Unsteady natural convection in a liquid-saturated porous enclosure with local thermal non-equilibrium effect

Siddheshwar, P. G.; Siddabasappa, C.

doi:10.1007/s11012-020-01198-y

Cited by 15 publications

(10 citation statements)

References 36 publications

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“…As like in Figure 2, for large values of

\gamma

, the profiles of

u

B

, and

J

are the same with the variation of

\gamma

, this is due to the fact that the temperature of the individual phases are the same and the regime is referred to LTE regime. Thus the LTNE situation will turn out into the LTE situation for large values of

\gamma

as like in convective stability (see Siddheshwar et al, 25 Siddheshwar and Siddabasappa 26 ) and it is important to assume the LTNE assumption when

\gamma

is very small.…”

Section: Resultsmentioning

confidence: 99%

“…As like in Figure 2, for large values of γ, the profiles of u, B, and J are the same with the variation of γ, this is due to the fact that the temperature of the individual phases are the same and the regime is referred to LTE regime. Thus the LTNE situation will turn out into the LTE situation for large values of γ as like in convective stability (see Siddheshwar et al, 25 Siddheshwar and Siddabasappa 26 ) and it is important to assume the LTNE assumption when γ is very small. With this information, we may note that the LTE model, in the case of MHD flow through a porous medium, predicts the thermodynamically incorrect results, whereas the LTNE model gives the exact flow behavior of the MHD flows through a porous medium.…”

Section: Validation Of the Studymentioning

confidence: 99%

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A numerical study on heat transfer and MHD flow of a Newtonian through a porous channel—Local thermal nonequilibrium model

Siddabasappa

Kalpana²,

Babitha

2022

Heat Trans

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Vast numbers of studies concentrate on the thermal equilibrium state whereas in many real‐world applications the model exists in the nonequilibrium state. Also, local thermal non‐equilibrium precisely represents the thermohydroflow characteristics. Therefore, the current study examines the heat transfer and fluid flow characteristics of the magnetohydrodynamic flow of a Newtonian fluid through a local thermal non‐equilibrium (LTNE) porous channel in the presence of the induced magnetic field. The mathematical model of the prescribed flow encloses the coupled nonlinear equations which are difficult to approach analytically. Hence, they are solved numerically using the shooting method with the Newton–Raphson method. The implications of various physical parameters of the problem on fluid flow, induced magnetic field, current density, temperature profiles, and heat transfer are elucidated with the aid of plots and tables. From the examination, it is clear that the porous medium significantly influences the characteristics of the fluid flow. That is, the least value of the Darcy number is related to a higher momentum field. Another interesting phenomenon is that the induced magnetic field remarkably enhances when the Darcy number is high, whereas the process is contrary to the current density. The effect of LTNE on the flow characteristics and heat transfer ceases for higher values of inter‐phase heat transfer coefficient and the ratio of thermal conductivities, which gives rise to the local thermal equilibrium (LTE) situation. Furthermore, the amount of heat transport is maximum in the LTE case compared to that of the LTNE case.

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“…As like in Figure 2, for large values of

\gamma

, the profiles of

u

B

, and

J

are the same with the variation of

\gamma

\gamma

as like in convective stability (see Siddheshwar et al, 25 Siddheshwar and Siddabasappa 26 ) and it is important to assume the LTNE assumption when

\gamma

is very small.…”

Section: Resultsmentioning

confidence: 99%

Section: Validation Of the Studymentioning

confidence: 99%

A numerical study on heat transfer and MHD flow of a Newtonian through a porous channel—Local thermal nonequilibrium model

Siddabasappa

Kalpana²,

Babitha

2022

Heat Trans

Self Cite

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“…By taking the above assumptions into account, the momentum equation and thermal energy equations 25–28 for the fluid phase and solid phase are provided below:

- \frac{dp}{dx} + μ \frac{d^{2} u}{d y^{2}} - \frac{μ}{K} u - η \frac{d^{4} u}{d y^{4}} - σ^{⁎} B_{0}^{2} u + ρ β_{T} g false(T_{l} - T_{0} false) = 0,

ϵ k_{l} \frac{d^{2} T_{l}}{d y^{2}} - \frac{d q_{r}}{dy} + μ {(\frac{du}{dy})}^{2} + η {(\frac{d^{2} u}{d y^{2}})}^{2} + σ^{⁎} B_{0}^{2} u^{2} + h false(T_{s} - T_{l} false) + Q_{0} false(T_{l} - T_{0} false) = 0,

false(1 - ϵ false) k_{s} \frac{d^{2} T_{s}}{d y^{2}} - h false(T_{s} - T_{l} false) = 0 .

…”

Section: Mathematical Analysismentioning

confidence: 99%

A study on entropy generation and heat transfer in a magnetohydrodynamic flow of a couple‐stress fluid through a thermal nonequilibrium vertical porous channel

2021

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The effect of local thermal nonequilibrium (LTNE) on the entropy generation and heat transfer characteristics in the magnetohydrodynamic flow of a couple‐stress fluid through a high‐porosity vertical channel is studied numerically using the higher‐order Galerkin technique. The Boussinesq approximation is assumed to be valid and the porous medium is considered to be isotropic and homogeneous. Two energy equations are considered one each for solid and fluid phases. The term involving the heat transfer coefficient in both equations renders them mutually coupled. Thermal radiation and an internal heat source are considered only in the fluid phase. The influence of inverse Darcy number, Hartmann number, couple‐stress fluid parameter, Grashof number, thermal radiation parameter, and interphase heat transfer coefficient on velocity and temperature profiles is depicted graphically and discussed. The entropy generation, friction factor, and Nusselt number are determined, and outcomes are presented via plots. The effect of LTNE on the temperature profile is found to cease when the value of the interphase heat transfer coefficient is high, and in this case, we get the temperature profiles of fluid and solid phases are uniform. The physical significance of LTNE is discussed in detail for different parameters' values. It is found that heat transport and friction drag are maximum in the case of LTNE and minimum in the case of local thermal equilibrium. We observe that LTNE opposes the irreversibility of the system. The corresponding results of a fluid‐saturated densely packed porous medium can be obtained as a limiting case of the current study.

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“…Increasing value thermal conductivity ratio and/or decreasing the thickness of solid wall can increase the maximum fluid temperature. Siddheshwar and Siddabasappa [13] investigated the thermoconvective stability in a fluid-saturated sparsely packed porous medium with local-thermal-non-equilibrium (LTNE) effect. They deployed free-free, adiabatic and rigid-rigid, adiabatic boundary conditions for the vertical walls and stress-free, isothermal and rigid-rigid, isothermal boundary combinations for the horizontal walls.…”

Section: Introductionmentioning

confidence: 99%

“…Since porous media are generally heterogenous in nature and feature randomly distributed pore spaces, simpler approaches have been deployed to simulate transport through such media. These include the Darcy model 11–17 which applies to steady flow through porous media and assumes the flow rate is proportional to the applied pressure gradient. However, when the porosity of the porous medium is close to unity and the regime is highly permeable, the flow of fluid is curvilinear, and curvature of the path gives rise to an inertia effect.…”

Section: Introductionmentioning

confidence: 99%

Numerical study of magnetohydrodynamic natural convection in a non-Darcian porous enclosure filled with electrically conducting helium gas

Bég¹,

Venkatadri²,

Prasad³

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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A theoretical and computational study of MHD natural convection in an isotropic non-Darcian porous medium saturated with electrically conducting helium gas in an enclosure in the presence of heat generation is presented. A Brinkman extended Darcy-Forchheimer model is employed and the working fluid is assumed to be incompressible. The model is non-dimensionalised and converted into pressure-velocity form. The Harlow-Welch marker and cell (MAC) finite difference technique is employed to solve the nonlinear boundary value problem via pressure-vorticity coupling. A parametric investigation of the influence of Grashof number ( Gr), Hartmann magnetic number ( Ha), Darcy number ( Da), and the internal heat generation parameter ( Γ) on streamline and isotherm distributions with Prandtl number ( Pr) is 0.71 (Helium) is conducted. The variation in local Nusselt number along the left and right walls of the computational 2 D enclosure is also studied. Validation house-computational numerical MATLAB code is tests are included. Local Nusselt number is elevated at both left and right walls with greater Darcy number (higher medium permeability) and Grashof number. However, with greater internal heat generation, local Nusselt number magnitudes are enhanced at the left (cold) wall only but suppressed at the right (hot) wall. Increasing magnetic field reduces local Nusselt number at both left and right walls. With increasing magnetic field, the single vortex is strongly distorted and skewed towards the top left and lower right corners of the enclosure. Temperature contours at the left and right wall are however less intense with greater magnetic field effect. The simulations are of relevance to hybrid electromagnetic gaseous fuel cells, magnetic field control of filtration processes and porous media materials processing systems.

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Unsteady natural convection in a liquid-saturated porous enclosure with local thermal non-equilibrium effect

Cited by 15 publications

References 36 publications

A numerical study on heat transfer and MHD flow of a Newtonian through a porous channel—Local thermal nonequilibrium model

A numerical study on heat transfer and MHD flow of a Newtonian through a porous channel—Local thermal nonequilibrium model

A study on entropy generation and heat transfer in a magnetohydrodynamic flow of a couple‐stress fluid through a thermal nonequilibrium vertical porous channel

Numerical study of magnetohydrodynamic natural convection in a non-Darcian porous enclosure filled with electrically conducting helium gas

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