A noncharacteristic cauchy problem for the heat equation

Hào, Ðinh Nho; Gorenflo, Rudolf

doi:10.1007/bf00047360

Cited by 24 publications

(1 citation statement)

References 84 publications

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“…The solution to the inverse heat conduction problem is not unique and finding its exact solution is extremely difficult. − The inverse heat conduction problem for moving boundary conditions is mainly calculated using optimization algorithms (conjugate gradient method, , variable metric method (VMM), Newton–Raphson method, Levenberg–Marquardt method, etc.). However, the application of the inverse heat conduction problem with moving boundaries is mainly focused on the thermal protection system (TPS) of space vehicles without a phase change.…”

Section: Introductionmentioning

confidence: 99%

Purity-Targeted Prediction of the Cooling Profile in Layer Melt Crystallization via Thermal Approximation

Bai

Chang

Sun

et al. 2023

Ind. Eng. Chem. Res.

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Predicting the cooling profile of layer melt crystallization based on the product purity or layer growth rate is an important practical topic. Herein, a numerical algorithm is proposed to give an approximate but quick solution to this inverse heat conduction problem. A thermal approximation method, in which the conduction heat of constant cooling temperature equals the required heat of crystallization at a radial location, was used to determine the cooling profile. The simulation results were verified using P-xylene as the model substance under conditions of either a constant layer growth rate or constant crystal layer purity. The results show that the error of the thermal approximation method can be neglected, and the experimental results meet the requirements. The linear relationship between the differential distribution coefficient and layer growth rate is determined. The cooling temperature at a constant layer growth rate keeps falling, while at constant layer purity, it rises after falling.

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