convexity).

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 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).

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

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 9
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 September 1999

Yedidi N. Murty

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

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 9 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Open Access
Article
Publication date: 7 December 2022

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

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 33 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 16 April 2020

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 RayleighBénard 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

Multidiscipline Modeling in Materials and Structures, vol. 16 no. 5
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 3 July 2017

Mohammad Saeid Aghighi and Amine Ammar

The purpose of this paper is to analyze two-dimensional steady-state RayleighBénard 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 RayleighBénard 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

Engineering Computations, vol. 34 no. 5
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 12 December 2018

Sahin Yigit and Nilanjan Chakraborty

This paper aims to conduct numerical simulations to investigate steady-state laminar RayleighBénard convection of yield stress fluids obeying Bingham model in rectangular…

Abstract

Purpose

This paper aims to conduct numerical simulations to investigate steady-state laminar RayleighBénard 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 RayleighBénard 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 Nūcy does not show a monotonic increase with increasing Ra for AR = 1 and ri/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 ri/L and asymptotically approaches the corresponding value obtained for rectangular enclosures (ri/L → ∞) for both CWT and CWHF boundary conditions for large values of ri/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.

Originality value

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

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 May 1993

BALASUBRAMANIAM RAMASWAMY

Sinusoidal gravity modulation fields imposed on two‐dimensional RayleighBenard convection flow are studied to understand the effects of periodic source (g‐jitter) on fluids…

Abstract

Sinusoidal gravity modulation fields imposed on two‐dimensional RayleighBenard 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

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 3 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 13 October 2023

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 RayleighBénard 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 RayleighBénard 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 RayleighBénard 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

Multidiscipline Modeling in Materials and Structures, vol. 19 no. 6
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 3 August 2015

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

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 25 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 6 February 2017

Sahin Yigit and Nilanjan Chakraborty

This paper aims to investigate the aspect ratio (AR; ratio of enclosure height:length) dependence of steady-state RayleighBénard convection of Bingham fluids within rectangular…

167

Abstract

Purpose

This paper aims to investigate the aspect ratio (AR; ratio of enclosure height:length) dependence of steady-state RayleighBénard 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 RayleighBénard 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 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, 103Ra ≤ 105 and Pr = 500.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

1 – 10 of 144