Search

Temperatures on inaccessible surfaces can be estimated by solving an inverse heat conduction problem (IHCP) based on the measured temperature on accessible surfaces. In this article, the transient temperatures on the front (heated) surface of a three-dimensional (3-D) object is recovered using the conjugate gradient method (CGM) based on temperatures measured on the back surface (opposite to the heated surface). The simulated measurement data are generated from the exact solution obtained by solving the direct problem, in which the front surface of the object is subjected to a moving heat source having an elliptic spot with a Gaussian profile. Random errors are artificially imposed on the back surface data. It is shown that the front-surface temperatures of the 3-D object can be well recovered using the algorithm presented here. Studies are also carried out to test the effect of large measurement errors on the accuracy of the inverse solution. [ABSTRACT FROM AUTHOR]

Temperature and heat flux at the heated surface can be estimated by solving an inverse heat conduction problem (IHCP) based on measured temperature and/or heat flux at the accessible locations (e.g., back surface). Most of the previous studies used temperature measurement data in the objective function, and little work has been done for the inverse numerical algorithm based on heat flux measurement data. In this study, a one-dimensional IHCP in a finite slab is solved by using the conjugate gradient method. The heat flux measurement data are, for the first time, incorporated into the objective function for a nonlinear heat conduction problem with temperature-dependent thermophysical properties. The results clearly show that the inverse approach of using heat flux measurement data in the objective function can provide much better predictions than the traditional approaches in which the temperature measurements are employed in the objective function. Parametric studies are performed to demonstrate the robustness of the formulated IHCP algorithm by testing it for two different materials under different frequencies of the imposed heat flux along with random errors of the measured heat flux at the back surface. [ABSTRACT FROM AUTHOR]

Abstract: The conjugate gradient method (CGM) is an efficient iterative regularization technique for solution of the inverse heat conduction problem (IHCP). However, most of the existing CGM schemes deal with linear boundary conditions and constant thermophysical properties. Little attention has been paid to formulate the CGM with radiation boundary condition and temperature-dependent thermophysical properties. In this study, a nonlinear CGM scheme is formulated to recover the front surface heating condition of a 3-D object, based on the temperature measurements at back surface. The 3-D object is subjected to a high-intensity Gaussian laser beam heating on the front surface and a combined radiation and convection boundary condition on the back surface. The derivations of the direct problem, adjoint problem and sensitivity problem are presented in detail. The results are presented for two materials and excellent agreement between the inverse and exact solutions are demonstrated. [Copyright &y& Elsevier]

Abstract: In many dynamic heat transfer situations, the temperature at the heated boundary is not directly measurable and can be obtained by solving an inverse heat conduction problem (IHCP) based on measured temperature or/and heat flux at the accessible boundary. In this study, IHCP in a two-dimensional rectangular object is solved by using the conjugate gradient method (CGM) with temperature and heat flux measured at the boundary opposite to the heated boundary. The inverse problem is formulated in such a way that the heat flux at heated boundary is chosen as the unknown function to be recovered, and the temperature at the heated boundary is computed as a byproduct of the IHCP solution. The measurement data, i.e., the temperature and heat flux at the opposite boundary, are obtained by numerically solving a direct problem where the heated boundary of the object is subjected to spatially and temporally varying heat flux. The robustness of the formulated IHCP algorithm is tested for different profiles of heat fluxes along with different random errors of the measured heat flux at the opposite boundary. The effects of the uncertainties of the thermophysical properties and back-surface temperature measurement on inverse solutions are also examined. [Copyright &y& Elsevier]

Abstract: Temperature and heat flux on inaccessible surfaces can be estimated by solving an inverse heat conduction problem (IHCP) based on the measured temperature and/or heat flux on accessible surfaces. In this study, the heat flux and temperature on the front (heated) surface of a three-dimensional (3D) object is recovered using the conjugate gradient method (CGM) with temperature and heat flux measured on back surface (opposite to the heated surface). The thermal properties of the 3D object are considered to be temperature-dependent. The simulated measurement data, i.e., the temperature and heat flux on the back surface, are obtained by numerically solving a direct problem where the front surface of the object is subjected to high intensity periodic laser heat flux with a Gaussian profile. The robustness of the formulated 3D IHCP algorithm is tested for two materials. The effects of the uncertainties in thermophysical properties on the inverse solutions are also examined. Efforts are made to reduce the total number of heat flux sensors on the back surface required to recover the front-surface heating condition. [Copyright &y& Elsevier]