A new stochastic approach to transient heat conduction modeling with uncertainty

• Published in: International journal of heat and mass transfer Vol. 46; no. 24; pp. 4681 - 4693
• Main Authors: Xiu, Dongbin, Karniadakis, George Em
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.11.2003; Elsevier
• Subjects: Analytical and numerical techniques; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Heat conduction; Heat transfer; Physics; Polynomial chaos; Random medium; Stochastic modeling; Transient heat conduction; Uncertainty; Uncertainty; Polynomial chaos; Stochastic modeling; Random medium; Transient heat conduction; Temperature distribution; Stochastic analysis; Algorithms; Digital simulation; Thermal conductivity; Modelling; Karhunen-Loeve transforms; Random media; Chip; Transitory; Thermal conduction
• ISSN: 0017-9310; 1879-2189
• DOI: 10.1016/S0017-9310(03)00299-0

We present a generalized polynomial chaos algorithm for the solution of transient heat conduction subject to uncertain inputs, i.e. random heat conductivity and capacity. The stochastic input and solution are represented spectrally by the orthogonal polynomial functionals from the Askey scheme, as a generalization of the original polynomial chaos idea of Wiener [Am. J. Math. 60 (1938) 897]. A Galerkin projection in random space is applied to derive the equations in the weak form. The resulting set of deterministic equations is subsequently discretized by the spectral/ hp element method in physical space and integrated in time. Numerical examples are given and the convergence of the chaos expansion is demonstrated for a model problem.