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

Abstract

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 Steady-State Conjugate Heat Transfer Problems Part 1: Emissivity, Fluid Temperature, and Conductance

“…In that case, the index on the right hand side of Eq. 35would hold the index k as was published in Rauch and Almbauer (2010a). In this paper the assumption of general flow is followed and Eq.…”

“…Figure 4 shows the diagonal a ii and Gerschgorin radii r entries of the solution matrix M, when all three heat transfer modes are included. In Rauch and Almbauer (2010a) figures are shown with radiation only, radiation and convection, and radiation and conduction terms included.…”

“…This paper is a revised version published by Rauch and Almbauer (2010a) and is concerned with deriving sensitivity equations for the element-centered steady-state finite difference method. It can be regarded as a continuation of Taylors's work by expanding his approach for conduction and convection.…”

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

“…More precisely, the Poljak approach is taken. Since the basic derivation for steadystate has been shown previously [9,10], some derivations are just reproduced in a concise way to help the reader in understanding the procedure. First, the basic equations for conjugate heat transfer are introduced, starting with the relation for a given boundary heat flux b as a function of radiosity q o , view factor F, and area A for an element k:…”

“…This paper is preceded by publications of the current author [9,10] that are concerned with deriving sensitivity equations for the element-centered steady-state finite difference method. It can be regarded as a continuation of Taylor's work [3,4] by expanding his approach by conduction and convection.…”