Non-Darcy mixed convection in a vertical pipe filled with porous medium

Kumar, Ashok; Bera, P.; Kumar, Jai

doi:10.1016/j.ijthermalsci.2010.11.018

Cited by 25 publications

(7 citation statements)

References 36 publications

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“…Other studies have included the so-called vorticity diffusion effect (Brinkman friction). Kumar et al (2011) used a Chebyshev spectral collocation method to study fully developed mixed convective flow in a vertical pipe filled with porous medium, driven by external pressure gradient and buoyancy force. Singh et al (2011) used a perturbation method to study the unsteady nonDarcian laminar natural convection flow in a vertical Computer Methods in Biomechanics and Biomedical Engineering 897 channel partially filled with porous medium.…”

Section: Introductionmentioning

confidence: 99%

Differential transform semi-numerical analysis of biofluid-particle suspension flow and heat transfer in non-Darcian porous media

Bég¹,

Rashidi

Bég

et al. 2013

Computer Methods in Biomechanics and Biomedical Engineering

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The differential transform method (DTM) is semi-numerical method which is used to study the steady, laminar buoyancy-driven convection heat transfer of a particulate biofluid suspension in a channel containing a porous material. A two-phase continuum model is used. A set of variables is implemented to reduce the ordinary differential equations for momentum and energy conservation (for both phases) to a dimensionless system. DTM solutions are obtained for the dimensionless system under appropriate boundary conditions. We examine the influence of momentum inverse Stokes number (Skm), Darcy number (Da), Forchheimer number (Fs), particle loading parameter (pL), particle-phase wall slip parameter (Ω) and buoyancy parameter (B) on the fluid-phase velocity (U) and particle-phase velocity (Up). Padé approximants are also employed to achieve satisfaction of boundary conditions. Excellent correlation is obtained between the DTM and numerical quadrature solutions. The results indicate that there is a strong decrease in fluid-phase velocities with increasing Darcian (first-order) drag and the second-order Forchheimer drag, and a weaker reduction in particle-phase velocity field. Fluid and particle-phase velocities are also strongly affected with inverse momentum Stokes number. DTM is shown to be a powerful tool providing engineers with an alternative simulation approach to other traditional methods for multi-phase computational biofluid mechanics. The model finds applications in haemotological separation and biotechnological processing.

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Section: Introductionmentioning

confidence: 99%

Differential transform semi-numerical analysis of biofluid-particle suspension flow and heat transfer in non-Darcian porous media

Bég¹,

Rashidi

Bég

et al. 2013

Computer Methods in Biomechanics and Biomedical Engineering

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“…The kth Chebyshev polynomial, T k (ξ ), is define on interval [-1,1] by T k (ξ ) = cos kθ (11) If ξ = cos(θ), Then T k (ξ ) = cos(kθ). The collocation points which are the extrema of the last retained Chebyshev polynomial T N (ξ ) in the truncated series are defined by…”

Section: Chebyshev Spectral Collocation Methodsmentioning

confidence: 99%

“…Here, the literature pertinent to the laminar Wall-bounded mixed convection in vertical systems has given. Some studies in wall bounded mixed convection through vertical channels ( [2], [3], [4], [5], [6], [7], [6], [8], [9], [10]) pipe ( [11]) and annulus ( [12], [13]) filled with porous medium are reported.…”

Section: Introductionmentioning

confidence: 99%

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Numerical investigation of mixed convective flow in parallel channel filled with porous medium

Kumar

Alam

Kapoor

2014

Nonlinear Engineering

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The present manuscript reports a numerical investigation of fully developed mixed convective flow in a parallel channel filled with porous medium. The motion in the channel is induced by external pressure gradient and buoyancy force. The non-Darcy Brinkman-Forchheimer extended model has been used. The Chebyshev spectral collocation method has been used to solve the coupled differential equations numerically. The main emphesize has been given on the influence of Forchheimer number (F), Darcy number (Da) and Rayleigh number (Ra) on velocity and temperature profiles. From this investegation we have found that the velocity as well as temperature profiles possess point of inflection beyond a threshold value of Ra. The back flow starts near the center of the channel on increasing the value of Ra beyond the threshold value of Ra. The point of inflection on the velocity as well as temperature profile dies out on decreasing of Da. The strength of the velocity is decreases on the increasing of F ′ , it also changes the velocity profile drastically. The point of inflection on the basic flow dies out on increasing of F ′ .

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“…He also employed a generalized energy method to demonstrate that the result of [156] is true in the fully three-dimensional case although the initial data must be restricted. Articles dealing with other interesting aspects of convection in a vertical porous slab or pipe involving effects like double diffusion, and LTNE, include the papers by [32,33,36,46,211,220,221,329,330,362] and [460]. The methods of energy stability techniques applied specifically to convection in a vertical porous slab are addressed in [144,229] and [356], and these are discussed in detail in the book by [414, pp.…”

Section: Chapter 5 Vertical Porous Convection With Ltnementioning

confidence: 99%

Convection with Local Thermal Non-Equilibrium and Microfluidic Effects

Straughan

2015

Advances in Mechanics and Mathematics

111

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In this chapter we describe work of [366] and of [393] on thermal convection in a Darcy porous material in a vertical layer subject to different temperatures on the vertical walls.For the case of a single temperature the problem where the porous medium occupies a vertical layer subject to differential heating from one side to the other has attracted much attention. This problem has much application to insulation, such as in the area of building design, and is of importance in window double glazing. For the single temperature situation the first proof that a vertical porous slab of Darcy type which is held at fixed but different temperatures on the vertical walls is stable to perturbations from the equilibrium state is due to [156]. His analysis is based on the linear theory and analyses the two-dimensional problem.[409] further analysed this problem but in three-dimensions and he treated the completely nonlinear situation by employing energy-like integral methods. In particular, [409] produced a threshold for the Rayleigh number which guarantees global nonlinear stability, i.e. regardless of how large the initial perturbation may be. He also employed a generalized energy method to demonstrate that the result of [156] is true in the fully three-dimensional case although the initial data must be restricted. Articles dealing with other interesting aspects of convection in a vertical porous slab or pipe involving effects like double diffusion, and LTNE, include the papers by [32, 33, 36, 46, 211, 220, 221, 329, 330, 362] and [460]. The methods of energy stability techniques applied specifically to convection in a vertical porous slab are addressed in [144, 229] and [356], and these are discussed in detail in the book by [414, pp. 126-134].The analogous problem in LTNE to that of [156] was first addressed by [366]. Specifically [366] dealt with the [156] problem of thermal convection in a vertical porous medium, but he employed the theory of local thermal non-equilibrium, allowing for different fluid and solid temperatures. The interesting work of [366] demonstrates that the vertical configuration is always stable according to linear theory, even with the much more complicated LTNE theory. [393] continued the problem of [366] but they analysed the complete nonlinear three-dimensional situation.

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Non-Darcy mixed convection in a vertical pipe filled with porous medium

Cited by 25 publications

References 36 publications

Differential transform semi-numerical analysis of biofluid-particle suspension flow and heat transfer in non-Darcian porous media

Differential transform semi-numerical analysis of biofluid-particle suspension flow and heat transfer in non-Darcian porous media

Numerical investigation of mixed convective flow in parallel channel filled with porous medium

Convection with Local Thermal Non-Equilibrium and Microfluidic Effects

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