A Thermal Conductivity Inversion Of Numerical Solution

IHCP—inverse heat conduction problems have been found wide application inengineering industry, so it is of great value to research this kind of problem. The IHCPis typical ill-posed problem, which is extremely sensitive to the error of the metricaldata. The random error is inevitable in measuring process, and the error will beenlarged when this kind of information with error is used in inversion calculation, sothe exact solution can hardly be obtained.In this paper, a local marching numerical method is developed to solve theone-dimensional inverse nonlinear heat conductivity problem (INHCP) which is notonly related to position but also the temperature, i.e. k=k(x, T).At the present time,many experts are researching thermal conductivity that is only related to position oronly related to position and time. Research about heat conductivity that is related toposition and temperature is rarely seen. In fact the mathematical model that is discretefrom the INHCP is discussed in the second chapter. The method stability as well asthe logarithm according to the processing method is analyzed in the third chapter. Inthe fourth chapter the numerical simulation is carried out and its result is discussed.Numerical analysis indicated that this method is stable. In this article use thetemperature date obtained by the surface to calculate interior heat conductivity of themedium. Then the IHCP solution can be got by Matlab programming. And fortunately,the solution has a good precision.Because the inverse heat conductivity problem is ill conditioned, we can not findthe solution directly. To solve the problem, need to regularize the equation. In thispaper, based on LC (L-curse criterion) regularization techniques, the stable numericalsolution is obtained. The result indicated that, this proposed method is highly effective,stable, the overall situation restrains and so on.