کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
659436 1458097 2012 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Identification of spacewise and time dependent source terms in 1D heat conduction equation from temperature measurement at a final time
موضوعات مرتبط
مهندسی و علوم پایه مهندسی شیمی جریان سیال و فرایندهای انتقال
پیش نمایش صفحه اول مقاله
Identification of spacewise and time dependent source terms in 1D heat conduction equation from temperature measurement at a final time
چکیده انگلیسی

Inverse problems of identifying the unknown spacewise and time dependent heat sources F(x) and H(t) of the variable coefficient heat conduction equation ut = (k(x)ux)x + F(x)H(t) from supplementary temperature measurement (uT(x)≔u(x, Tf)) at a given single instant of time Tf > 0, are investigated. For both inverse source problems, defined to be as ISPF and ISPH respectively, explicit formulas for the Fréchet gradients of corresponding cost functionals are derived. Fourier analysis of these problems shows that although ISPF has a unique solution, ISPH may not have a unique solution. The conjugate gradient method (CGM) with the explicit gradient formula for the cost functional J1(F) is then applied for numerical solution of ISPF. New collocation algorithm, based on the piecewise linear approximation of the unknown source H(t), is proposed for the numerical solution of the integral equation corresponding to ISPH. The proposed two numerical algorithms are examined through numerical examples for reconstruction of continuous and discontinuous heat sources F(x) and H(t). Computational results, with noise free and noisy data, show efficiency and high accuracy of the proposed algorithms.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: International Journal of Heat and Mass Transfer - Volume 55, Issues 7–8, March 2012, Pages 2069–2080
نویسندگان
,