The four-sided lid driven square cavity using stream function-vorticity formulation

Bagai, Shobha; Kumar, Manoj; Patel, Arvind

doi:10.17512/jamcm.2020.2.02

Cited by 5 publications

(4 citation statements)

References 16 publications

(23 reference statements)

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“…We have chosen the relevant parameters in the governing equations like Prandtl number (Pr) and Darcy number (Da), porosity (ε), Grashof number (Gr) compatible with the considered problem. for each interior grid point from ( 14) and (18) using and values at interior points. (vi) Update , at the boundaries using and values at internal points.…”

Section: Numerical Computationsmentioning

confidence: 99%

“…Hidayathulla Khan et al [16] investigated the mixed convection under the effect of radiation inside a porous square cavity whose top and bottom walls are kept at a constant temperature, while some portions of the left and right walls of the cavity are partially heated. Vusala and Kumar [17], and Bagai et al [18,19] have used the stream functionvorticity formulation to investigate the mixed convection problem with heat or mass transfer in a two-sided or four-sided lid-driven square porous or without a porous cavity.…”

Section: Introductionmentioning

confidence: 99%

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Mixed Convection in a Two-Sided and Four-Sided Lid-Driven Square Porous Cavity

Bagai¹,

Kumar²,

Patel³

2021

IJHT

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The present paper investigates the mixed convection in a two-sided and four-sided lid-driven square cavity in porous media. In the two-sided porous cavity, the left and right walls of the enclosure are maintained at constant but different temperatures, while the top and bottom walls are adiabatic. The top and the bottom walls of the enclosure move with a constant speed from left to right. In the four-sided porous cavity, the top and the bottom walls of the enclosure move from left to right and right to left, respectively, while the left and the right walls move from top to bottom and bottom to top, respectively, with a constant speed. The left and right walls of the enclosure are maintained at different heat fluxes, while the top and bottom walls are maintained at hot and cold temperatures, respectively. The governing equations are discretized by the fully implicit finite difference method, namely, Alternating-Direction-Implicit (ADI) method. The numerical results are analyzed for the effect of Darcy number (Da = 0.001, 0.01), Prandtl number (Pr = 7), Grashof number (Gr = 50,000), porosity (ε = 0.2) and viscosity ratio (Λ = 1, 3). The stability and convergence of the considered problem have been proved using the Matrix method.

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Section: Numerical Computationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mixed Convection in a Two-Sided and Four-Sided Lid-Driven Square Porous Cavity

Bagai¹,

Kumar²,

Patel³

2021

IJHT

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“…Azwadi et al 11 present the Adams–Bashforth approach for simulating a four‐sided lid‐driven square cavity (4S‐LDSC) flow exhibiting stable velocity on all sides under the threshold Reynolds level. Bagai et al 12,13 used the stream function‐vorticity

(\psi -\xi )

formulation to study the mixed or natural convection flow with/without porous materials in square cavities driven by two‐ and four‐sided lids with sinusoidal heat distributions. Bagai et al 14 have studied mixed convection in a four‐sided lid‐driven sinusoidally heated porous cavity under two different cases of the direction of moving lid, namely, antiparallel diagonal and antiparallel antidiagonal.…”

Section: Introductionmentioning

confidence: 99%

Heat and mass transfer under MHD mixed convection in a four‐sided lid‐driven square cavity

Patel,

Kumar,

Bagai

2024

Heat Trans

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This paper investigates the heat and mass transfer under magnetohydrodynamic mixed convection flow of a binary gas mixture in a four‐sided lid‐driven square cavity. The enclosure's left wall is sinusoidally heated and acts as a source term, while the right wall functions as a sink. The cavity's horizontal walls are adiabatic and impermeable to mass transfer. The governing equations under Boussinesq approximation and stream function‐vorticity formulation are solved using the alternating‐direction‐implicit scheme, a finite‐difference method. The numerical scheme's consistency and stability are demonstrated using the matrix method. The MATLAB code is written, validated against some existing studies, and used to perform numerical simulations. The numerical solutions are graphically examined by visualizing the streamline, isotherm, and concentration contours for nondimensional parameters, such as Hartmann number , heat absorption or generation coefficient , Richardson number , and buoyancy ratio . The magnetic field modifies the temperature and concentration distribution in the cavity, depending on the convection mode. The magnetic field forces the fluid to stagnate in different regions of the cavity, depending on the mode of convection. It was found that the difference between the maximum and minimum temperature and concentration at the cavity's midpoint increases up to 13 and 10 times, respectively, in the natural convection compared with the forced convection. The average Nusselt number on the vertical walls of the cavity is maximum in natural convection in the absence of a magnetic field but reaches a minimum value at in forced and mixed convection. The average Sherwood number on the cavity's vertical walls decreases with the magnetic field in mixed and natural convection.

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“…Azwadi et al [3] have used the Adams-Bashforth method to investigate the fluid flow inside a four-sided lid-driven square cavity, at below the critical Reynolds numbers (Re ≤ 127) . Bagai et al [4] have examined the problem of heat and mass transfer of a 2-D unsteady incompressible fluid flow in a four-sided lid-driven square cavity with the help of stream functionvorticity formulation and ADI method. Chattopadhyay et al [6] have investigated the 2-D mixed convection flow in a two-sided lid-driven square cavity for three different cases according to the motion of the vertical walls, with retaining the right wall at a sinusoidal temperature condition and the left wall as cold temperature.…”

Section: Introductionmentioning

confidence: 99%

Mixed convection in four-sided lid-driven sinusoidally heated porous cavity using stream function-vorticity formulation

2020

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This study presents the mixed convection inside a four-sided lid-driven square porous cavity whose right wall is maintained at a sinusoidal temperature condition, the left wall of the cavity is maintained at a cold temperature, while the top and the bottom walls are adiabatic. We have discussed two different cases depending upon the direction of the moving walls. Brinkmann-extended Darcy model is represented in terms of and using the stream function-vorticity formulation to simulate the momentum transfer in the porous medium. This formulation is used to solve the governing equations as a coupled system of equations which consists of the field variables, vorticity () , stream function () , and temperature (T). The velocity components (u, v) are derived from the stream function () whereas the average Nusselt number is derived from temperature. The stability and consistency of the applied numerical scheme to the considered problem has been proven by matrix method. The numerical results are investigated by ranging the various dimensionless numbers such as Grashof number (10 3 ≤ Gr ≤ 10 5) , Darcy number (10 −1 ≤ Da ≤ 10 −5) , Reynolds number (10 ≤ Re ≤ 1000) and keeping the Prandtl number (Pr = 0.7) fixed.

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The four-sided lid driven square cavity using stream function-vorticity formulation

Cited by 5 publications

References 16 publications

Mixed Convection in a Two-Sided and Four-Sided Lid-Driven Square Porous Cavity

Mixed Convection in a Two-Sided and Four-Sided Lid-Driven Square Porous Cavity

Heat and mass transfer under MHD mixed convection in a four‐sided lid‐driven square cavity

Mixed convection in four-sided lid-driven sinusoidally heated porous cavity using stream function-vorticity formulation

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