Hybrid Eigenfunction-Discretization Methodology for Solving Convective Heat Transfer Problems

2012 ◽  
Author(s):  
D. J. M. N. Chalhub ◽  
L. A. Sphaier ◽  
L. S. de B. Alves
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Integral Transform ◽  
Integral Transformation ◽  
Temperature Dependent ◽  
Discretization Schemes ◽  
Upwind Discretization ◽  
Transfer Problems ◽  
Approximation Parameter

This paper presents a novel methodology for the solution of problems that include diffusion and advection effects, as naturally occur in convective heat transfer problems. The methodology is based on writing the unknown temperature field in terms of eigenfunction expansions, as traditionally carried-out with the Generalized Integral Transform Technique (GITT). However, a different approach is used for handling advective derivatives. Rather than transforming the advection terms as done in traditional GITT solutions, upwind discretization schemes (UDS) are used prior to the integral transformation. With the introduction of upwind approximations, numerical diffusion is introduced, which can be used to reduce unwanted oscillations that arise at higher Péclet values. This combined methodology is termed the GITT-UDS for convective problems. The procedure is illustrated for a simple case of one-dimensional Burgers’ equation with temperature-dependent velocities. Numerical results are calculated, showing that augmenting the upwind approximation parameter can effectively reduce solution oscillations for higher Péclet values.

Comparisons Between Integral Transform, Finite Volumes and Combined Solution Strategies for Convective Heat Transfer Problems

2011 ◽  
Author(s):  
D. J. N. M. Chalhub ◽  
L. A. Sphaier
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Integral Transform ◽  
Flow Direction ◽  
The Other ◽  
Finite Volumes ◽  
Solution Strategies ◽  
Combined Solution ◽  
Transfer Problems

Both traditional discretization-based numerical methods and alternative hybrid analytical-numerical techniques have been successfully applied for solving a considerable number of convective heat transfer problems. Despite the number of studies dedicated to separately solving a given problem by one methodology or the other, there are very few studies dedicated to comparing the computational solution performance of these approaches. In this context, this paper presents a comparison of solutions using the Finite Volumes Method (FVM) and the Generalized Integral Transform Technique (GITT) for a three dimensional steady-state convective heat transfer problem. The selected problem is that of thermally developing laminar flow within a square duct. The flow is considered kinetically developed and a constant wall temperature condition is employed. Both solutions are computationally implemented using the Mathematica system and, in order to guarantee a fair comparison, both implementations employ the same numerical ODE integrator to handle the solution in the flow direction. The comparisons are made by observing the convergence behavior of the Nusselt number for different positions along the flow direction, for both methodologies. In addition to these comparisons, combined solution strategies are analyzed, in which the velocity is obtained by one methodology and the temperature by the other.

scholarly journals Construction of a parallel computational algorithm based on the Galerkin discontinuous method for solving convective heat transfer problems on unstructured staggered grids

2018 ◽  
Vol 20 (4) ◽  
pp. 448-459
Author(s):  
R. V. Zhalnin ◽  
V. F. Masyagin ◽  
E. E. Peskova
Keyword(s):  
Heat Transfer ◽  
Galerkin Method ◽  
Convective Heat Transfer ◽  
Parallel Algorithm ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Convective Heat ◽  
Computational Algorithm ◽  
Staggered Grids ◽  
Transfer Problems

The present paper is devoted to the construction of a parallel computational algorithm for solving convective heat transfer problems using the discontinuous Galerkin method on unstructured staggered grids. The computational algorithm is implemented on the basis of MPI parallel computing technology. A special feature of the algorithm is that auxiliary variables that occur when the diffusion terms are approximated by the discontinuous Galerkin method are not involved in interprocessor exchange. The developed parallel algorithm is applied to modelling of temperature dynamics in formation with a vertical injection well and hydraulic fracturing. The paper presents the results of a computational experiment and estimates the effectiveness of a parallel algorithm.

scholarly journals Conjugate Problems in Convective Heat Transfer: Review

2009 ◽  
Vol 2009 ◽  
pp. 1-27 ◽  
Author(s):  
Abram Dorfman ◽  
Zachary Renner
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Analytical Solutions ◽  
Modern Approach ◽  
Current Time ◽  
Aerospace Systems ◽  
The One ◽  
Transfer Problems ◽  
Technology Processes

A review of conjugate convective heat transfer problems solved during the early and current time of development of this modern approach is presented. The discussion is based on analytical solutions of selected typical relatively simple conjugate problems including steady-state and transient processes, thermal material treatment, and heat and mass transfer in drying. This brief survey is accompanied by the list of almost two hundred publications considering application of different more and less complex analytical and numerical conjugate models for simulating technology processes and industrial devices from aerospace systems to food production. The references are combined in the groups of works studying similar problems so that each of the groups corresponds to one of selected analytical solutions considered in detail. Such structure of review gives the reader the understanding of early and current situation in conjugate convective heat transfer modeling and makes possible to use the information presented as an introduction to this area on the one hand, and to find more complicated publications of interest on the other hand.

Evaluation of Nanofluids as Potential Novel Coolant for Aircraft Applications: The Case of De-ionized Water-Based Alumina Nanofluids

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
Javier A. Narvaez ◽  
Aaron R. Veydt ◽  
Robert J. Wilkens
Keyword(s):  
Heat Transfer ◽  
Pressure Drop ◽  
Convective Heat Transfer ◽  
Air Force ◽  
Convective Heat ◽  
Military Aircraft ◽  
Particle Settling ◽  
Water Based ◽  
Transfer Problems

There is a critical need for improved coolants for military aircraft applications. The objective of this research is to evaluate nanofluids as potential replacement for the coolant currently used by the Air Force. Alumina/DI water nanofluids were evaluated. It was observed that at the same volumetric flow there was no significant improvement in convective heat transfer. Problems associated with the nanofluids were observed: increase of pressure drop with concentration, particle settling, and especially evidence of vaporization promoted by the nanoparticles. Results raised doubts about the applicability of using nanofluids as alternative coolants for avionic applications.

scholarly journals Efficient Simulations of Large Scale Convective Heat Transfer Problems

2021 ◽  
Vol 22 (4) ◽  
Author(s):  
Damian Goik ◽  
Krzysztof Banaś ◽  
Jan Bielański ◽  
Kazimierz Chłoń
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Large Scale ◽  
Stokes Equations ◽  
Parallel Implementation ◽  
Navier Stokes ◽  
Flow Equations ◽  
Transfer Problems

We describe an approach for efficient solution of large scale convective heat transfer problems, formulated as coupled unsteady heat conduction and incompressible fluid flow equations. The original problem is discretized in time using classical implicit methods, while stabilized finite elements are used for space discretization. The algorithm employed for the discretization of the fluid flow problem uses Picard's iterations to solve the arising nonlinear equations. Both problems, heat transfer and Navier-Stokes quations, give rise to large sparse systems of linear equations. The systems are solved using iterative GMRES solver with suitable preconditioning. For the incompressible flow equations we employ a special preconditioner based on algebraic multigrid (AMG) technique. The paper presents algorithmic and implementation details of the solution procedure, which is suitably tuned, especially for ill conditioned systems arising from discretizations of incompressible Navier-Stokes equations. We describe parallel implementation of the solver using MPI and elements of PETSC library. The scalability of the solver is favourably compared with other methods such as direct solvers and standard GMRES method with ILU preconditioning.  

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