Natural Convection in a Square Cavity with Uniformly Heated and/or Insulated Walls Using Marker-and-Cell Method

Khan, B. Md. Hidayathulla; Venkatadri, K.; Bég, O. Anwar; Prasad, V. Ramachandra; Mallikarjuna, B.

doi:10.1007/s40819-018-0492-z

Cited by 10 publications

(5 citation statements)

References 35 publications

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“…A similar analysis has been conducted by Valencia and Frederick 17 with partially active walls. The role of partially heated verticals on heat transfer in air of square enclosure has been reported by Kane et al 18 Recent studies of natural or mixed convection in a square cavity filled with different fluids and with different supplementary effects (eg, magnetic body forces, lid‐driven boundary, etc) have been presented in References 19–25 …”

Section: Introductionmentioning

confidence: 91%

Simulation of unsteady natural convection flow of a Casson viscoplastic fluid in a square enclosure utilizing a MAC algorithm

Devi

Lakshmi

Venkatadri³

et al. 2020

Heat Trans

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Non-Newtonian fluids are increasingly being deployed in energy systems and materials processing. Motivated by these developments, in the current study, a numerical simulation is performed on twodimensional, unsteady buoyancy-driven flow in a square cavity filled with non-Newtonian fluid (Casson liquid). The enclosure geometry features vertical isothermal walls (with one at higher temperature than the other) and thermally insulated horizontal walls. The conservation equations for mass, momentum, and energy are normalized via appropriate transformations and the resulting dimensionless partial differential boundary value problem is solved computationally with a marker and cell algorithm, which features a finite difference scheme along with a staggered grid system. The projection method is employed to evaluate the pressure term. Extensive visualizations of the impact of emerging physical parameters (Rayleigh number and Casson viscoplastic parameter) on streamline and isotherm distributions in the cavity are presented for fixed Prandtl number. Nusselt number, that is, heat transfer rate, is increased with rising values of the Casson viscoplastic fluid parameter for any value of Rayleigh number. The density of streamlines increases with increasing values of Casson viscoplastic fluid parameter upto 1. Overall, the Casson fluid parameter plays a vital role in controlling the convective heat transfer within the enclosure. The computations are relevant to hybrid solar collectors, materials fabrication (polymer melts), etc. K E Y W O R D S finite difference scheme, flow visualization, free convection, isotherms, non-Newtonian (Casson) fluid, projection method, square enclosure, unsteady flow

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Section: Introductionmentioning

confidence: 91%

Simulation of unsteady natural convection flow of a Casson viscoplastic fluid in a square enclosure utilizing a MAC algorithm

Devi

Lakshmi

Venkatadri³

et al. 2020

Heat Trans

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Section: Problem Formulationmentioning

confidence: 99%

“…Numerical procedure and code validation:. The MAC method 30,[32][33][34][35] is utilized to solve the heat transfer and fluid flow equations ( 13)-( 15) using the boundary conditions ( 16)- (17). The continuity equation ( 12) is utilized to calculate the pressure distribution.…”

Section: ∂T ∂Tmentioning

confidence: 99%

“…Table 1 exhibits the thermophysical characteristics of nanoparticles and base-fluid. The governing equations which represent the above considerations with Boussinesq approximation can be presented as follows 30,31 : where x and y in order represent the Cartesian coordinates calculated along the enclosure's horizontal wall and enclosure's vertical wall, u and v in order represent the x -axis and y -axis velocity components, g represents the gravitational acceleration, Q 0 represents the heat absorption/generation rate, p represents the fluid pressure, K represents the permeability and T represents the temperature of the fluid.…”

Section: Introductionmentioning

confidence: 99%

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Numerical simulation of hybrid nanofluid (Cu/Al₂O₃-water) flow in a porous enclosure with heated corners and non-Fourier heat flux

Vijayalakshmi

Sivaraj

2022

Proceedings of the Institution of Mechanical Engineers, Part E:

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The current model manifests the characteristics of hybrid nanofluid (copper/aluminium oxide-water) flow within an enclosure saturated with a porous medium by adopting the non-Fourier heat flux model. In this model, the permeable enclosure is deemed to be heated by a four-sided corner heater. Besides the corners, the centre region of the upper and lower walls of the square enclosure is thermally insulated whereas the centre region of the left and right walls maintains an invariant temperature. The momentum and energy equations with boundary conditions are dimensionalized by using the appropriate non-similar quantities. The nondimensionalized governing equations along with the boundary conditions are solved by adopting the marker and cell technique. The present results are in good accordance with the earlier literature results which indicates that the adopted scheme is computationally significant. The pertinent parameters that arise from the flow field equations such as heat generation/absorption parameter, thermal relaxation parameter, Darcy number, Rayleigh number, length of constant/adiabatic temperature portion, and length of heat source position are visualized through streamlines and isotherms. Results indicate that the magnifications in the heat generation parameter have the propensity to amplify the local heat transfer rate. An amplification in the thermal relaxation parameter enhances the heat transfer rate. The impact of the cold and hot regions of the enclosure notably influences the fluid temperature within the enclosure. The strength of the streamlines is slightly lessened by enhancing the Darcy number. Natural convective hybrid nanofluid flow inside the porous cavity has a vital role in various engineering and industrial processes, for instance, extrusion of polymers and aerodynamic extrusion.

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“…The flow field examiners are conducted pioneer work past few decades on fluid flow characteristics inside the cavity with various numerical techniques by using appropriate numerical grid system [14][15][16]. Several numerical investigators have been investigating the fluid flow behavior within the top lid driven cavity for moderate Reynolds number (Re) values.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Slip effect on Lid-Driven Cavity Flow Problem for High Reynolds Number: Vorticity – Stream Function Approach

Fazuruddin¹,

Sreekanth²,

Raju³

2021

MMEP

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Incompressible 2-D Navier-stokes equations for various values of Reynolds number with and without partial slip conditions are studied numerically. The Lid-Driven cavity (LDC) with uniform driven lid problem is employed with vorticity - Stream function (VSF) approach. The uniform mesh grid is used in finite difference approximation for solving the governing Navier-stokes equations and developed MATLAB code. The numerical method is validated with benchmark results. The present work is focused on the analysis of lid driven cavity flow of incompressible fluid with partial slip conditions (imposed on side walls of the cavity). The fluid flow patterns are studied with wide range of Reynolds number and slip parameters.

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Natural Convection in a Square Cavity with Uniformly Heated and/or Insulated Walls Using Marker-and-Cell Method

Abstract: Hi d ay a t h ull a Kh a n, BM d, Venk a t a d ri, K, B e g, OA, R a m a c h a n d r a P r a s a d, V a n d M allik a rj u n a, B h t t p:// dx.

Cited by 10 publications

References 35 publications

Simulation of unsteady natural convection flow of a Casson viscoplastic fluid in a square enclosure utilizing a MAC algorithm

Simulation of unsteady natural convection flow of a Casson viscoplastic fluid in a square enclosure utilizing a MAC algorithm

Numerical simulation of hybrid nanofluid (Cu/Al₂O₃-water) flow in a porous enclosure with heated corners and non-Fourier heat flux

Numerical Simulation of Slip effect on Lid-Driven Cavity Flow Problem for High Reynolds Number: Vorticity – Stream Function Approach

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Natural Convection in a Square Cavity with Uniformly Heated and/or Insulated Walls Using Marker-and-Cell Method

Abstract: Hi d ay a t h ull a Kh a n, BM d, Venk a t a d ri, K, B e g, OA, R a m a c h a n d r a P r a s a d, V a n d M allik a rj u n a, B h t t p:// dx.

Cited by 10 publications

References 35 publications

Simulation of unsteady natural convection flow of a Casson viscoplastic fluid in a square enclosure utilizing a MAC algorithm

Simulation of unsteady natural convection flow of a Casson viscoplastic fluid in a square enclosure utilizing a MAC algorithm

Numerical simulation of hybrid nanofluid (Cu/Al2O3-water) flow in a porous enclosure with heated corners and non-Fourier heat flux

Numerical Simulation of Slip effect on Lid-Driven Cavity Flow Problem for High Reynolds Number: Vorticity – Stream Function Approach

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Numerical simulation of hybrid nanofluid (Cu/Al₂O₃-water) flow in a porous enclosure with heated corners and non-Fourier heat flux