On Uncertainty and Local Sensitivity Analysis for Steady-State Conjugate Heat Transfer Problems Part 1: Emissivity, Fluid Temperature, and Conductance

Abstract

In recent years, significant effort has been placed 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. A numerical analysis on the stability of the solution matrix is being conducted. Partial uncertainties and the relative importance of the heat transfer modes are investigated by their uncertainty factors and conclusions are being drawn.

Including Solar Radiation in Sensitivity and Uncertainty Analysis for Conjugate Heat Transfer Problems

“…Since thermal stresses and deformations were investigated, deformed view factors were approximated by a first order Taylor series expansion, which showed some descent results. In another paper (Bhatia & Livne, 2009) they also showed a way to put all temperature dependent parameters into the main diagonal of a matrix with consequent This article is a continuation of previously published papers (Rauch & Almbauer, 2010a;Rauch, 2011b) that dealt with steady-state uncertainty estimations of some parameters for conjugate heat transfer with cavity radiation. Later, the transient (Rauch, 2011a) case was investigated.…”

“…12 dimensionless UF for q solar , fluid temperature T f , and conductance C are shown. The corresponding equations were published in Rauch & Almbauer (2010a) and Rauch (2011b). In none of the nodes investigated, exceeded the UF the value 1.…”

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.…”