Heatlines visualization of convective heat flow during differential heating of porous enclosures with concave/convex side walls

2018 ◽  
Vol 28 (7) ◽  
pp. 1506-1538 ◽  
Author(s):  
Pratibha Biswal ◽  
Tanmay Basak
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Porous Media ◽  
Natural Convection ◽  
Heat Flow ◽  
Flow Visualization ◽  
Convex Side ◽  
Content Type ◽  
Side Walls ◽  
Element Method

Purpose This paper is aimed to study natural convection in enclosures with curved (concave and convex) side walls for porous media via the heatline-based heat flow visualization approach. Design/methodology/approach The numerical scheme involving the Galerkin finite element method is used to solve the governing equations for several Prandtl numbers (Prm) and Darcy numbers (Dam) at Rayleigh number, Ram = 106, involving various wall curvatures. Finite element method is advantageous for curved domain, as the biquadratic basis functions can be used for adaptive automated mesh generation. Findings Smooth end-to-end heatlines are seen at the low Dam involving all the cases. At the high Dam, the intense heatline cells are seen for the Cases 1-2 (concave) and Cases 1-3 (convex). Overall, the Case 1 (concave) offers the largest average Nusselt number ( Nur¯) at the low Dam for all Prm. At the high Dam, Nur¯ for the Case 1 (concave) is the largest involving the low Prm, whereas Nur¯ is the largest for Case 1 (convex) involving the high Prm. Practical implications Thermal management for flow systems involving curved surfaces which are encountered in various practical applications may be complicated. The results of the current work may be useful for the material processing, thermal storage and solar heating applications Originality/value The heatline approach accompanied by energy flux vectors is used for the first time for the efficient heat flow visualization during natural convection involving porous media in the curved walled enclosures involving various wall curvatures.

Semi-analytical finite element method for simulating chemical dissolution-front instability problems in fluid-saturated porous media

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Chongbin Zhao ◽  
B.E. Hobbs ◽  
Alison Ord
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Porous Media ◽  
Chemical Dissolution ◽  
Saturated Porous Media ◽  
Content Type ◽  
Front Instability ◽  
Fluid Saturated Porous Media ◽  
Dissolution Front ◽  
Element Method

PurposeThe objective of this paper is to develop a semi-analytical finite element method for solving chemical dissolution-front instability problems in fluid-saturated porous media.Design/methodology/approachThe porosity, horizontal and vertical components of the pore-fluid velocity and solute concentration are selected as four fundamental unknown variables for describing chemical dissolution-front instability problems in fluid-saturated porous media. To avoid the use of numerical integration, analytical solutions for the property matrices of a rectangular element are precisely derived in a purely mathematical manner. This means that the proposed finite element method is a kind of semi-analytical method. The column pivot element solver is used to solve the resulting finite element equations of the chemical dissolution-front instability problem.FindingsThe direct use of horizontal and vertical components of the pore-fluid velocity as fundamental unknown variables can improve the accuracy of the related numerical solution. The column pivot element solver is useful for solving the finite element equations of a chemical dissolution-front instability problem. The proposed semi-analytical finite element method can produce highly accurate numerical solutions for simulating chemical dissolution-front instability problems in fluid-saturated porous media.Originality/valueAnalytical solutions for the property matrices of a rectangular element are precisely derived for solving chemical dissolution-front instability problems in fluid-saturated porous media. The proposed semi-analytical finite element method provides a useful way for understanding the underlying dynamic mechanisms of the washing land method involved in the contaminated land remediation.

An efficient iterative algorithm for the natural convection equations based on finite element method

2018 ◽  
Vol 28 (3) ◽  
pp. 584-605 ◽  
Author(s):  
Lei Wang ◽  
Jian Li ◽  
Pengzhan Huang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Natural Convection ◽  
Iterative Method ◽  
Error Correction ◽  
Computational Time ◽  
Content Type ◽  
Natural Convection Problem ◽  
New Iterative Method ◽  
Element Method

Purpose This paper aims to propose a new highly efficient iterative method based on classical Oseen iteration for the natural convection equations. Design/methodology/approach First, the authors solve the problem by the Oseen iterative scheme based on finite element method, then use the error correction strategy to control the error arising. Findings The new iterative method not only retains the advantage of the Oseen scheme but also saves computational time and iterative step for solving the considered problem. Originality/value In this work, the authors introduce a new iterative method to solve the natural convection equations. The new algorithm consists of the Oseen scheme and the error correction which can control the errors from the iterative step arising for solving the nonlinear problem. Comparing with the classical iterative method, the new scheme requires less iterations and is also capable of solving the natural convection problem at higher Rayleigh number.

Magneto-hydrodynamic natural convection of CuO-water nanofluid in complex shaped enclosure considering various nanoparticle shapes

2019 ◽  
Vol 29 (5) ◽  
pp. 1663-1679 ◽  
Author(s):  
A.S. Dogonchi ◽  
F. Selimefendigil ◽  
D.D. Ganji
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Finite Element ◽  
Natural Convection ◽  
Hartmann Number ◽  
Control Volume ◽  
Content Type ◽  
Control Volume Finite Element ◽  
Nanoparticle Shapes ◽  
Element Method

Purpose The purpose of this study is to peruse natural convection in a CuO-water nanofluid-filled complex-shaped enclosure under the influence of a uniform magnetic field by using control volume finite element method. Design/methodology/approach Governing equations formulated in dimensionless stream function, vorticity and temperature variables using the single-phase nanofluid model with the Koo–Kleinstreuer–Li correlation for the effective dynamic viscosity and the effective thermal conductivity have been solved numerically by control volume finite element method. Findings Effects of various pertinent parameters such as Rayleigh number, Hartmann number, volume fraction of nanofluid and shape factor of nanoparticle on the convective heat transfer characteristics are analysed. It was observed that local and average heat transfer rates increase for higher value of Rayleigh number and lower value of Hartmann number. Among various nanoparticle shapes, platelets were found to be best in terms of heat transfer performance. The amount of average Nusselt number reductions was found to be different when nanofluids with different solid particle volume fractions were considered due to thermal and electrical conductivity enhancement of fluid with nanoparticle addition. Originality/value A comprehensive study of the natural convection in a CuO-water nanofluid-filled complex-shaped enclosure under the influence of a uniform magnetic field by using control volume finite element method is addressed.

Analysis of efficiency of convection in porous geometries (square vs triangular) with multiple discrete heaters on walls

2019 ◽  
Vol 29 (9) ◽  
pp. 3305-3346 ◽  
Author(s):  
Debayan Das ◽  
Leo Lukose ◽  
Tanmay Basak
Keyword(s):  
Finite Element ◽  
Porous Media ◽  
Natural Convection ◽  
Heat Flow ◽  
Isosceles Triangle ◽  
Temperature Elevation ◽  
Content Type ◽  
Wide Range ◽  
Single Heater ◽  
Triangular Design

PurposeThe purpose of the paper is to study natural convection within porous square and triangular geometries (design 1: regular isosceles triangle, design 2: inverted isosceles triangle) subjected to discrete heating with various locations of double heaters along the vertical (square) or inclined (triangular) arms.Design/methodology/approachGalerkin finite element method is used to solve the governing equations for a wide range of modified Darcy number,Dam= 10−5–10−2with various fluid saturated porous media,Prm= 0.015 and 7.2 at a modified Rayleigh number,Ram= 106involving the strategic placement of double heaters along the vertical or inclined arms (types 1-3). Adaptive mesh refinement is implemented based on the lengths of discrete heaters. Finite element based heat flow visualization via heatlines has been adopted to study heat distribution at various portions.FindingsThe strategic positioning of the double heaters (types 1-3) and the convective heatline vortices depict significant overall temperature elevation at bothDam= 10−4and 10−2compared to type 0 (single heater at each vertical or inclined arm). Types 2 and 3 are found to promote higher temperature uniformity and greater overall temperature elevation atDam= 10−2. Overall, the triangular design 2 geometry is also found to be optimal in achieving greater temperature elevation for the porous media saturated with various fluids (Prm).Practical implicationsMultiple heaters (at each side [left or right] wall) result in enhanced temperature elevation compared to the single heater (at each side [left or right] wall). The results of the current work may be useful for the material processing, thermal storage and solar heating applications.Originality/valueThe heatline approach is used to visualize the heat flow involving double heaters along the side (left or right) arms (square and triangular geometries) during natural convection involving porous media. The heatlines depict the trajectories of heat flow that are essential for thermal management involving larger thermal elevation. The mixing cup or bulk average temperature values are obtained for all types of heating (types 0-3) involving all geometries, and overall temperature elevation is examined based on higher mixing cup temperature values.

Recovery-based error estimator for the natural-convection problem based on penalized finite element method

2019 ◽  
Vol 29 (12) ◽  
pp. 4850-4874
Author(s):  
Lulu Li ◽  
Haiyan Su ◽  
Jianping Zhao ◽  
Xinlong Feng
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Natural Convection ◽  
Posteriori Error ◽  
Optimal Error Estimates ◽  
Error Estimator ◽  
Content Type ◽  
Convection Problem ◽  
Natural Convection Problem ◽  
Element Method

Purpose This paper aims to proposes and analyzes a novel recovery-based posteriori error estimator for the stationary natural-convection problem based on penalized finite element method. Design/methodology/approach The optimal error estimates of the penalty FEM are established by using the lower-order finite element pair P1-P0-P1 which does not satisfy the discrete inf-sup condition. Besides, a new recovery type posteriori estimator in view of the gradient recovery and superconvergent theory to deal with the discontinuity of the gradient of numerical solution. Findings The stability, accuracy and efficiency of the proposed method are confirmed by several numerical investigations. Originality/value The provided reliability and efficiency analysis is shown that the true error can be effectively bounded by the recovery-based error estimator.

Parallel finite-element method using domain decomposition and Parareal for transient motor starting analysis

2019 ◽  
Vol 38 (5) ◽  
pp. 1507-1520 ◽  
Author(s):  
Yasuhito Takahashi ◽  
Koji Fujiwara ◽  
Takeshi Iwashita ◽  
Hiroshi Nakashima
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Parallel Computing ◽  
Domain Decomposition ◽  
Parallel Computation ◽  
Domain Decomposition Method ◽  
Space Time ◽  
Content Type ◽  
Parallel Performance ◽  
Element Method

Purpose This paper aims to propose a parallel-in-space-time finite-element method (FEM) for transient motor starting analyses. Although the domain decomposition method (DDM) is suitable for solving large-scale problems and the parallel-in-time (PinT) integration method such as Parareal and time domain parallel FEM (TDPFEM) is effective for problems with a large number of time steps, their parallel performances get saturated as the number of processes increases. To overcome the difficulty, the hybrid approach in which both the DDM and PinT integration methods are used is investigated in a highly parallel computing environment. Design/methodology/approach First, the parallel performances of the DDM, Parareal and TDPFEM were compared because the scalability of these methods in highly parallel computation has not been deeply discussed. Then, the combination of the DDM and Parareal was investigated as a parallel-in-space-time FEM. The effectiveness of the developed method was demonstrated in transient starting analyses of induction motors. Findings The combination of Parareal with the DDM can improve the parallel performance in the case where the parallel performance of the DDM, TDPFEM or Parareal is saturated in highly parallel computation. In the case where the number of unknowns is large and the number of available processes is limited, the use of DDM is the most effective from the standpoint of computational cost. Originality/value This paper newly develops the parallel-in-space-time FEM and demonstrates its effectiveness in nonlinear magnetoquasistatic field analyses of electric machines. This finding is significantly important because a new direction of parallel computing techniques and great potential for its further development are clarified.

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