Analytically solving a three-dimensional （3-D） bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green func...Analytically solving a three-dimensional （3-D） bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green function method are introduced to deal with the cryopreservation process of in vitro biomaterials. Exact solutions for the 3-D temperature transients of tissues under various boundary conditions, such as totally convective cooling, totally fixed temperature cooling and a hybrid between them on tissue surfaces, are obtained. Furthermore, the cryosurgical process in living tissues subject to freezing by a single or multiple cryoprobes is also analytically solved. A closed-form analytical solution to the bioheat phase change process is derived by considering contributions from blood perfusion heat transfer, metabolic heat generation, and heat sink of a cryoprobe. The present method is expected to have significant value for analytically solving complex bioheat transfer problems with phase change.展开更多
We consider the one-dimensional bio-heat transfer equation with quadratic temperature-dependent blood perfusion, which governs the temperature distribution inside biological tissues. Using an extended mapping method w...We consider the one-dimensional bio-heat transfer equation with quadratic temperature-dependent blood perfusion, which governs the temperature distribution inside biological tissues. Using an extended mapping method with symbolic computation, we obtain the exact analytical thermal traveling wave solution, which describes the non-uniform temperature distribution inside the bodies. The found exact solution is used to investigate the temperature distribution in the tissues. It is found that the surrounding medium with higher temperature does not necessarily imply that the tissue will quickly (after a short duration of heating process) reach the desired temperature. It is also found that increased perfusion causes a decline in local temperature.展开更多
In this paper,we present a unified finite volume method preserving discrete maximum principle(DMP)for the conjugate heat transfer problems with general interface conditions.We prove the existence of the numerical solu...In this paper,we present a unified finite volume method preserving discrete maximum principle(DMP)for the conjugate heat transfer problems with general interface conditions.We prove the existence of the numerical solution and the DMP-preserving property.Numerical experiments show that the nonlinear iteration numbers of the scheme in[24]increase rapidly when the interfacial coefficients decrease to zero.In contrast,the nonlinear iteration numbers of the unified scheme do not increase when the interfacial coefficients decrease to zero,which reveals that the unified scheme is more robust than the scheme in[24].The accuracy and DMP-preserving property of the scheme are also veri ed in the numerical experiments.展开更多
Stochastic temperature distribution should be carefully inspected in the thermal-failure design of heterogeneous solids with unexpected random energy excitations.Stochastic multiscale modeling for these problems invol...Stochastic temperature distribution should be carefully inspected in the thermal-failure design of heterogeneous solids with unexpected random energy excitations.Stochastic multiscale modeling for these problems involve multiscale and highdimensional uncertain thermal parameters,which remains limitation of prohibitive computation.In this paper,we propose a multi-modes based constrained energy minimization generalized multiscale finite element method(MCEM-GMsFEM),which can transform the original stochastic multiscale model into a series of recursive multiscale models sharing the same deterministic material parameters by multiscale analysis.Thus,MCEM-GMsFEM reveals an inherent low-dimensional representation in random space,and is designed to effectively reduce the complexity of repeated computation of discretized multiscale systems.In addition,the convergence analysis is established,and the optimal error estimates are derived.Finally,several typical random fluctuations on multiscale thermal conductivity are considered to validate the theoretical results in the numerical examples.The numerical results indicate that the multi-modes multiscale approach is a robust integrated method with the excellent performance.展开更多
Using the inverse algorithm of heat transfer and the nonlinear estimation method, matching calculated values with measured ones, the interfacial heat transfer coefficient at casting/Cu mould interface was determined.T...Using the inverse algorithm of heat transfer and the nonlinear estimation method, matching calculated values with measured ones, the interfacial heat transfer coefficient at casting/Cu mould interface was determined.The results show that the interfacial heat transfer coefficient at Al/Cu interface changes in a range of 4.0×10 3 1.0×10 5 W·m -2 ·K -1 and its average value is in a range of 5.0×10 37.0×10 3 W·m -2 ·K -1 .展开更多
The accurate material physical properties, initial and boundary conditions are indispensable to the numerical simulation in the casting process, and they are related to the simulation accuracy directly. The inverse he...The accurate material physical properties, initial and boundary conditions are indispensable to the numerical simulation in the casting process, and they are related to the simulation accuracy directly. The inverse heat conduction method can be used to identify the mentioned above parameters based on the temperature measurement data. This paper presented a new inverse method according to Tikhonov regularization theory. A regularization functional was established and the regularization parameter was deduced, the Newton-Raphson iteration method was used to solve the equations. One detailed case was solved to identify the thermal conductivity and specific heat of sand mold and interfacial heat transfer coefficient (IHTC) at the meantime. This indicates that the regularization method is very efficient in decreasing the sensitivity to the temperature measurement data, overcoming the ill-posedness of the inverse heat conduction problem (IHCP) and improving the stability and accuracy of the results. As a general inverse method, it can be used to identify not only the material physical properties but also the initial and boundary conditions' parameters.展开更多
The steady, laminar, incompressible flow and heat transfer of a viscous fluid between two circular cylinders for two different types of thermal boundary conditions are investigated. The governing Navier-Stokes and the...The steady, laminar, incompressible flow and heat transfer of a viscous fluid between two circular cylinders for two different types of thermal boundary conditions are investigated. The governing Navier-Stokes and thermal equations of the flow are reduced to a nonlinear system of ordinary differential equations. The equations are solved analyt- ically using the homotopy analysis method （HAM）. Convergence of the HAM solutions is discussed in detail. These solutions are then compared with recently obtained numericM and perturbative solutions. Plots of the velocity and temperature profiles are provided for various values of the relevant parameters.展开更多
Nonlinear nonstationary heat conduction problem for infinite circular cylinder under a complex heat transfer taking into account the temperature dependence of thermophysical characteristics of materials is solved nume...Nonlinear nonstationary heat conduction problem for infinite circular cylinder under a complex heat transfer taking into account the temperature dependence of thermophysical characteristics of materials is solved numerically by the method of lines. Directing it to the Cauchy’s problem for systems of ordinary differential equations studied feature which takes place on the cylinder axis. Taken into account the dependence on the temperature coefficient of heat transfer that the different interpretation of its physical content makes it possible to consider both convective and convective-ray or heat ray. Using the perturbation method, the corresponding thermoelasticity problem taking into account the temperature dependence of mechanical properties of the material is construed. The influence of the temperature dependence of the material on the distribution of temperature field and thermoelastic state of infinite circular cylinder made of titanium alloy Ti-6Al-4V by radiant heat transfer through the outer surface has been analyzed.展开更多
A similarity analysis for Marangoni convection induced flow over a vapor-liquid interface due to an imposed temperature gradient was carried out. The analysis assumes that the surface tension varies linearly with temp...A similarity analysis for Marangoni convection induced flow over a vapor-liquid interface due to an imposed temperature gradient was carried out. The analysis assumes that the surface tension varies linearly with temperature but the temperature variation is a power law function of the location. The similarity solutions are presented numerically and the associated transfer characteristics are discussed.展开更多
The interfacial heat transfer coefficient(IHTC)between the casting and the mould is essential to the numerical simulation as one of boundary conditions.A new inverse method was presented according to the Tikhonov regu...The interfacial heat transfer coefficient(IHTC)between the casting and the mould is essential to the numerical simulation as one of boundary conditions.A new inverse method was presented according to the Tikhonov regularization theory.A regularized functional was established and the regularization parameter was deduced.The functional was solved to determine the interfacial heat transfer coefficient by using the sensitivity coefficient and Newton-Raphson iteration method.The temperature measurement experiment was done to ZL102 sand mold casting,and the appropriate mathematical model of the IHTC was established.Moreover, the regularization method was used to determinate the IHTC.The results indicate that the regularization method is very efficient in overcoming the ill-posedness of the inverse heat conduction problem(IHCP),and ensuring the accuracy and stability of the solutions.展开更多
The study presented in this article involves the estimation of the overall heat transfer coefficient of cooling system in RF capacitive hyperthermia treatment using inverse problem based on the conjugate gradient meth...The study presented in this article involves the estimation of the overall heat transfer coefficient of cooling system in RF capacitive hyperthermia treatment using inverse problem based on the conjugate gradient method to provide improved distribution of temperature. The temperature data computed numerically from the direct problem using the finite difference time domain method are used to simulate the temperature measurements. The effects of the errors and sensor positions upon the precision of the estimated results are also considered. The results show that a reasonable estimation of the unknown can be obtained. Finally, measurements in a tissue-equivalent phantom are employed to appraise the reliability of the presented method. The comparison of computed data with measurements shows a good agreement between numerical and experimental results.展开更多
The decentralized fuzzy inference method(DFIM)is employed as an optimization technique to reconstruct time-and space-dependent heat flux of two-dimensional(2D)participating medium.The forward coupled radiative and con...The decentralized fuzzy inference method(DFIM)is employed as an optimization technique to reconstruct time-and space-dependent heat flux of two-dimensional(2D)participating medium.The forward coupled radiative and conductive heat transfer problem is solved by a combination of finite volume method and discrete ordinate method.The reconstruction task is formulated as an inverse problem,and the DFIM is used to reconstruct the unknown heat flux.No prior information on the heat flux distribution is required for the inverse analysis.All retrieval results illustrate that the time-and spacedependent heat flux of participating medium can be exactly recovered by the DFIM.The present method is proved to be more efficient and accurate than other optimization techniques.The effects of heat flux form,initial guess,medium property,and measurement error on reconstruction results are investigated.Simulated results indicate that the DFIM is robust to reconstruct different kinds of heat fluxes even with noisy data.展开更多
The presence of non-gray radiative properties in a reheating furnace’s medium that absorbs,emits,and involves non-gray creates more complex radiative heat transfer problems.Furthermore,it adds difficulty to solving t...The presence of non-gray radiative properties in a reheating furnace’s medium that absorbs,emits,and involves non-gray creates more complex radiative heat transfer problems.Furthermore,it adds difficulty to solving the coupled conduction,convection,and radiation problem,leading to suboptimal efficiency that fails to meet real-time control demands.To overcome this difficulty,comparable gray radiative properties of non-gray media are proposed and estimated by solving an inverse problem.However,the required iteration numbers by using a least-squares method are too many and resulted in a very low inverse efficiency.It is necessary to present an efficient method for the equivalence.The Levenberg-Marquardt algorithm is utilized to solve the inverse problem of coupled heat transfer,and the gray-equivalent radiative characteristics are successfully recovered.It is our intention that the issue of low inverse efficiency,which has been observed when the least-squares method is employed,will be resolved.To enhance the performance of the Levenberg-Marquardt algorithm,a modification is implemented for determining the damping factor.Detailed investigations are also conducted to evaluate its accuracy,stability of convergence,efficiency,and robustness of the algorithm.Subsequently,a comparison is made between the results achieved using each method.展开更多
In this paper, the linear complementary method for moving boundary problems with phase transformation is presented, in which a pair of unknown vectors of heat source with phase transforming and the temperature field c...In this paper, the linear complementary method for moving boundary problems with phase transformation is presented, in which a pair of unknown vectors of heat source with phase transforming and the temperature field can be solved exactly, and a large amount of iterative calculations can be avoided.展开更多
Finite element method (FEM) and differential quadrature method (DQM) are among important numerical techniques used in engineering analyses. Usually elements are sub-divided uniformly in FEM (conventional FEM, CFEM) to...Finite element method (FEM) and differential quadrature method (DQM) are among important numerical techniques used in engineering analyses. Usually elements are sub-divided uniformly in FEM (conventional FEM, CFEM) to obtain temperature distribution behavior in a fin or plate. Hence, extra computational complexity is needed to obtain a fair solution with required accuracy. In this paper, non-uniform sub-elements are considered for FEM (efficient FEM, EFEM) solution to reduce the computational complex-ity. Then this EFEM is applied for the solution of one-dimensional heat transfer problem in a rectangular thin fin. The obtained results are compared with CFEM and efficient DQM (EDQM), with non-uniform mesh generation). It is found that the EFEM exhibit more accurate results than CFEM and EDQM showing its potentiality.展开更多
A second order heat equation with convection in an infinite medium isstudied. Suitable similarity transformations are used to reduce the parabolic heat equation to aClass of singular nonlinear boundary value problems....A second order heat equation with convection in an infinite medium isstudied. Suitable similarity transformations are used to reduce the parabolic heat equation to aClass of singular nonlinear boundary value problems. Numerical solutions are presented for differentrepresehtations of heat conduction, heat convection, heat flux, and power law parameters byutilizing the shooting technique. The results reveal the heat transfer characteristic and the effectof parameters on the solutions.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 50776097)
文摘Analytically solving a three-dimensional （3-D） bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green function method are introduced to deal with the cryopreservation process of in vitro biomaterials. Exact solutions for the 3-D temperature transients of tissues under various boundary conditions, such as totally convective cooling, totally fixed temperature cooling and a hybrid between them on tissue surfaces, are obtained. Furthermore, the cryosurgical process in living tissues subject to freezing by a single or multiple cryoprobes is also analytically solved. A closed-form analytical solution to the bioheat phase change process is derived by considering contributions from blood perfusion heat transfer, metabolic heat generation, and heat sink of a cryoprobe. The present method is expected to have significant value for analytically solving complex bioheat transfer problems with phase change.
文摘We consider the one-dimensional bio-heat transfer equation with quadratic temperature-dependent blood perfusion, which governs the temperature distribution inside biological tissues. Using an extended mapping method with symbolic computation, we obtain the exact analytical thermal traveling wave solution, which describes the non-uniform temperature distribution inside the bodies. The found exact solution is used to investigate the temperature distribution in the tissues. It is found that the surrounding medium with higher temperature does not necessarily imply that the tissue will quickly (after a short duration of heating process) reach the desired temperature. It is also found that increased perfusion causes a decline in local temperature.
基金National Natural Science Foundation of China(11971069,12071045)Foundation of CAEP(CX20210042)Science Challenge Project(No.TZ2016002).
文摘In this paper,we present a unified finite volume method preserving discrete maximum principle(DMP)for the conjugate heat transfer problems with general interface conditions.We prove the existence of the numerical solution and the DMP-preserving property.Numerical experiments show that the nonlinear iteration numbers of the scheme in[24]increase rapidly when the interfacial coefficients decrease to zero.In contrast,the nonlinear iteration numbers of the unified scheme do not increase when the interfacial coefficients decrease to zero,which reveals that the unified scheme is more robust than the scheme in[24].The accuracy and DMP-preserving property of the scheme are also veri ed in the numerical experiments.
基金the Natural Science Foundation of Shanghai(No.21ZR1465800)the Science Challenge Project(No.TZ2018001)+2 种基金the Interdisciplinary Project in Ocean Research of Tongji University,the Aeronautical Science Foundation of China(No.2020001053002)the National Key R&D Program of China(No.2020YFA0713603)the Fundamental Research Funds for the Central Universities.
文摘Stochastic temperature distribution should be carefully inspected in the thermal-failure design of heterogeneous solids with unexpected random energy excitations.Stochastic multiscale modeling for these problems involve multiscale and highdimensional uncertain thermal parameters,which remains limitation of prohibitive computation.In this paper,we propose a multi-modes based constrained energy minimization generalized multiscale finite element method(MCEM-GMsFEM),which can transform the original stochastic multiscale model into a series of recursive multiscale models sharing the same deterministic material parameters by multiscale analysis.Thus,MCEM-GMsFEM reveals an inherent low-dimensional representation in random space,and is designed to effectively reduce the complexity of repeated computation of discretized multiscale systems.In addition,the convergence analysis is established,and the optimal error estimates are derived.Finally,several typical random fluctuations on multiscale thermal conductivity are considered to validate the theoretical results in the numerical examples.The numerical results indicate that the multi-modes multiscale approach is a robust integrated method with the excellent performance.
基金This work was partially supported by NSFC Project （Grant No. 11031006, 91130002, 11171281）, the Key Project of Scientific Research Fund of Hunan Provincial Science and Technology Department （Grant No. 2011FJ2011）, Hunan Provincial Natural Science Foundation of China （Grant No. 12JJ3010）.
文摘Using the inverse algorithm of heat transfer and the nonlinear estimation method, matching calculated values with measured ones, the interfacial heat transfer coefficient at casting/Cu mould interface was determined.The results show that the interfacial heat transfer coefficient at Al/Cu interface changes in a range of 4.0×10 3 1.0×10 5 W·m -2 ·K -1 and its average value is in a range of 5.0×10 37.0×10 3 W·m -2 ·K -1 .
文摘The accurate material physical properties, initial and boundary conditions are indispensable to the numerical simulation in the casting process, and they are related to the simulation accuracy directly. The inverse heat conduction method can be used to identify the mentioned above parameters based on the temperature measurement data. This paper presented a new inverse method according to Tikhonov regularization theory. A regularization functional was established and the regularization parameter was deduced, the Newton-Raphson iteration method was used to solve the equations. One detailed case was solved to identify the thermal conductivity and specific heat of sand mold and interfacial heat transfer coefficient (IHTC) at the meantime. This indicates that the regularization method is very efficient in decreasing the sensitivity to the temperature measurement data, overcoming the ill-posedness of the inverse heat conduction problem (IHCP) and improving the stability and accuracy of the results. As a general inverse method, it can be used to identify not only the material physical properties but also the initial and boundary conditions' parameters.
文摘The steady, laminar, incompressible flow and heat transfer of a viscous fluid between two circular cylinders for two different types of thermal boundary conditions are investigated. The governing Navier-Stokes and thermal equations of the flow are reduced to a nonlinear system of ordinary differential equations. The equations are solved analyt- ically using the homotopy analysis method （HAM）. Convergence of the HAM solutions is discussed in detail. These solutions are then compared with recently obtained numericM and perturbative solutions. Plots of the velocity and temperature profiles are provided for various values of the relevant parameters.
文摘Nonlinear nonstationary heat conduction problem for infinite circular cylinder under a complex heat transfer taking into account the temperature dependence of thermophysical characteristics of materials is solved numerically by the method of lines. Directing it to the Cauchy’s problem for systems of ordinary differential equations studied feature which takes place on the cylinder axis. Taken into account the dependence on the temperature coefficient of heat transfer that the different interpretation of its physical content makes it possible to consider both convective and convective-ray or heat ray. Using the perturbation method, the corresponding thermoelasticity problem taking into account the temperature dependence of mechanical properties of the material is construed. The influence of the temperature dependence of the material on the distribution of temperature field and thermoelastic state of infinite circular cylinder made of titanium alloy Ti-6Al-4V by radiant heat transfer through the outer surface has been analyzed.
基金The work was financially supported by the National Natural Science Foundations of China (No.50476083).
文摘A similarity analysis for Marangoni convection induced flow over a vapor-liquid interface due to an imposed temperature gradient was carried out. The analysis assumes that the surface tension varies linearly with temperature but the temperature variation is a power law function of the location. The similarity solutions are presented numerically and the associated transfer characteristics are discussed.
文摘The interfacial heat transfer coefficient(IHTC)between the casting and the mould is essential to the numerical simulation as one of boundary conditions.A new inverse method was presented according to the Tikhonov regularization theory.A regularized functional was established and the regularization parameter was deduced.The functional was solved to determine the interfacial heat transfer coefficient by using the sensitivity coefficient and Newton-Raphson iteration method.The temperature measurement experiment was done to ZL102 sand mold casting,and the appropriate mathematical model of the IHTC was established.Moreover, the regularization method was used to determinate the IHTC.The results indicate that the regularization method is very efficient in overcoming the ill-posedness of the inverse heat conduction problem(IHCP),and ensuring the accuracy and stability of the solutions.
文摘The study presented in this article involves the estimation of the overall heat transfer coefficient of cooling system in RF capacitive hyperthermia treatment using inverse problem based on the conjugate gradient method to provide improved distribution of temperature. The temperature data computed numerically from the direct problem using the finite difference time domain method are used to simulate the temperature measurements. The effects of the errors and sensor positions upon the precision of the estimated results are also considered. The results show that a reasonable estimation of the unknown can be obtained. Finally, measurements in a tissue-equivalent phantom are employed to appraise the reliability of the presented method. The comparison of computed data with measurements shows a good agreement between numerical and experimental results.
基金Project supported by the Natural Science Foundation of Chongqing(CSTC,Grant No.2019JCYJ-MSXMX0441).
文摘The decentralized fuzzy inference method(DFIM)is employed as an optimization technique to reconstruct time-and space-dependent heat flux of two-dimensional(2D)participating medium.The forward coupled radiative and conductive heat transfer problem is solved by a combination of finite volume method and discrete ordinate method.The reconstruction task is formulated as an inverse problem,and the DFIM is used to reconstruct the unknown heat flux.No prior information on the heat flux distribution is required for the inverse analysis.All retrieval results illustrate that the time-and spacedependent heat flux of participating medium can be exactly recovered by the DFIM.The present method is proved to be more efficient and accurate than other optimization techniques.The effects of heat flux form,initial guess,medium property,and measurement error on reconstruction results are investigated.Simulated results indicate that the DFIM is robust to reconstruct different kinds of heat fluxes even with noisy data.
基金supported by the Na⁃tional Natural Science Foundation of China(No.12172078)the Fundamental Research Funds for the Central Univer⁃sities(No.DUT24MS007).
文摘The presence of non-gray radiative properties in a reheating furnace’s medium that absorbs,emits,and involves non-gray creates more complex radiative heat transfer problems.Furthermore,it adds difficulty to solving the coupled conduction,convection,and radiation problem,leading to suboptimal efficiency that fails to meet real-time control demands.To overcome this difficulty,comparable gray radiative properties of non-gray media are proposed and estimated by solving an inverse problem.However,the required iteration numbers by using a least-squares method are too many and resulted in a very low inverse efficiency.It is necessary to present an efficient method for the equivalence.The Levenberg-Marquardt algorithm is utilized to solve the inverse problem of coupled heat transfer,and the gray-equivalent radiative characteristics are successfully recovered.It is our intention that the issue of low inverse efficiency,which has been observed when the least-squares method is employed,will be resolved.To enhance the performance of the Levenberg-Marquardt algorithm,a modification is implemented for determining the damping factor.Detailed investigations are also conducted to evaluate its accuracy,stability of convergence,efficiency,and robustness of the algorithm.Subsequently,a comparison is made between the results achieved using each method.
文摘In this paper, the linear complementary method for moving boundary problems with phase transformation is presented, in which a pair of unknown vectors of heat source with phase transforming and the temperature field can be solved exactly, and a large amount of iterative calculations can be avoided.
文摘Finite element method (FEM) and differential quadrature method (DQM) are among important numerical techniques used in engineering analyses. Usually elements are sub-divided uniformly in FEM (conventional FEM, CFEM) to obtain temperature distribution behavior in a fin or plate. Hence, extra computational complexity is needed to obtain a fair solution with required accuracy. In this paper, non-uniform sub-elements are considered for FEM (efficient FEM, EFEM) solution to reduce the computational complex-ity. Then this EFEM is applied for the solution of one-dimensional heat transfer problem in a rectangular thin fin. The obtained results are compared with CFEM and efficient DQM (EDQM), with non-uniform mesh generation). It is found that the EFEM exhibit more accurate results than CFEM and EDQM showing its potentiality.
基金This work was supported by Cross-Century Talents Projects of Educational Ministry of China the "973" Key Foundation under the contract No.G1998061510.]
文摘A second order heat equation with convection in an infinite medium isstudied. Suitable similarity transformations are used to reduce the parabolic heat equation to aClass of singular nonlinear boundary value problems. Numerical solutions are presented for differentrepresehtations of heat conduction, heat convection, heat flux, and power law parameters byutilizing the shooting technique. The results reveal the heat transfer characteristic and the effectof parameters on the solutions.
