Global Matrix-Free Finite-Element Scheme for Natural Convection in a Square Cavity with Step Blockage

Murugesan, K.; Lo, D. C.; Young, D. L.; Fan, Chia-Ming; Chen, C. W.

doi:10.1080/10407790600604742

Cited by 14 publications

(4 citation statements)

References 16 publications

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“…A second order accuracy Crank-Nicolson scheme is used to discretize the time derivative. The governing equations are finally transformed to simultaneous algebraic equations and conjugate gradient (CG) iterative solver with global matrix free algorithm 32 is used to solve the flow variables. An in-house built FORTRAN code is developed for this purpose and it is being thoroughly used by the authors’ group.…”

Section: Problem Descriptionmentioning

confidence: 99%

Optimization of double diffusive mixed convection in a BFS channel filled with Alumina nanoparticle using Taguchi method and utility concept

Nath

Murugesan

2019

Sci Rep

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This research work focuses on the implementation of Taguchi method and utility concept for optimization of flow, geometrical and thermo-physical parameters for mixed convective heat and mass transfer in a backward facing step (BFS) channel filled with Alumina nanoparticle doped in water-ethylene glycol mixture. Mass, momentum, energy and solutal conservation equations for the flow field are cast in velocity-vorticity form of Navier-Stokes equations, which are solved using Galerkin’s weighted residual finite element method through isoparametric formulation. The following six parameters, expansion ratio of the BFS channel (H/h), Reynolds number (Re), buoyancy ratio (N), nanoparticle volume fraction (χ), shape of nanoparticles and thermal Grashof number (GrT) at three levels are considered as controlling parameters for optimization using Taguchi method. An L27 orthogonal array has been chosen to get the levels of the six parameters for the 27 trial runs. Simulation results were obtained for 27 trial runs from which three different sets of optimum levels of the control parameters were obtained for maximum Nu and Sh and minimum wall shear stress during double diffusive mixed convection in the channel. Then, in order to obtain a single set of optimum levels of the control parameters to achieve maximum heat and mass transfer and minimum wall shear stress concurrently, utility concept has been implemented. Taguchi results indicate that expansion ratio and volume fraction of nanoparticles are the significant contributing parameters to achieve maximum heat and mass transfer and minimum wall shear stress. Utility concept predicts the average Nusselt number less by 2% and Sherwood number less by 3% compared to the Taguchi method with equal weightage of 40% assumed for Nusselt and Sherwood numbers and 20% for wall shear stress.

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Section: Problem Descriptionmentioning

confidence: 99%

Optimization of double diffusive mixed convection in a BFS channel filled with Alumina nanoparticle using Taguchi method and utility concept

Nath

Murugesan

2019

Sci Rep

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“…Governing equations at elemental level are formulated and are converted into algebraic form by integration using Gaussian quadrature method. The assembly procedure is completely eliminated in this work by implementing global matrix free finite element algorithm (Murugesan et al 2006). The advantage of this algorithm is, in this procedure the element level matrices are not assembled to form global matrices, instead they are kept in element level itself, and then the boundary conditions are included at element level matrices for those elements contributing to the boundary nodes.…”

Section: Solution Methodologymentioning

confidence: 99%

Numerical Study of Vorticity and Heat Flow in Bottom Heated DDC Systems at Nominal Rayleigh Number

Reddy¹,

Murugesan²

2018

JAFM

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Double diffusive convection (DDC) flows are widely seen in many industrial processes where the thermo-solutal buoyancy forces generates vorticity and initiates convective heat and mass transfer. In this paper numerical computations are conducted on this behaviour inside cavities of different aspect ratio at nominal Rayleigh number using a finite element based code. Velocity -vorticity form of Navier-Stokes equations are solved along with energy and solutal concentration conservation equations simultaneously using Galerkin's weighted residual method. Bottom wall is assumed hot and salted while top wall is maintained as sink, both side walls of the cavity are assumed to be adiabatic to heat and mass flow. Generally cavities with the present boundary conditions exhibit weak vorticity and convection characteristic especially at low Rayleigh number. In this numerical work an attempt is made to explore the role of variation in relative strength of thermal and solutal buoyancy forces on flow characteristics and mode of heat and mass transfer in such conditions. Simulation results have been reported for different buoyancy ratios in the range -2≤N≤2 , Rayleigh number varying from 1.0e5 to 1.0e3, for cavities of aspect ratios, 0.5(shallow), 1 (square) and 2 (deep). Flow contours are well validated with the results in the literature. The fluid rotation patterns are captured and reported under different operating conditions chosen, the vorticity generation is observed relatively low for deep cavity when compared to other two. Investigations revealed that fluid convection gets greatly hampered when operated in negative buoyancy ratio regime and require relatively higher Rayleigh number to change the mode of heat transfer from diffusion to convection.

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“…The governing equations (4)- (7) are solved with the initial (Equation (8)) and boundary (Equation (9)) conditions using Galerkin's weighted residual finite-element method [25]. In this method an approximate solution is assumed for the governing equation.…”

Section: Finite-element Solution Proceduresmentioning

confidence: 99%

“…In the present work global matrix-free finite-element algorithm [25] has been used to obtain the weak form of the governing equations. In this method all the equations are integrated at element level and are stored at element level itself without forming global matrices.…”

mentioning

confidence: 99%

Effect of thermo‐solutal stratification on recirculation flow patterns in a backward‐facing step channel flow

Kumar

Murugesan

Gupta

2009

Numerical Methods in Fluids

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SUMMARYThis paper presents results on the combined effect of thermo-solutal buoyancy forces on the recirculatory flow behavior in a horizontal channel with backward-facing step and the ensuing impact on heat and mass transfer phenomena. The governing equations for double diffusive mixed convection are represented in velocity-vorticity form of momentum equations, velocity Poisson equations, energy and concentration equations. Galerkin's finite-element method has been employed to solve the governing equations. Recirculatory flow fields with heat and mass transfer are simulated for opposing and aiding thermo-solutal buoyancy forces by assuming suitable boundary conditions for energy and concentration equations. The effect of Richardson number (0.1 Ri 10) and buoyancy ratio (−10 N 10) on the recirculation bubble and Nusselt and Sherwood numbers are studied in detail. For Richardson number greater than unity, distinct variations in the gradients of Nusselt number and Sherwood number with buoyancy ratio are observed for flow regimes with opposing and aiding buoyancy forces.

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Global Matrix-Free Finite-Element Scheme for Natural Convection in a Square Cavity with Step Blockage

Cited by 14 publications

References 16 publications

Optimization of double diffusive mixed convection in a BFS channel filled with Alumina nanoparticle using Taguchi method and utility concept

Optimization of double diffusive mixed convection in a BFS channel filled with Alumina nanoparticle using Taguchi method and utility concept

Numerical Study of Vorticity and Heat Flow in Bottom Heated DDC Systems at Nominal Rayleigh Number

Effect of thermo‐solutal stratification on recirculation flow patterns in a backward‐facing step channel flow

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