The Effect of Internal and External Heating on the Free Convective Flow of a Bingham Fluid in a Vertical Porous Channel

Rees, D. Andrew S.; Bassom, Andrew P.

doi:10.3390/fluids4020095

Cited by 8 publications

(5 citation statements)

References 11 publications

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“…Most of these are boundary layer flows; see Rees 11 for a discussion of these works. A series of four papers by Rees and Bassom [12][13][14][15] is devoted to different aspects of onedimensional flows and it covers similar ground to works by Yang and Yeh 16 , Kleppe and Marner 17 , Patel and Ingham 18 , Bayazitoglu et al 19 and Barletta and Magyari 20 . Rees 21 has also presented nonlinear computations for convection in a sidewall-heated cavity and found that the presence of a Bingham fluid means that there is a critical value of the Darcy-Rayleigh number above which convection arises.…”

Section: Introductionmentioning

confidence: 95%

Darcy–Bénard–Bingham convection

Rees

2020

Physics of Fluids

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The present paper is the first to consider Darcy-Bénard-Bingham convection. A Bingham fluid saturates a horizontal porous layer which is subjected to heating from below. It is shown that this simple extension to the classical Darcy-Bénard problem is linearly stable to small-amplitude disturbances but nevertheless admits strongly nonlinear convection. The Pascal model for a Bingham fluid occupying a porous medium is adopted, and this law is regularized in a frame-invariant manner to yield a set of two-dimensional governing equations which are then solved numerically using finite difference approximations. A weakly nonlinear theory of the regularized Pascal model is used to show that the onset of convection is via a fold bifurcation. Some parametric studies are performed to show that this nonlinear onset of convection arises at increasing values of the Darcy-Rayleigh number as the Rees-Bingham number increases, and that for a fixed Rees-Bingham number the wavenumber at which the rate of heat transfer is maximised increases with the Darcy-Rayleigh number.

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Section: Introductionmentioning

confidence: 95%

Darcy–Bénard–Bingham convection

Rees

2020

Physics of Fluids

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“…The convective flow of Bingham fluid in a vertical channel has also been studied; for the Couette-Poiseuille flow, the natural convection is studied in [20]. In a porous channel, the influence of exterior and internal heating on the free convective flow has been explored using Pascal's piecewise-linear law for Poiseuille flow in [21] and in [22] for mixed convection of non-Newtonian fluids, the analytic solutions have been produced.…”

Section: Introductionmentioning

confidence: 99%

Computational Analysis of Fluid Forces on an Obstacle in a Channel Driven Cavity: Viscoplastic Material Based Characteristics

et al. 2022

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In the current work, an investigation has been carried out for the Bingham fluid flow in a channel-driven cavity with a square obstacle installed near the inlet. A square cavity is placed in a channel to accomplish the desired results. The flow has been induced using a fully developed parabolic velocity at the inlet and Neumann condition at the outlet, with zero no-slip conditions given to the other boundaries. Three computational grids, C1, C2, and C3, are created by altering the position of an obstacle of square shape in the channel. Fundamental conservation and rheological law for viscoplastic Bingham fluids are enforced in mathematical modeling. Due to the complexity of the representative equations, an effective computing strategy based on the finite element approach is used. At an extra-fine level, a hybrid computational grid is created; a very refined level is used to obtain results with higher accuracy. The solution has been approximated using P2 − P1 elements based on the shape functions of the second and first-order polynomial polynomials. The parametric variables are ornamented against graphical trends. In addition, velocity, pressure plots, and line graphs have been provided for a better physical understanding of the situation Furthermore, the hydrodynamic benchmark quantities such as pressure drop, drag, and lift coefficients are assessed in a tabular manner around the external surface of the obstacle. The research predicts the effects of Bingham number (Bn) on the drag and lift coefficients on all three grids C1, C2, and C3, showing that the drag has lower values on the obstacle in the C2 grid compared with C1 and C3 for all values of Bn. Plug zone dominates in the channel downstream of the obstacle with augmentation in Bn, limiting the shear zone in the vicinity of the obstacle.

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“…Existence of weak solutions for the system governing the motion is investigated in [3], studies nonlinear stability of Poiseuille flow in pipes and plane channels in [4], spatial decay estimates are obtained for the problem of entry flow in a pipe in [5], and Couette-Poiseuille flow in a porous channel is studied with slip conditions in [6]. Some papers deal with the convective flow of a Bingham fluid in a vertical channel: the natural convection is studied in [7] for the Couette-Poiseuille flow and in [8,9] for the Poiseuille flow, the effect of internal and external heating on the free convective flow in a porous channel is investigated using Pascal's piecewise-linear law in [10], and the mixed convection is analyzed in [11].…”

Section: Introductionmentioning

confidence: 99%

“…10 , c 11 , c 12 are given in the Appendix A. Now, we search the plug region [y 0 , y 1 ] where y 1 satisfies the equation t 12 (y) = B, i.e.,…”

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confidence: 99%

Magnetohydrodynamic Flow of a Bingham Fluid in a Vertical Channel: Mixed Convection

Borrelli

Giantesio

Patria

2021

Fluids

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In this paper, we describe our study of the mixed convection of a Boussinesquian Bingham fluid in a vertical channel in the absence and presence of an external uniform magnetic field normal to the walls. The velocity, the induced magnetic field, and the temperature are analytically obtained. A detailed analysis is conducted to determine the plug regions in relation to the values of the Bingham number, the buoyancy parameter, and the Hartmann number. In particular, the velocity decreases as the Bingham number increases. Detailed considerations are drawn for the occurrence of the reverse flow phenomenon. Moreover, a selected set of diagrams illustrating the influence of various parameters involved in the problem is presented and discussed.

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The Effect of Internal and External Heating on the Free Convective Flow of a Bingham Fluid in a Vertical Porous Channel

Cited by 8 publications

References 11 publications

Darcy–Bénard–Bingham convection

Darcy–Bénard–Bingham convection

Computational Analysis of Fluid Forces on an Obstacle in a Channel Driven Cavity: Viscoplastic Material Based Characteristics

Magnetohydrodynamic Flow of a Bingham Fluid in a Vertical Channel: Mixed Convection

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