Numerical Solutions Of Inverse Heat Conduction Problems With Multi-Variables

The inverse heat conduction problem (IHCP) is usually defined as the estimations of boundary/initial conditions, thermal parameters and heat source by utilizing the known temperature measurements inside the body or on the surface. The study on IHCP is an interdisciplinary field related to the heat transfer, physics, mathematics, computing, and experiment technique, etc., and has significant applications in many engineering aspects, such as aerospace, nuclear engineering, metal casting, chemical, machine making, metal-lurgy, medical diagnostics, civil engineering and food science,etc.Due to the ill-posedness and nonlinearity, solving IHCP is usually much more difficult than solving direct heat conduction problem (DHCP). Although large amounts of achievement has been made in this area, further investigation and effort are greatly demanded.With the consideration of practical requirements of both single and combined identification of thermal parameters, heat source, and boundary/initial conditions, inverse heat conduction problems with multi-variables are investigated in this dissertation, a couple of numerical models, facilitating to the sensitivity analysis, are developed to solve inverse steady/transient heat conduction problems with multi-variables. By utilizing different sensitivity based algorithms, a number of numerical tests, considering the effects of some factors on the results, are carried out to verify the proposed models with satisfactory results. Since there seems to be quite few work directly relevant to inverse heat conduction problems with multi-variables by authors best knowledge, the work presented in this dissertation is not only theoretically valuable, but also practically applicable.The major work of this dissertation includes1 Numerical models solving inverse steady heat conduction and coupled heat-mass transfer problems with multi-variables are presented, and single/combined identifications are implemented for the thermal/moist parameters and boundary conditions etc. A solving strategy for nonlinear inverse steady heat conduction via 2-Clevel sensitivity analysis is presented.2 A numerical model solving inverse one- order transient heat conduction problems with multi-variables is proposed, and single/combined identifications are carried out for the thermal parameters and boundary conditions etc. Finite difference technique and a precise algorithm in the time domain are employed in the time-dependent analysis. In addition, single/combined identifications are also carried out for the time-dependent heat source.3 Numerical models solving direct/inverse two-order transient heat conduction problems with multi-variables are presented, and single/combined identifications are conducted for the thermal parameters and boundary conditions etc. A precise algorithm in the time domain is employed in the time-dependent analysis.4 With the consideration of material inhomogeneity and spacial distribution of parameters, all the numerical models above are numerically verified with satisfactory results.A variety of object functions, such as L₂ ,L_x and D-function based regularizing functional,and a variety of sensitivity based algorithms, such as Gauss-Newton method, homotopy method, homotopy regularization method, conjugate gradient method. and Brayden-Fletcher-Goldfarb-Shanno (BFGS) method etc. are utilized to solve inverse problems. The computing accuracy/efficiency, and the ability of anti-noisy data as well are discussed. With the comparison with the case of single variable identification, a number of factors including noisy data, location of sample points, size of time step, and initial guess of unknowns are investigated with regard to their effects on the solutions, providing valuable reference for the further investigation on IHCP with multi-variables.