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
Thermal phase change problems are widespread in mathematics,nature,and science.They are particularly useful in simulating the phenomena of melting and solidification in materials science.In this paper we propose a nov...Thermal phase change problems are widespread in mathematics,nature,and science.They are particularly useful in simulating the phenomena of melting and solidification in materials science.In this paper we propose a novel class of arbitrarily high-order and unconditionally energy stable schemes for a thermal phase changemodel,which is the coupling of a heat transfer equation and a phase field equation.The unconditional energy stability and consistency error estimates are rigorously proved for the proposed schemes.A detailed implementation demonstrates that the proposed method requires only the solution of a system of linear elliptic equations at each time step,with an efficient scheme of sufficient accuracy to calculate the solution at the first step.It is observed from the comparison with the classical explicit Runge-Kutta method that the new schemes allow to use larger time steps.Adaptive time step size strategies can be applied to further benefit from this unconditional stability.Numerical experiments are presented to verify the theoretical claims and to illustrate the accuracy and effectiveness of our method.展开更多
A mathematical model for describing gas solid two phase steady mixed convection with phase change has been developed and numerical calculation methods presented.A melting liquid droplet failing a counter gas currenl e...A mathematical model for describing gas solid two phase steady mixed convection with phase change has been developed and numerical calculation methods presented.A melting liquid droplet failing a counter gas currenl expe- riences three processes,cooling of liquid droplet,solidification and cooling of the solid particle.The turbulent model used for Rayleigh number greater than 10~6 is a two equation(k—ε)model of turbulence.For phase change,an improved enthalpy method with varied time step is proposed.The gas particle two phase flow is described by using Eulerian-Lagrangian approach.Modified SIMPLE algorithm and Runge-Kutta method are used in interative calcu- lation.As an example of calculation,the flow in a special 2-dimensional axi-symmetrical prilling tower of diameter 20 m and height 50 m has been performed.Buoyancy effect is important for moving droplet with phase change. The model to be developed and analysis of results obtained in this paper are useful for engineering design in indus- try.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Thermal phase change problems are widespread in mathematics,nature,and science.They are particularly useful in simulating the phenomena of melting and solidification in materials science.In this paper we propose a novel class of arbitrarily high-order and unconditionally energy stable schemes for a thermal phase changemodel,which is the coupling of a heat transfer equation and a phase field equation.The unconditional energy stability and consistency error estimates are rigorously proved for the proposed schemes.A detailed implementation demonstrates that the proposed method requires only the solution of a system of linear elliptic equations at each time step,with an efficient scheme of sufficient accuracy to calculate the solution at the first step.It is observed from the comparison with the classical explicit Runge-Kutta method that the new schemes allow to use larger time steps.Adaptive time step size strategies can be applied to further benefit from this unconditional stability.Numerical experiments are presented to verify the theoretical claims and to illustrate the accuracy and effectiveness of our method.
文摘A mathematical model for describing gas solid two phase steady mixed convection with phase change has been developed and numerical calculation methods presented.A melting liquid droplet failing a counter gas currenl expe- riences three processes,cooling of liquid droplet,solidification and cooling of the solid particle.The turbulent model used for Rayleigh number greater than 10~6 is a two equation(k—ε)model of turbulence.For phase change,an improved enthalpy method with varied time step is proposed.The gas particle two phase flow is described by using Eulerian-Lagrangian approach.Modified SIMPLE algorithm and Runge-Kutta method are used in interative calcu- lation.As an example of calculation,the flow in a special 2-dimensional axi-symmetrical prilling tower of diameter 20 m and height 50 m has been performed.Buoyancy effect is important for moving droplet with phase change. The model to be developed and analysis of results obtained in this paper are useful for engineering design in indus- try.
