Numerical Modeling Of Direct/Inverse Heat Transfer Problems With Interval Uncertainty

Uncertainty is one of the important factors necessary to take into account for the heat transfer problem because it exhibits significant impact on the heat transfer system.This dissertation focuses on the study of heat transfer problems with interval uncertainty.Interval model is an effective and convenient mean to tackle with uncertainty problems because the interval description on uncertainty only needs the bounds of changes of the uncertain parameters, instead of the uncertainty distribution inside their definition ranges or some other prior knowledge as probabilistic and fuzzy models required. The study on the interval uncertainty problems has been attracting eyes of scholars and engineering. However in comparison with the structural engineering and some other engineering aspects, the interval uncertainty heat transfer problem is really inadequately concerned, and is generally difficult to solve out analytically. Therefore this dissertation is dedicated to the investigation on numerical solutions of this kind of problem.The major contribution of this dissertation includes(1) Tow numerical models are presented for solving the forward steady state interval heat conduction problem and convection-diffusion heat transfer problems, respectively. In the modeling process, uncertainty problems are converted into deterministic ones using Taylor or Neumann series expansion, and two deterministic numerical models are developed. Therefore the lower and upper bounds of the uncertain intervals of temperatures can be estimated when thermal parameters are interval variables in terms of interval medians and radius, and a platform convenient for the sensitivity analysis based numerical solutions of inverse interval problems is built up.(2) Two numerical models are presented for solving the forward transient interval heat conduction problem and convection-diffusion heat transfer problems. The time-variant lower and upper bounds of temperature can be estimated steadily when thermal parameters are interval variables. In the modeling process, uncertainty problems are converted into deterministic ones using Taylor series expansion, and a temporally piecewise adaptive algorithm is employed to maintain a steady computing accuracy when the size of time steps varies.(3) On the basis of above forward models, numerical models are proposed for solving the inverse steady and transient interval heat conduction problems and convection-diffusion heat transfer problems. The single/combined identification of lower and upper bounds of the intervals of unknown thermal parameters can be realized when temperatures measurement contains interval uncertainty. In the modeling and computing process, the lower and upper bounds of temperature are described in term of interval median and radius. Two target functions related to measurement intervals are constructed, and minimized using L-M method, so as to gain the unknown interval median and radius.In the solution process of inverse problem, the known parameters can be deterministic or interval arguments.(4) A numerical model is presented for solving a forward transient nonlinear interval heat conduction problem. The time-variant lower and upper bounds of temperature can be estimated steadily when thermal parameters related to the nonlinear term are interval variables. In the modeling process, the uncertainty problem is converted into a deterministic one using Taylor series expansion, and the nonlinear initial and boundary value problem is converted into a series of FE recursive equations which can be adaptively solved, no iteration and any approximate assumption concerned with the nonlinear term are required, and a steady computing accuracy can be maintained when the size of time steps varies. Also a numerical model is presented for solving the corresponding inverse problem. The lower and upper bounds of the intervals of unknown thermal parameters can be identified when temperatures measurements are characterized by interval variables. In the solution process of inverse problem, the known parameters can be deterministic or interval arguments.Numerical verifications are provided via a number of numerical tests, and the effects of several factors are considered. Satisfactory results can be observed.