The boundary estimation in two-dimensional inverse heat conduction problems

Abstract

A direct method is developed to estimate the boundary condition in two-dimensional inverse heat conduction problems. At the beginning of the study, finite-difference methods are employed to discretize the problem domain and then a linear inverse model is constructed to identify the boundary condition. The linear least-squares method is adopted for the linear model and thus iteration times can be limited to one cycle and the uniqueness of the solutions can be identified easily. Results from the examples confirm that the proposed method is effective and applicable to solution of multidimensional inverse heat conduction problems. In the example problems, three kinds of measuring methods are adopted to estimate the surface temperature. The result shows that only a few measuring points is sufficient to estimate the surface temperature when the measurement errors are neglected. When the measurement errors are considered, more measuring points are needed in order to increase the congruence of the estimated results to the exact solutions.

Direct and inverse solutions with non-Fourier effect on the irregular shape

“…This paper is theoretically based on linear least-squares error method [14], but changes with the finite element method in spatial discretion to solve spatial stiffness matrix of irregular shape, and adds sequential algorithm concept to build a universal solving process. Thus, the method proposed by Yang and Chen [14] can be further applied in more complex geometries. In regard to non-Fourier transient heat conduction problem of 2D irregular shape, the differential equation of its heat transfer relaxation time s q can be expressed as ( [5]) …”

Numerical Determination of Thermal-Diffusivity Coefficients of Some Nematic Liquid Crystals in Situ

“…This method is used for estimating the functional value of unknown points. It is represented with thermal differences at the spatial temperature nodes and is required for several numerical procedures of calculations [9][10][11][12][13].…”

Application of conjugate gradient method for estimation of the wall heat flux of a supersonic combustor

“…Oliveria and Orlande [6] evaluated surface heat flux of ablative material using CGM. Mohammadium et al [7] studied accuracy and numerical stability of CGM when the measured temperatures (as the input data) had noises [8,9]. However, most of the previous conjugate gradient methods are implemented with the assumption that thermal properties of wall material such as thermal conductivity or specific heat are constant [7][8][9].…”

“…Mohammadium et al [7] studied accuracy and numerical stability of CGM when the measured temperatures (as the input data) had noises [8,9]. However, most of the previous conjugate gradient methods are implemented with the assumption that thermal properties of wall material such as thermal conductivity or specific heat are constant [7][8][9]. It is known that for gas turbine engine or ramjet/scramjet combustor, temperature across the combustor wall can vary from room temperature on the outer wall to more than 1000 K on the inner wall due to large heat flux with magnitudes of MW/m 2 [10,11].…”