Analysis of effects of Thermal Non-Equilibrium and Non-Darcy Flow on Natural Convection in a Square Porous Enclosure Provided with a Heated L Shape Plate

Alomar, Omar Rafae; Basher, Noor Moneer; Yousif, Anwar Ahmed

doi:10.1016/j.ijmecsci.2020.105704

Cited by 32 publications

(8 citation statements)

References 38 publications

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“…This model includes the impact of pressure gradient, surface boundary layer, viscous shear stress, inertia, and body force. The variations in density has been considered to follow the Boussinesq approximation 42,43 . By adopting the above assumptions, the set of the governing equations are obtained as follows 43 :

\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} = 0,

\frac{μ}{K} (][, \frac{\partial u}{\partial y} - \frac{\partial v}{\partial x}) + \frac{ρ b}{K} (][, \frac{\partial}{\partial y} ((∣∣, V) \cdot u) - \frac{\partial}{\partial x} ((∣∣, V) \cdot v)) = - ρ_{f \circ} g β \frac{\partial T_{f}}{\partial x} + μ (][, \frac{\partial}{\partial y} (\frac{\partial^{2} u}{\partial x^{2}} + \frac{\partial^{2} u}{\partial y^{2}}) - \frac{\partial}{\partial x} (\frac{\partial^{2} v}{\partial x^{2}} + \frac{\partial^{2} v}{\partial y^{2}})),

{(ρ C_{p})}_{f} (][, u \frac{\partial T_{f}}{\partial x} + v \frac{\partial T_{f}}{\partial y}) = φ k_{f} (][, \frac{\partial^{2} T_{f}}{\partial x^{2}} + \frac{\partial^{2} T_{f}}{\partial y^{2}}) + h (T_{S} - T_{f}),

…”

Section: Theoretical Modelmentioning

confidence: 99%

“…Based on this, the conservation Equations (1)–(4) can be written in the dimensionless form as follows 42,43 :

\frac{\partial \overset{u}{true}}{\partial \overset{x}{true}} + \frac{\partial \overset{v}{true}}{\partial \overset{y}{true}} = 0,

\frac{\partial^{2} \overset{ψ}{true}}{\partial {\hat{y}}^{2}} + \frac{\partial^{2} \overset{ψ}{true}}{\partial {\hat{x}}^{2}} = \frac{F s}{{italicPr}^{*}} (][, \frac{\partial}{\partial \overset{y}{true}} ((∣∣, \hat{V}) \cdot \overset{u}{true}) - \frac{\partial}{\partial \overset{x}{true}} ((∣∣, \hat{V}) \cdot \overset{v}{true})) + R a^{*} \frac{\partial θ_{f}}{\partial \overset{x}{true}} - D a (][, \frac{\partial^{2} \overset{ω}{true}}{\partial {\hat{y}}^{2}} + \frac{\partial^{2} \overset{ω}{true}}{\partial {\hat{x}}^{2}}),

\frac{\partial \overset{ψ}{true}}{\partial \overset{x}{true}} \cdot \frac{\partial θ_{f}}{\partial \overset{y}{true}} - \frac{\partial \overset{ψ}{true}}{\partial \overset{y}{true}} \cdot \frac{\partial θ_{f}}{\partial \overset{x}{true}} = (\frac{\partial^{2} θ_{f}}{\partial {\hat{x}}^{2}} + \frac{\partial^{2} θ_{f}}{\partial ...})

…”

Section: Theoretical Modelmentioning

confidence: 99%

“…Numerical solutions illustrated that the variable properties and magnetic field considerably affect the wall shear stress and rate of heat transfer. Alomar et al 42 presented a numerical on free convection induced by orthogonal hot surface immersed inside square porous duct to investigate the effect of LTNE and non‐Darcian assumptions. The solutions display that the assumptions of non‐Darcy flow and LTNE model have substantial impacts on the behaviors of flow and rate of heat transfer.…”

Section: Introductionmentioning

confidence: 99%

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A thermal nonequilibrium model to natural convection inside non‐Darcy porous layer surrounded by horizontal heated plates with periodic boundary temperatures

2021

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This article displays a numerical investigation on natural convection within non‐Darcy porous layer surrounded by two horizontal surfaces having sinusoidal temperature profiles with difference in phase and wave number. The Darcy–Brinkman–Forchheimer model and local thermal nonequilibrium condition have been employed. Simulations have been performed for wide ranges of inertia coefficient (10–4 ≤ Fs/Pr* ≤ 10–2), thermal conductivity ratio (0.1 ≤ K r ≤ 100), phase difference (0 ≤ β ≤ π), modified Rayleigh number (200 ≤ Ra* ≤ 1000), wavelength (3 ≤ k ≤ 12), and nondimensional heat transfer coefficient (0.1 ≤ H ≤ 100). Results demonstrate that Nusselt number highly relies on Fs/Pr*, K r, β, Ra*, and k as compared to H. A considerable enhancement in fluid, solid, and overall Nusselt numbers has been observed with diminishing Fs/Pr* and β and increasing k, K r, and H. The raising in β has a significant impact on Nu for smaller k and this effect is almost ignored when k > 12. The increase in Ra*, K r, β, and H and decrease in Fs/Pr* and k acts to reduce the severity of nonequilibrium zone and increase the size of thermal equilibrium zone. The influence of H on nonequilibrium area is more evident than K r.

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\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} = 0,

\frac{μ}{K} (][, \frac{\partial u}{\partial y} - \frac{\partial v}{\partial x}) + \frac{ρ b}{K} (][, \frac{\partial}{\partial y} ((∣∣, V) \cdot u) - \frac{\partial}{\partial x} ((∣∣, V) \cdot v)) = - ρ_{f \circ} g β \frac{\partial T_{f}}{\partial x} + μ (][, \frac{\partial}{\partial y} (\frac{\partial^{2} u}{\partial x^{2}} + \frac{\partial^{2} u}{\partial y^{2}}) - \frac{\partial}{\partial x} (\frac{\partial^{2} v}{\partial x^{2}} + \frac{\partial^{2} v}{\partial y^{2}})),

{(ρ C_{p})}_{f} (][, u \frac{\partial T_{f}}{\partial x} + v \frac{\partial T_{f}}{\partial y}) = φ k_{f} (][, \frac{\partial^{2} T_{f}}{\partial x^{2}} + \frac{\partial^{2} T_{f}}{\partial y^{2}}) + h (T_{S} - T_{f}),

…”

Section: Theoretical Modelmentioning

confidence: 99%

“…Based on this, the conservation Equations (1)–(4) can be written in the dimensionless form as follows 42,43 :

\frac{\partial \overset{u}{true}}{\partial \overset{x}{true}} + \frac{\partial \overset{v}{true}}{\partial \overset{y}{true}} = 0,

\frac{\partial^{2} \overset{ψ}{true}}{\partial {\hat{y}}^{2}} + \frac{\partial^{2} \overset{ψ}{true}}{\partial {\hat{x}}^{2}} = \frac{F s}{{italicPr}^{*}} (][, \frac{\partial}{\partial \overset{y}{true}} ((∣∣, \hat{V}) \cdot \overset{u}{true}) - \frac{\partial}{\partial \overset{x}{true}} ((∣∣, \hat{V}) \cdot \overset{v}{true})) + R a^{*} \frac{\partial θ_{f}}{\partial \overset{x}{true}} - D a (][, \frac{\partial^{2} \overset{ω}{true}}{\partial {\hat{y}}^{2}} + \frac{\partial^{2} \overset{ω}{true}}{\partial {\hat{x}}^{2}}),

\frac{\partial \overset{ψ}{true}}{\partial \overset{x}{true}} \cdot \frac{\partial θ_{f}}{\partial \overset{y}{true}} - \frac{\partial \overset{ψ}{true}}{\partial \overset{y}{true}} \cdot \frac{\partial θ_{f}}{\partial \overset{x}{true}} = (\frac{\partial^{2} θ_{f}}{\partial {\hat{x}}^{2}} + \frac{\partial^{2} θ_{f}}{\partial ...})

…”

Section: Theoretical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A thermal nonequilibrium model to natural convection inside non‐Darcy porous layer surrounded by horizontal heated plates with periodic boundary temperatures

2021

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“…Tripathi and Bég [40] utilised the Darcy-Brinkman model to quantify the periodic peristaltic propulsion of Maxwell viscoelastic fluids through a porous medium. The Darcy-Forcheimmer model was implemented by Alomar et al [41] to simulate the natural convection in a two-dimensional porous enclosure It has also been deployed by Bég et al [42] in unsteady rotating channel flows and by Bég et al [43] for two-phase natural convection in biofluid transport in non-Darcian porous media. However, these models of non-Darcy flow neglected the influence of Forccheimer effect on viscous heating.…”

Section: Introductionmentioning

confidence: 99%

“…The Darcy–Forcheimmer model was implemented by Alomar et al. [41] to simulate the natural convection in a two‐dimensional porous enclosure It has also been deployed by Bég et al. [42] in unsteady rotating channel flows and by Bég et al.…”

Section: Introductionmentioning

confidence: 99%

Numerical study of natural convection dissipative electro‐magnetic non‐Newtonian flow through a non‐Darcy channel

et al. 2022

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Inspired by simulating duct thermal processing of novel functional polymers, a novel mathematical model is developed for buoyancy‐driven heat transfer in non‐Newtonian Williamson fluid flow in a vertical parallel plate duct containing a permeable medium, under mutually orthogonal electrical and magnetic fields. The momentum equation features electrical and magnetic body force terms, and the Darcy–Brinkman–Forchheimer mode is used for non‐Darcy effects. The energy balance equation includes thermal buoyancy (natural convection body force) and a modified viscous dissipation term. The conservation equations with associated boundary conditions are reframed into a system of coupled non‐linear ordinary differential equations via appropriate similarity transformations. The emerging dimensionless boundary value problem is then solved with a differential transform method (DTM). Validation of DTM solutions with the bvp4c MATLAB collocation solver is included. The influence of key parameters on velocity, temperature and average Nusselt number, are computed and illustrated graphically. With elevation in Weissenberg (non‐Newtonian) number, velocity and temperature are reduced. Velocity is suppressed with increasing non‐Darcian parameter (Forchheimer effect) whereas it is enhanced with increment in buoyancy convection parameter. With increasing Forchheimer, Darcy number and Hartmann number, the average Nusselt number is boosted whereas it is decreased with higher values of buoyancy convection parameter, Brinkman number and Weissenberg number. A strong reduction in temperature is computed with increment in ratio of Joule electrical heating to heat conduction parameter. DTM is shown to be an exceptionally accurate and versatile approach for simulating non‐Newtonian electromagnetohydrodynamic transport in ducts.

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Conjugate local thermal nonequilibrium and non‐Darcy flow inside porous enclosure: Analysis of localized heating and cooling arrangements

Basher

Yousif

2023

Heat Trans

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This study covers a simulation on conjugate free convective in a porous enclosure containing a side wall thickness and partially heated and cooled from sides under the considerations of local thermal nonequilibrium (LTNE) and non‐Darcy flow. Interest has been focused on how the side wall thickness and the locations of cooled and heated parts affect the effectiveness of the Nusselt number (Nu). Three different cases of localized heating and cooling locations have been implemented for the following ranges: scaled heat transfer coefficient (), wall to fluid thermal conductivity ratio (), modified Rayleigh number (), wall width (), inertial parameter (), and thermal conductivity ratio (). Outcomes show that and the locations of cooled and heated parts have remarkable impacts on all the Nusselt numbers. The intensity of LTNE region considerably relies on , and . The total average NuT is highly dependent on , , , , and as compared to H. The increase in leads to change of the convective mechanism to conductive mode. The rise in guides to increase Nu, where can control the flow strength. The actions of on Nuf is more evident than Nus. For low H and Kr, the size of LTNE zone is considerably affected by H as compared to Kr although Kr has a high influence on Nu. For high Kr and H, the LTNE zone has closely vanished. Findings display that the Case 2 provided the highest Nu for all tested parameters except the case of . Finally, it is evident that for the problems that employed solid conduction wall with localized heating and cooling sections, Case 2 is recommended for future use in the applications that implement a porous medium and depend on free convection.

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Analysis of effects of Thermal Non-Equilibrium and Non-Darcy Flow on Natural Convection in a Square Porous Enclosure Provided with a Heated L Shape Plate

Cited by 32 publications

References 38 publications

A thermal nonequilibrium model to natural convection inside non‐Darcy porous layer surrounded by horizontal heated plates with periodic boundary temperatures

A thermal nonequilibrium model to natural convection inside non‐Darcy porous layer surrounded by horizontal heated plates with periodic boundary temperatures

Numerical study of natural convection dissipative electro‐magnetic non‐Newtonian flow through a non‐Darcy channel

Conjugate local thermal nonequilibrium and non‐Darcy flow inside porous enclosure: Analysis of localized heating and cooling arrangements

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