A Method to Solve Conjugate Heat Transfer Problems: The Case of Fully Developed Laminar Flow in a Pipe

1985 ◽  
Vol 107 (1) ◽  
pp. 77-83 ◽  
Author(s):  
G. S. Barozzi ◽  
G. Pagliarini
Keyword(s):  
Heat Transfer ◽  
Laminar Flow ◽  
Conjugate Heat Transfer ◽  
General Procedure ◽  
Superposition Principle ◽  
Relative Importance ◽  
Axial Conduction ◽  
Flow Through ◽  
Transfer Problems ◽  
Fluid Conductivity

A simple, fast, and rather general procedure combining the superposition principle with a finite element method is proposed to deal with conjugate heat transfer problems. The method is employed to consider the wall conduction effect on heat transfer to fully developed laminar flow through a pipe whose exterior boundary is uniformly heated along a finite length. Results are given for two values of each of the four parameters determining the relative importance of axial conduction: the Peclet number of the fluid, the wall to fluid conductivity ratio, and the dimensionless thickness and length of the heated section of the pipe.

On Uncertainty and Local Sensitivity Analysis for Steady-State Conjugate Heat Transfer Problems

2010 ◽  
Author(s):  
Christian Rauch ◽  
Raimund Almbauer
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Conjugate Heat Transfer ◽  
Relative Importance ◽  
Physics Simulation ◽  
The Stability ◽  
Transfer Problems ◽  
Solution Matrix ◽  
Significant Effort ◽  
Stability Of The Solution

In recent years, significant effort has been put into developing automated multi-physics simulation. The exchange of boundary conditions has lead to more realistic as well as more complex simulations with usually slower convergence rate when the coupling is being performed between two different codes. In this paper the equations of local sensitivities for element centered steady-state combined convection, conduction, and thermal radiation problems are being derived along with some implementation details. A numerical analysis on the stability of the solution matrix is being conducted. The relative importance of the heat transfer modes at various locations are investigated by their uncertainty factors and conclusions are being drawn.

On Uncertainty and Local Sensitivity Analysis for Transient Conjugate Heat Transfer Problems

2011 ◽  
Author(s):  
Christian Rauch
Keyword(s):  
Heat Transfer ◽  
Conjugate Heat Transfer ◽  
Transfer Model ◽  
Relative Importance ◽  
Uncertainty Factors ◽  
The Stability ◽  
Transfer Problems ◽  
Physical Phenomena ◽  
Sensitivity And Uncertainty Analysis ◽  
Element Method

The need for simulating real-world behavior of automobiles has led to add more and more sophisticated models of various physical phenomena for being coupled together. This increases the number of parameters to be set and, consequently, the required knowledge of their relative importance for the solution and the theory behind them. Sensitivity and uncertainty analysis provides the knowledge of parameter importance. In this paper a thermal radiation solver is considered, that performs conduction calculations and receives heat transfer coefficient and fluid temperate at a thermal node. The equations of local, discrete, and transient sensitivities for the conjugate heat transfer model solved by the finite difference method are being derived for some parameters. In the past, formulations for the boundary element method and the finite element method have been published. This paper builds on the steady-state formulation published previously by the author. A numerical analysis on the stability of the solution matrix is being conducted. From those normalized sensitivity coefficients dimensionless uncertainty factors are calculated. On a simplified example the relative importance of the heat transfer modes at various locations are then investigated by those uncertainty factors.

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