Natural convection problem in a Bingham fluid using the operator-splitting method

Huilgol, R. R.; Kefayati, Gholamreza

doi:10.1016/j.jnnfm.2014.06.005

Cited by 74 publications

(33 citation statements)

References 22 publications

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“…This difficulty is circumvented via the use of a Lagrange multiplier related to the stress tensor. Similarly, there have been some developments in the use of operator -splitting method [35]. For the benchmark problem of cavity flow, these predictions are in line with that of the exponential regularization, at least at low Bingham numbers.…”

Section: Streamlines and Isotherm Contoursmentioning

confidence: 61%

Effect of Fluid Yield Stress on Natural Convection From Horizontal Cylinders in a Square Enclosure

Baranwal

Chhabra

2016

Heat Transfer Engineering

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In this study, laminar natural convection heat transfer to Bingham plastic fluids from two differentially heated isothermal cylinders confined in a square enclosure (with isothermal walls) has been investigated numerically. The governing partial differential equations have been solved over the ranges of the dimensionless parameters, namely, Rayleigh number, 10 2 to 10 6 ; Prandtl number, 10 to 100 and Bingham number, 0.01 to 100 for seven locations of inner cylinders as, 0.25, 0.2, 0.1 and 0. These values correspond to the range of Grashof number varying from 10 to 10 5 . The detailed flow and temperature fields are visualized in terms of the streamlines and isotherm contours. Further insights are developed by examining the iso-shear rate contours and the yield surfaces delineating the fluid-like and solid-like regions. The corresponding heat transfer results are analyzed in terms of the distribution of local Nusselt number along the cylinder surface together with its surface averaged value as functions of the Rayleigh number, Prandtl number, Bingham number and positions of the cylinders. It is found that the average Nusselt number increases with the increasing values of the Rayleigh number and decreases with the increasing Bingham number. For sufficiently large values of the Bingham number, the average Nusselt number reaches its asymptotic value wherein heat transfer takes place solely by conduction. Based on the present numerical results, simple correlations for the prediction of the average Nusselt number and the limiting Bingham number have been developed. Also, a dimensionless criterion denoting the cessation of convection regime is outlined for this configuration.

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Section: Streamlines and Isotherm Contoursmentioning

confidence: 61%

Effect of Fluid Yield Stress on Natural Convection From Horizontal Cylinders in a Square Enclosure

Baranwal

Chhabra

2016

Heat Transfer Engineering

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“…As an aside, Huilgol & Kefayati (2015) also consider the critical Bingham number (denoted Bn) in a square cavity and examine its variation with Ra and Pr. Their parameter Bn is given by independent of Ra and Pr, Bn cr ∼ Ra 0.5 Pr −0.5 .…”

Section: Discussionmentioning

confidence: 99%

“…Finally, a few studies have considered flows for which a limiting value of the yield stress results in a static regime (e.g. Vikhansky 2010a,b; Karimfazli & Frigaard 2013;Huilgol & Kefayati 2015). It is these static regimes that have importance in the current study as being purely conductive.…”

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confidence: 99%

“…Turan et al (2010Turan et al ( , 2011 have utilized the regularized biviscosity model available in FLUENT to study the variation of heat transfer with the aspect ratio h and other dimensionless groups. Huilgol & Kefayati (2015) recently studied the same problem in a square cavity using operator splitting methods with no regularization. Although the above-mentioned works use similar dimensionless formulations, we have chosen to use a different set of dimensionless parameters.…”

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confidence: 99%

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A novel heat transfer switch using the yield stress

2015

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International audienceWe explore the feasibility of a novel method for the regulation of heat transfer across a cavity, by using a controllable yield stress in order to suppress the convective heattransfer. Practically, this type of control can be actuated with electro-rheological ormagneto-rheological fluids. We demonstrate that above a given critical yield stressvalue only static steady regimes are possible, i.e. a purely conductive unyielded fluidfills the cavity. We show that this limit is governed by a balance of yield stressand buoyancy stresses, here described by B. With proper formulation the criticalstate can be described as a function of the domain geometry, and is independent ofother dimensionless flow parameters (Rayleigh number, Ra, and Prandtl number, Pr).On the theoretical side, we examine the conditional stability of the static regime.We derive conservative conditions on disturbance energy to ensure that perturbationsfrom a static regime decay to zero. Assuming stability, we show that the kineticenergy of the perturbed field decays to zero in a finite time, and give estimatesfor the stopping time, t0. This allows us to predict the response of the system insuppressing advective heat transfer. The unconditional stability is also considered forthe first time, illustrating the role of yield stress. We focus on the hydrodynamiccharacteristics of Bingham fluids in transition between conductive and convectivelimits. We use computational simulations to resolve the Navier–Stokes and energyequations for different yield stresses, and for different imposed controls. We showthat depending on the initial conditions, a yield stress less than the critical value canresult in temporary arrest of the flow. The temperature then develops conductivelyuntil the fluid yields and the flow restarts. We provide estimates of the hydrodynamictimescales of the problem and examples of flow transitions. In total, the theoreticaland computational results establish that this methodology is feasible as a control, atleast from a hydrodynamic perspective

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“…However, there is a growing interest in the use of the operator-splitting method which obviates the need for the regularization of such inherently discontinuous yield-stress viscosity model, e.g. see [33] for recent results for the benchmark problem of cavity flow. While the predictions based on this approach and that on the use of bi-viscous model [34] are in good agreement for small Bingham numbers, but these somewhat differ from each other with the increasing value of the Bingham number.…”

Section: Problem Statement and Formulationmentioning

confidence: 99%

Effect of aiding buoyancy on heat transfer from an isothermal elliptical cylinder in Newtonian and Bingham plastic fluids

Patel

Chhabra

2015

International Journal of Heat and Mass Transfer

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Natural convection problem in a Bingham fluid using the operator-splitting method

Cited by 74 publications

References 22 publications

Effect of Fluid Yield Stress on Natural Convection From Horizontal Cylinders in a Square Enclosure

Effect of Fluid Yield Stress on Natural Convection From Horizontal Cylinders in a Square Enclosure

A novel heat transfer switch using the yield stress

Effect of aiding buoyancy on heat transfer from an isothermal elliptical cylinder in Newtonian and Bingham plastic fluids

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