Application of Domain Decomposition in Modelling Flow and Heat Transfer Problems

1996 ◽  
Vol 210 (6) ◽  
pp. 519-528 ◽  
Author(s):  
K Muralidhar ◽  
A Chatterjee ◽  
B V Nagabhushana Rao
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Domain Decomposition ◽  
Oil Recovery ◽  
Transient Flow ◽  
Two Dimensions ◽  
Processing Unit ◽  
Central Processing ◽  
Flow And Heat Transfer ◽  
Transfer Problems

The present work is concerned with the application of the domain decomposition technique for modelling transient flow and heat transfer problems. The solutions obtained within each subdomain are matched at the interfaces using Uzawa's algorithm. This algorithm has been originally developed in the context of steady heat conduction. The objective of the present study is to test and extend the algorithm to a wider class of problems. Examples considered are non-linear heat conduction in one and two dimensions, simulation of oil recovery from porous formations using water injection, movement of a plane thermal front and heat transfer from a cylinder placed in Darcian flow. The suitability of Uzawa's algorithm for interface treatment with up to nine subdomains has been studied. The method is found to converge to the full-domain solution in all cases considered. Besides this, results show that there are additional advantages which include the generation of small matrices and, in certain cases, a marginal reduction in CPU (central processing unit) time, even on sequential machines.

Numerical and Experimental Investigation of Heat Transfer Enhancement Using Heat Pipes for Electronic Cooling

2018 ◽  
Author(s):  
Ning Zhang ◽  
Pankaj R. Chandra ◽  
Ryan Robledo ◽  
Sree Harsha Balijepalli
Keyword(s):  
Heat Transfer ◽  
Heat Pipes ◽  
Copper Plate ◽  
Heat Sinks ◽  
Modern World ◽  
Processing Unit ◽  
Maximum Heat ◽  
Central Processing ◽  
Load Combination ◽  
Maximum Heat Transfer

Computers are crucial to nearly every endeavor in the modern world. Some computers, particularly those used in military applications, are required to endure extreme conditions with limited maintenance and few parts. Units such as these will hereafter be referred to as “rugged computers.” This series of experiments aims to produce improvements to rugged computers currently in service. Using heat pipes and finned heat sinks on an enclosed box, a computer’s Central Processing Unit (CPU) is able to reject heat without suffering contamination from unforgiving environments. A modular prototype was designed to allow for three distinct cases; a case with no heat pipes and fins, a cast with heat-pipes mounted internally with exterior fins and a case with heat-pipes extended externally with exterior fins. Each case was tested at three different heat loads, with a copper plate heated by a silicone heat strip simulating the heat load generated by a CPU. Each case/load combination was run many times to check for repeatability. The aim of this research is to discover the ideal case for maximum heat transfer from the CPU to the external environment. In addition to the experiments, numerical simulation of these modular prototypes with different designs of heat pipes were conducted in this research. Creating an accurate model for computer simulations will provide validation for the experiments and will prove useful in testing cases not represented by the modular prototype. The flow and heat transfer simulations were conducted using Autodesk CFD. The aim here is to create a model that accurately reflects the experimentally-verified results from the modular prototype’s cases and loads, thereby providing a base from whence further designs can branch off and be simulated with a fair degree of accuracy.

Computational Study of Streamfunction-Vorticity Formulation of Incompressible Flow and Heat Transfer Problems

2011 ◽  
Vol 52-54 ◽  
pp. 511-516 ◽  
Author(s):  
Arup Kumar Borah
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Boundary Conditions ◽  
Incompressible Flow ◽  
Computational Study ◽  
The Other ◽  
Governing Equations ◽  
Flow And Heat Transfer ◽  
Continuity Constraint ◽  
Transfer Problems

In this paper we have studied the streamfunction-vorticity formulation can be advantageously used to analyse steady as well as unsteady incompressible flow and heat transfer problems, since it allows the elimination of pressure from the governing equations and automatically satisfies the continuity constraint. On the other hand, the specification of boundary conditions for the streamfunction-vorticity is not easy and a poor evaluation of these conditions may lead to serious difficulties in obtaining a converged solution. The main issue addressed in this paper is the specification in the boundary conditions in the context of finite element of discretization, but approach utilized can be easily extended to finite volume computations.

Mathematical Modeling of Transient Flow and Heat Transfer in Gas Stirred Molten Steel

2001 ◽  
Author(s):  
J. L. Xia ◽  
T. Ahokainen
Keyword(s):  
Heat Transfer ◽  
Molten Steel ◽  
Thermal Stratification ◽  
Transient Flow ◽  
Liquid Interface ◽  
Turbulent Dispersion ◽  
Steel Ladle ◽  
Bubble Liquid ◽  
Flow And Heat Transfer ◽  
Heat Transfer Correlations

Abstract Transient two phase flow and heat transfer in a gas-stirred steel ladle are numerically investigated. An Eulerian two fluid approach is used. The drag, lift and turbulent dispersion forces are taken into account for the interface interactions. Different interface heat transfer correlations such as Ranz-Marshall and Hughmark relations are used to examine the influence of heat transfer between gas-liquid interface on the flow. The flow pattern, the histories of both gas and molten steel temperatures, and the thermal stratification history are presented. Results show that gas injection can homogenize thermal field and result in a thermal stratification of about 2 °C only (not complete homogenization). The different heat transfer correlations examined for the bubble-liquid interface have negligible impact on the flow and thermal fields. Predictions are compared with experimental data measured in an industrial ladle and a reasonable agreement is achieved.

A Meshless Finite Difference Method for Conjugate Heat Conduction Problems

2009 ◽  
Author(s):  
Chandrashekhar Varanasi ◽  
Jayathi Y. Murthy ◽  
Sanjay Mathur
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Conjugate Heat Transfer ◽  
Sparse Matrix ◽  
Complex Geometries ◽  
Meshless Finite Difference Method ◽  
Transfer Problems

In recent years, there has been a great deal of interest in developing meshless methods for computational fluid dynamics (CFD) applications. In this paper, a meshless finite difference method is developed for solving conjugate heat transfer problems in complex geometries. Traditional finite difference methods (FDMs) have been restricted to an orthogonal or a body-fitted distribution of points. However, the Taylor series upon which the FDM is based is valid at any location in the neighborhood of the point about which the expansion is carried out. Exploiting this fact, and starting with an unstructured distribution of mesh points, derivatives are evaluated using a weighted least squares procedure. The system of equations that results from this discretization can be represented by a sparse matrix. This system is solved with an algebraic multigrid (AMG) solver. The implementation of Neumann, Dirichlet and mixed boundary conditions within this framework is described, as well as the handling of conjugate heat transfer. The method is verified through application to classical heat conduction problems with known analytical solutions. It is then applied to the solution of conjugate heat transfer problems in complex geometries, and the solutions so obtained are compared with more conventional unstructured finite volume methods. Metrics for accuracy are provided and future extensions are discussed.

Research and Numerical Simulation of Heat Transfer Problems in the Industrial Production

2013 ◽  
Vol 756-759 ◽  
pp. 1679-1683
Author(s):  
Dong Mei Li ◽  
Xin Chun Wang ◽  
Li Nan Shi ◽  
Bo Chao Qu
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Steel Industry ◽  
Heat Transfer Mode ◽  
Radiation Model ◽  
Transfer Mode ◽  
The Difference ◽  
Transfer Problems ◽  
Direct Problems ◽  
The Impact

This article focuses on heat conduction problems in the process of steel industry. Modeling the direct problems of heat transfer, establish heat conduction and thermal radiation model. Model discretization method are used, discussion process from one dimension to two. We give the difference schemes, and the numerical example. Through the results we compare differences between one and two dimensional models, and the impact to the results of the two heat transfer mode.

scholarly journals Identification of nonlinear heat conduction laws

2015 ◽  
Vol 23 (5) ◽  
Author(s):  
Herbert Egger ◽  
Jan-Frederik Pietschmann ◽  
Matthias Schlottbom
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Unknown Parameter ◽  
Stability Estimate ◽  
Uniqueness Result ◽  
Stationary Case ◽  
Nonlinear Heat Conduction ◽  
Additional Measurement ◽  
Transfer Problems ◽  
Parameter Function

AbstractWe consider the identification of nonlinear heat conduction laws in stationary and instationary heat transfer problems. Only a single additional measurement of the temperature on a curve on the boundary is required to determine the unknown parameter function on the range of observed temperatures. We first present a new proof of Cannon's uniqueness result for the stationary case, which allows us to derive a corresponding stability estimate, and then extend our argument to instationary problems which are close to steady state.

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