We consider an inverse heat conduction problem with variable coefficient on an annulus domain.In many practice applications,we cannot know the initial temperature during heat process,therefore we consider a non-charac...We consider an inverse heat conduction problem with variable coefficient on an annulus domain.In many practice applications,we cannot know the initial temperature during heat process,therefore we consider a non-characteristic Cauchy problem for the heat equation.The method of fundamental solutions is applied to solve this problem.Due to ill-posedness of this problem,we first discretize the problem and then regularize it in the form of discrete equation.Numerical tests are conducted for showing the effectiveness of the proposed method.展开更多
An exact solution of laminar heat transfer problem for a uniform flow perpendicular to a rotating disk was obtained. Radial velocity at the outer edge of the boundary layer increases linearly in the radial direction, ...An exact solution of laminar heat transfer problem for a uniform flow perpendicular to a rotating disk was obtained. Radial velocity at the outer edge of the boundary layer increases linearly in the radial direction, while the temperature difference between the disk and outer flow follows a power law. The problem is solved using self-similar velocity and temperature profiles. Nusselt numbers were computed for the Prandtl numbers Pr=1 and 0.71 at different values of parameters affecting flow and heat transfer. Special flow regime was identified where rotating disk heat transfer is determined only by peculiarities of the impinging flow. Results of predictions agree well with known experiments in the vicinity of the stagnation point.展开更多
In this paper,a meshless regularization method of fundamental solutions is proposed for a two-dimensional,two-phase linear inverse Stefan problem.The numerical implementation and analysis are challenging since one nee...In this paper,a meshless regularization method of fundamental solutions is proposed for a two-dimensional,two-phase linear inverse Stefan problem.The numerical implementation and analysis are challenging since one needs to handle composite materials in higher dimensions.Furthermore,the inverse Stefan problem is ill-posed since small errors in the input data cause large errors in the desired output solution.Therefore,regularization is necessary in order to obtain a stable solution.Numerical results for several benchmark test examples are presented and discussed.展开更多
基金partially supported by the Natural Science Foundation of Northwest Normal University,China(No.NWNU-LKQN-17-5).
文摘We consider an inverse heat conduction problem with variable coefficient on an annulus domain.In many practice applications,we cannot know the initial temperature during heat process,therefore we consider a non-characteristic Cauchy problem for the heat equation.The method of fundamental solutions is applied to solve this problem.Due to ill-posedness of this problem,we first discretize the problem and then regularize it in the form of discrete equation.Numerical tests are conducted for showing the effectiveness of the proposed method.
文摘An exact solution of laminar heat transfer problem for a uniform flow perpendicular to a rotating disk was obtained. Radial velocity at the outer edge of the boundary layer increases linearly in the radial direction, while the temperature difference between the disk and outer flow follows a power law. The problem is solved using self-similar velocity and temperature profiles. Nusselt numbers were computed for the Prandtl numbers Pr=1 and 0.71 at different values of parameters affecting flow and heat transfer. Special flow regime was identified where rotating disk heat transfer is determined only by peculiarities of the impinging flow. Results of predictions agree well with known experiments in the vicinity of the stagnation point.
基金T.Reeve would like to acknowledge the financial support received from the EPSRC.
文摘In this paper,a meshless regularization method of fundamental solutions is proposed for a two-dimensional,two-phase linear inverse Stefan problem.The numerical implementation and analysis are challenging since one needs to handle composite materials in higher dimensions.Furthermore,the inverse Stefan problem is ill-posed since small errors in the input data cause large errors in the desired output solution.Therefore,regularization is necessary in order to obtain a stable solution.Numerical results for several benchmark test examples are presented and discussed.
