Mixed convection in a double lid-driven sinusoidally heated porous cavity

Chattopadhyay, Anirban; Pandit, Swapan K.; Sarma, Sreejata Sen; Pop, Ioan

doi:10.1016/j.ijheatmasstransfer.2015.10.010

Cited by 46 publications

(18 citation statements)

References 40 publications

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“…Using the Boussinesq approximations, the governing equations of mixed convection in a sinusoidally heated liddriven porous cavity in non-dimensional form with stream function ( ) and vorticity ( ) [6] can be expressed as where The non-dimensional parameters are…”

Section: Governing Equationsmentioning

confidence: 99%

“…The LU decomposition method is used to solve the obtained tri-diagonal system of equations. The discretized finite-difference formulation of the vorticity transport equation (2) in both y and x directions respectively, are given by equations (5) and (6).…”

Section: Numerical Discretizationmentioning

confidence: 99%

“…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. Chen et al [7] have used Keller's continuation method to analyze the multiple solutions and flow bifurcation at various Reynolds numbers inside a four-sided lid-driven square cavity.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Governing Equationsmentioning

confidence: 99%

Section: Numerical Discretizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2020

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“…Pandit et al [18] have proposed fourth order compact scheme for the convectiondiffusion equations with considering reaction and nonhomogeneous source terms, to compute flow in a two sided lid-driven differentially heated square cavity filled with a fluid saturated porous medium. Chattopadhyay et al [6] have numerically simulated 2-D mixed convection flow in a sinusoidally heated porous cavity whose two vertical walls (lids) are in motion.…”

Section: Introductionmentioning

confidence: 99%

Numerical solutions of 2-D unsteady incompressible flow with heat transfer in a driven square cavity using streamfunction-vorticity formulation

Ambethkar¹,

Kumar²

2017

IJHT

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In this paper, we have used a streamfunction-vorticity (ψ-ξ) formulation to investigate the problem of 2-D unsteady viscous incompressible flow with heat transfer in a driven square cavity with moving top and bottom walls. We used this formulation to solve the governing equations along with no-slip and slip wall boundary conditions. A general algorithm was used for this formulation in order to compute the numerical solutions for the low Reynolds numbers Re ≤ 50. The numerical solutions of temperature are calculated for different Prandtl numbers 0.7 (for air) and 6.75 (for water). We have executed this with the aid of a computer programme developed and run in C++ compiler. We have proved the stability and convergence of the numerical scheme using matrix method. Heat transfer is studied by using the local Nusselt number. The uvelocity, v-velocity, pressure, temperature profiles along the horizontal and vertical line through geometric center of the square cavity, isotherms and isobars at different Reynolds numbers Re = 15 and 50 have been depicted.

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“…They found that Richardson number and the moving parameter play a dominant role in the transfer of heat and mass and other flow characteristics within a cavity. More studies on mixed convection in cavity can be found in [5,6,7,8,9,10].…”

Section: Introductionmentioning

confidence: 99%

MHD mixed convection and entropy generation of water–alumina nanofluid flow in a double lid driven cavity with discrete heating

Hussain

Mehmood

Sagheer

2016

Journal of Magnetism and Magnetic Materials

106

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Mixed convection in a double lid-driven sinusoidally heated porous cavity

Cited by 46 publications

References 40 publications

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

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

Numerical solutions of 2-D unsteady incompressible flow with heat transfer in a driven square cavity using streamfunction-vorticity formulation

MHD mixed convection and entropy generation of water–alumina nanofluid flow in a double lid driven cavity with discrete heating

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