The objective of the current study is to investigate the importance of entropy generation and thermal radiation on the patterns of velocity,isentropic lines,and temperature contours within a thermal energy storage dev...The objective of the current study is to investigate the importance of entropy generation and thermal radiation on the patterns of velocity,isentropic lines,and temperature contours within a thermal energy storage device filled with magnetic nanoencapsulated phase change materials(NEPCMs).The versatile finite element method(FEM)is implemented to numerically solve the governing equations.The effects of various parameters,including the viscosity parameter,ranging from 1 to 3,the thermal conductivity parameter,ranging from 1 to 3,the Rayleigh parameter,ranging from 102 to 3×10^(2),the radiation number,ranging from 0.1 to 0.5,the fusion temperature,ranging from 1.0 to 1.2,the volume fraction of NEPCMs,ranging from 2%to 6%,the Stefan number,ranging from 1 to 5,the magnetic number,ranging from 0.1 to 0.5,and the irreversibility parameter,ranging from 0.1 to 0.5,are examined in detail on the temperature contours,isentropic lines,heat capacity ratio,and velocity fields.Furthermore,the heat transfer rates at both the cold and hot walls are analyzed,and the findings are presented graphically.The results indicate that the time taken by the NEPCMs to transition from solid to liquid is prolonged inside the chamber region as the fusion temperatureθf increases.Additionally,the contours of the heat capacity ratio Cr decrease with the increase in the Stefan number Ste.展开更多
The seasonal change in depths of the frozen and thawed soils within their active layer is reduced to a moving boundary problem, which describes the dynamics of the total ice content using an independent mass balance e...The seasonal change in depths of the frozen and thawed soils within their active layer is reduced to a moving boundary problem, which describes the dynamics of the total ice content using an independent mass balance equation and treats the soil frost/thaw depths as moving (sharp) interfaces governed by some Stefan-type moving boundary conditions, and hence simultaneously describes the liquid water and solid ice states as well as the positions of the frost/thaw depths in soil. An adaptive mesh method for the moving boundary problem is adopted to solve the relevant equations and to determine frost/thaw depths, water content and temperature distribution. A series of sensitivity experiments by the numerical model under the periodic sinusoidal upper boundary condition for temperature are conducted to validate the model, and to investigate the effects of the model soil thickness, ground surface temperature, annual amplitude of ground surface temperature and thermal conductivity on frost/thaw depths and soil temperature. The simulated frost/thaw depths by the model with a periodical change of the upper boundary condition have the same period as that of the upper boundary condition, which shows that it can simulate the frost/thaw depths reasonably for a periodical forcing.展开更多
The existence of a local classical solution to the Mullins-Sekerka problem and the convergence to the two-phase quasi-stationary Stefan problem are proved when surface tension approaches zero. This convergence gives a...The existence of a local classical solution to the Mullins-Sekerka problem and the convergence to the two-phase quasi-stationary Stefan problem are proved when surface tension approaches zero. This convergence gives a proof of the existence of a local classical solution of quasi-stationary Stefan problem. The methods work in all dimensions.展开更多
Permafrost and its spatiotemporal variation considerably influence the surface and sub-surface hydrological processes,biogeochemical cycles,fauna and flora growth and cold region engineering projects in the Three-Rive...Permafrost and its spatiotemporal variation considerably influence the surface and sub-surface hydrological processes,biogeochemical cycles,fauna and flora growth and cold region engineering projects in the Three-River Source Region(TRSR),Qinghai–Tibet Plateau.However,the dynamics of permafrost over a relatively long term duration(e.g.>100 years)in the TRSR is not well quantified.Thus,the spatial and temporal variations of the temperature at the top of the perennially frozen/unfrozen ground(TTOP),active layer thickness(ALT)in permafrost regions and the maximum depth of frost penetration(MDFP)in the seasonally frozen ground of the TRSR during 1901–2020 were simulated using the TTOP model and Stefan equation driven by the widely used reanalysis Climatic Research Unit 4.05 dataset.Results revealed that the permafrost in the TRSR over the past 120 years did not degrade monotonically but experienced considerable fluctuations in area with the decadal oscillations of climate warming and cooling:shrinking from 263.9×10^(3)km^(2)in the 1900s to 233.3×10^(3)km^(2)in the 1930s,expanding from 232.3×10^(3)km^(2)in the 1940s to 260.9×10^(3)km^(2)in the 1970s and shrinking again from 254.1×10^(3)km^(2)in the 1980s to 228.9×10^(3)km^(2)in the 2010s.The regional average TTOP increased from−1.34±2.74℃in the 1910s to−0.48±2.69℃in the 2010s,demonstrating the most noticeable change for the extremely stable permafrost(TTOP<−5℃)from 8%to 1%.The regional average ALT increased from 2.68±0.52 m to 2.87±0.46 m,with the area proportion of ALT>3.0 m by 12%from 1901 to 2020.Notably,minor changes were observed for the regional average MDFP,probably due to the increase in the area proportion of MDFP<3.0 m(caused by climate warming)and MDFP>3.5 m(owing to the transformation of permafrost to seasonally frozen ground)by 7.39%and 4.77%,respectively.These findings can facilitate an in-depth understanding of permafrost dynamics and thus provide a scientific reference for eco-environment protection and sustainable development展开更多
We investigate a blowup problem of a reaction-advection-diffusion equa-tion with double free boundaries and aim to use the dynamics of such a problem to describe the heat transfer and temperature change of a chemical ...We investigate a blowup problem of a reaction-advection-diffusion equa-tion with double free boundaries and aim to use the dynamics of such a problem to describe the heat transfer and temperature change of a chemical reaction in advective environment with the free boundary representing the spreading front of the heat.We study the influence of the advection on the blowup properties of the solutions and con-clude that large advection is not favorable for blowup.Moreover,we give the decay estimates of solutions and the two free boundaries converge to a finite limit for small initial data.展开更多
A mathematical model for the unsteady forced convection over rotating stretchable disk in nanofluid containing microorganisms and taking into account Stefan blowing effect is presented theoretically and numerically.Ap...A mathematical model for the unsteady forced convection over rotating stretchable disk in nanofluid containing microorganisms and taking into account Stefan blowing effect is presented theoretically and numerically.Appropriate transfonnations are used to transform the governing boundary layer equations into non-linear ordinary differential equations,before being solved numerically using the Runge-Kutta-Fehlberg method.The effect of the governing parameters on the dimensionless velocities,temperature,nanoparticle volume fraction(concentration),density of motile microorganisms as well as on the local skin friction,local Nusselt,Sherwood number and motile microorganisms numbers are thoroughly examined via graphs.It is observed that the Stefan blowing increases the local skin friction and reduces the heat transfer,mass transfer and microorganism transfer rates.The numerical results are in good agreement with those obtained from previous literature.Physical quantities results from this investigation show that the effects of higher disk stretching strength and suction case provides a good medium to enhance the heat,mass and microorganisms transfer compared to blowing case.展开更多
One-dimensional non-Darcy flow in a semi-infinite porous media is investigated. We indicate that the non-Darcy relation which is usually determined from experimental results can always be described by a piecewise line...One-dimensional non-Darcy flow in a semi-infinite porous media is investigated. We indicate that the non-Darcy relation which is usually determined from experimental results can always be described by a piecewise linear function, and the problem can be equivalently transformed to a multiphase implicit Stefan problem. The novel feature of this Stefan problem is that the phases of the porous media are divided by hydraulic gradients, not the excess pore water pressures. Using the similarity transformation technique, an exact solution for the situation that the external load increases in proportion to the square root of time is developed. The study on the existence and uniqueness of the solution leads to the requirement of a group of inequalities. A similar Stefan problem considering constant surface seepage velocity is also investigated, and the solution, which we indicate to be uniquely existent under all conditions, is established. Meanwhile, the relation between our Stefan problem and the traditional multiphase Stefan problem is demonstrated. In the end, computational examples of the solution are presented and discussed. The solution provides a useful benchmark for verifying the accuracy of general approximate algorithms of Stefan problems, and it is also attractive in the context of inverse problem analysis.展开更多
The Stefan equation provides a useful and widely used method for predicting the depth of thawing and freezing in a soil where little site-specific information is available. The original Stefan equation was derived for...The Stefan equation provides a useful and widely used method for predicting the depth of thawing and freezing in a soil where little site-specific information is available. The original Stefan equation was derived for only a homogeneous medium, and some algorithms have been developed for its use in a multilayered system. However, although the Stefan equation was derived more than 100 years ago, there is not a unified understanding for its use in a multilayered system. This paper examines the use of the Stefan equation in multilayered soil, based on comparing three algorithms(JL-algorithm, NM-algorithm, and XG-algorithm). We conclude that the JL and NM algorithms are incorrect, as they arose from flawed mathematical derivations. Both of these algorithms failed to recognize that the thawing depth in a multilayered soil is a piecewise function and not a continuous function of time. This work asserts that the XG-algorithm is a correct and rigorous method to determine the freezing–thawing fronts in multilayered soil.展开更多
The study reveals analytically on the 3-dimensional viscous time-dependent gyrotactic bioconvection in swirling nanofluid flow past from a rotating disk.It is known that the deformation of the disk is along the radial...The study reveals analytically on the 3-dimensional viscous time-dependent gyrotactic bioconvection in swirling nanofluid flow past from a rotating disk.It is known that the deformation of the disk is along the radial direction.In addition to that Stefan blowing is considered.The Buongiorno nanofluid model is taken care of assuming the fluid to be dilute and we find Brownian motion and thermophoresis have dominant role on nanoscale unit.The primitive mass conservation equation,radial,tangential and axial momentum,heat,nano-particle concentration and micro-organism density function are developed in a cylindrical polar coordinate system with appropriate wall(disk surface)and free stream boundary conditions.This highly nonlinear,strongly coupled system of unsteady partial differential equations is normalized with the classical von Kármán and other transformations to render the boundary value problem into an ordinary differential system.The emerging 11th order system features an extensive range of dimensionless flow parameters,i.e.,disk stretching rate,Brownian motion,thermophoresis,bioconvection Lewis number,unsteadiness parameter,ordinary Lewis number,Prandtl number,mass convective Biot number,Péclet number and Stefan blowing parameter.Solutions of the system are obtained with developed semi-analytical technique,i.e.,Adomian decomposition method.Validation of the said problem is also conducted with earlier literature computed by Runge-Kutta shooting technique.展开更多
2014年10月8日,瑞典皇家科学院将2014年诺贝尔化学奖授予美国的埃里克·白兹格（Eric Betzig）教授、威廉姆·艾斯科·莫尔纳尔（William E Moerner）教授和德国的斯特凡·W·赫尔（Stefan W Hell）教授,以表彰他...2014年10月8日,瑞典皇家科学院将2014年诺贝尔化学奖授予美国的埃里克·白兹格（Eric Betzig）教授、威廉姆·艾斯科·莫尔纳尔（William E Moerner）教授和德国的斯特凡·W·赫尔（Stefan W Hell）教授,以表彰他们为发展超分辨率荧光显微镜所作的贡献[1]。展开更多
This paper considers the quasi-stationary Stefan problem:△u(x,t)=0 in space-time domain,u=0 and Vv +(?)u/(?)u=0 on the free boundary.Under the natural conditions the existence of classical solution locally in time is...This paper considers the quasi-stationary Stefan problem:△u(x,t)=0 in space-time domain,u=0 and Vv +(?)u/(?)u=0 on the free boundary.Under the natural conditions the existence of classical solution locally in time is proved bymaking use of the property of Frechet derivative operator and fixed point theorem. For thesake of simplicity only the one-phase problem is dealt with. In fact two-phase problem can bedealt with in a similar way with more complicated calculation.展开更多
In this paper,the relaxation algorithm and two Uzawa type algorithms for solving discretized variational inequalities arising from the two-phase Stefan type problem are proposed.An analysis of their convergence is pre...In this paper,the relaxation algorithm and two Uzawa type algorithms for solving discretized variational inequalities arising from the two-phase Stefan type problem are proposed.An analysis of their convergence is presented and the upper bounds of the convergence rates are derived.Some numerical experiments are shown to demonstrate that for the second Uzawa algorithm which is an improved version of the first Uzawa algorithm,the convergence rate is uniformly bounded away from 1 if τh^-2 is kept bounded,where τ is the time step size and h the space mesh size.展开更多
There are many works (i.e. [1]) aiming to find out numerically how positive feedback affects the formation of invadopodia and invasion of cancer cells;however, studies on the cancer cell invasion model with free bound...There are many works (i.e. [1]) aiming to find out numerically how positive feedback affects the formation of invadopodia and invasion of cancer cells;however, studies on the cancer cell invasion model with free boundary are fairly rare. In this paper, we study modified cancer cell invasion model with free boundary, where, free boundary stands for cancer cell membrane, so that we can more precisely describe the positive feedback affects. Firstly, we simplized the model by means of characteristic curve and semi-groups’ property, and obtained the Stefan-like problem by introducing Gaussian Kernel and Green function. Secondly, based on the classical Stefan problem, we derived the integral solution of simplified model, which could lead us a further step to find the solution of modified cancer cell invasion model.展开更多
In this paper, we prove the existence theorems of locbal or global classical solutions to Stefan problems with various kinetic conditions at the free boundary.
The current mathematical model explains the influence of non-linear thermal radiation on the Casson liquid flow over a moving thin needle by considering Buongiorno’s nanofluid model.The influences of Stefan blowing,D...The current mathematical model explains the influence of non-linear thermal radiation on the Casson liquid flow over a moving thin needle by considering Buongiorno’s nanofluid model.The influences of Stefan blowing,Dufour and Soret effects are also considered in the model.The equations which represent the described flow pattern are reduced to ordinary differential equations(ODEs)by using apt similarity transformations and then they are numerically solved with Runge–Kutta-Fehlberg’s fourth fifth-order method(RKF-45)with shooting process.The impacts of pertinent parameters on thermal,mass and velocity curves are deliberated graphically.Skin friction,rate of heat and mass transfer are also discussed graphically.Results reveal that,the increase in values of Brownian motion,thermophoresis,Dufour number,heating and radiative parameters improves the heat transfer.The increasing values of the Schmidt number deteriorates the mass transfer but a converse trend is seen for increasing values of the Soret number.Finally,the escalating values of the radiative parameter decays the rate of heat transfer.展开更多
A Stefan problem with nonlinear boundary flux and internal convection of a material are considered. The existence, uniqueness and continuous dependence of globally weak solution of this problem are obtained. This pape...A Stefan problem with nonlinear boundary flux and internal convection of a material are considered. The existence, uniqueness and continuous dependence of globally weak solution of this problem are obtained. This paper extends the results of Fahuai Yi and T.M.Shih, relaxes restrictions that does not be to accord with reality very much on internal convection and boundary conditions in their articles.展开更多
A one-phase Stefan problem for the nonhomogeneous heat equation with the source term depending on an unknown parameter p(t) is considered. The existence and uniqueness of the solution (p, s, u) are also demonstrated.
A numerical analysis was carried out to study the moving boundary problem in the physical process of pulsed Nd-YAG laser surface melting prior to vaporization.The enthalpy method was applied to solve this two-phase ax...A numerical analysis was carried out to study the moving boundary problem in the physical process of pulsed Nd-YAG laser surface melting prior to vaporization.The enthalpy method was applied to solve this two-phase axisymmetrical mehing problem.Computational results of tempera ture fields were obtained,which provide useful information to practical lair treatment processing. The validity of enthalpy method in solving such problems is presented.展开更多
Reuse of abandoned or underused historic buildings and sites has become an increasing global trend within the built environment in the past two decades(Bullen and Love 2011;Gravagnuolo et al.2017).Bypassing the wastef...Reuse of abandoned or underused historic buildings and sites has become an increasing global trend within the built environment in the past two decades(Bullen and Love 2011;Gravagnuolo et al.2017).Bypassing the wasteful processes of demolition and new construction,adaptive reuse prolongs the lifespan of cultural heritage,contributes to environmental sustainability and enhances urban livability(Ikiz Kaya et al.2021).Focusing on three Asian global cities—Hong Kong,Shanghai and Singapore,the book of Asian Revitalization:Adaptive Reuse in Hong Kong,Shanghai,and Singapore,edited by Cummer and DiStefano,provides a needed analysis of adaptive reuse trends,policies and practices in Asian context.展开更多
文摘The objective of the current study is to investigate the importance of entropy generation and thermal radiation on the patterns of velocity,isentropic lines,and temperature contours within a thermal energy storage device filled with magnetic nanoencapsulated phase change materials(NEPCMs).The versatile finite element method(FEM)is implemented to numerically solve the governing equations.The effects of various parameters,including the viscosity parameter,ranging from 1 to 3,the thermal conductivity parameter,ranging from 1 to 3,the Rayleigh parameter,ranging from 102 to 3×10^(2),the radiation number,ranging from 0.1 to 0.5,the fusion temperature,ranging from 1.0 to 1.2,the volume fraction of NEPCMs,ranging from 2%to 6%,the Stefan number,ranging from 1 to 5,the magnetic number,ranging from 0.1 to 0.5,and the irreversibility parameter,ranging from 0.1 to 0.5,are examined in detail on the temperature contours,isentropic lines,heat capacity ratio,and velocity fields.Furthermore,the heat transfer rates at both the cold and hot walls are analyzed,and the findings are presented graphically.The results indicate that the time taken by the NEPCMs to transition from solid to liquid is prolonged inside the chamber region as the fusion temperatureθf increases.Additionally,the contours of the heat capacity ratio Cr decrease with the increase in the Stefan number Ste.
基金the National Basic Research Program(Grant No.2005CB321703)the Knowledge Innovation Project of Chinese Academy of Sciences(Grant Nos.KZCX2-yw-126-2,KZCX2-yw-217)the Chinese Coordinated Observation and Prediction of the Earth System project(Grant No.GYHY20070605)
文摘The seasonal change in depths of the frozen and thawed soils within their active layer is reduced to a moving boundary problem, which describes the dynamics of the total ice content using an independent mass balance equation and treats the soil frost/thaw depths as moving (sharp) interfaces governed by some Stefan-type moving boundary conditions, and hence simultaneously describes the liquid water and solid ice states as well as the positions of the frost/thaw depths in soil. An adaptive mesh method for the moving boundary problem is adopted to solve the relevant equations and to determine frost/thaw depths, water content and temperature distribution. A series of sensitivity experiments by the numerical model under the periodic sinusoidal upper boundary condition for temperature are conducted to validate the model, and to investigate the effects of the model soil thickness, ground surface temperature, annual amplitude of ground surface temperature and thermal conductivity on frost/thaw depths and soil temperature. The simulated frost/thaw depths by the model with a periodical change of the upper boundary condition have the same period as that of the upper boundary condition, which shows that it can simulate the frost/thaw depths reasonably for a periodical forcing.
文摘The existence of a local classical solution to the Mullins-Sekerka problem and the convergence to the two-phase quasi-stationary Stefan problem are proved when surface tension approaches zero. This convergence gives a proof of the existence of a local classical solution of quasi-stationary Stefan problem. The methods work in all dimensions.
基金the CAS Western Young Scholars Project(D.Luo)and the National Natural Science Foundation of China(U2243214 and 41671060).
文摘Permafrost and its spatiotemporal variation considerably influence the surface and sub-surface hydrological processes,biogeochemical cycles,fauna and flora growth and cold region engineering projects in the Three-River Source Region(TRSR),Qinghai–Tibet Plateau.However,the dynamics of permafrost over a relatively long term duration(e.g.>100 years)in the TRSR is not well quantified.Thus,the spatial and temporal variations of the temperature at the top of the perennially frozen/unfrozen ground(TTOP),active layer thickness(ALT)in permafrost regions and the maximum depth of frost penetration(MDFP)in the seasonally frozen ground of the TRSR during 1901–2020 were simulated using the TTOP model and Stefan equation driven by the widely used reanalysis Climatic Research Unit 4.05 dataset.Results revealed that the permafrost in the TRSR over the past 120 years did not degrade monotonically but experienced considerable fluctuations in area with the decadal oscillations of climate warming and cooling:shrinking from 263.9×10^(3)km^(2)in the 1900s to 233.3×10^(3)km^(2)in the 1930s,expanding from 232.3×10^(3)km^(2)in the 1940s to 260.9×10^(3)km^(2)in the 1970s and shrinking again from 254.1×10^(3)km^(2)in the 1980s to 228.9×10^(3)km^(2)in the 2010s.The regional average TTOP increased from−1.34±2.74℃in the 1910s to−0.48±2.69℃in the 2010s,demonstrating the most noticeable change for the extremely stable permafrost(TTOP<−5℃)from 8%to 1%.The regional average ALT increased from 2.68±0.52 m to 2.87±0.46 m,with the area proportion of ALT>3.0 m by 12%from 1901 to 2020.Notably,minor changes were observed for the regional average MDFP,probably due to the increase in the area proportion of MDFP<3.0 m(caused by climate warming)and MDFP>3.5 m(owing to the transformation of permafrost to seasonally frozen ground)by 7.39%and 4.77%,respectively.These findings can facilitate an in-depth understanding of permafrost dynamics and thus provide a scientific reference for eco-environment protection and sustainable development
基金supported by Natural Science Foundation of China(No.11901238)Natural Science Foundation of Shandong Province(No.ZR2019MA063).
文摘We investigate a blowup problem of a reaction-advection-diffusion equa-tion with double free boundaries and aim to use the dynamics of such a problem to describe the heat transfer and temperature change of a chemical reaction in advective environment with the free boundary representing the spreading front of the heat.We study the influence of the advection on the blowup properties of the solutions and con-clude that large advection is not favorable for blowup.Moreover,we give the decay estimates of solutions and the two free boundaries converge to a finite limit for small initial data.
基金support from Universiti Sains Malaysia,RU Grant 1001/PMATHS/81125.
文摘A mathematical model for the unsteady forced convection over rotating stretchable disk in nanofluid containing microorganisms and taking into account Stefan blowing effect is presented theoretically and numerically.Appropriate transfonnations are used to transform the governing boundary layer equations into non-linear ordinary differential equations,before being solved numerically using the Runge-Kutta-Fehlberg method.The effect of the governing parameters on the dimensionless velocities,temperature,nanoparticle volume fraction(concentration),density of motile microorganisms as well as on the local skin friction,local Nusselt,Sherwood number and motile microorganisms numbers are thoroughly examined via graphs.It is observed that the Stefan blowing increases the local skin friction and reduces the heat transfer,mass transfer and microorganism transfer rates.The numerical results are in good agreement with those obtained from previous literature.Physical quantities results from this investigation show that the effects of higher disk stretching strength and suction case provides a good medium to enhance the heat,mass and microorganisms transfer compared to blowing case.
基金supported by the Fundamental Research Funds for the Central Universities(Grant 2015XKMS014)
文摘One-dimensional non-Darcy flow in a semi-infinite porous media is investigated. We indicate that the non-Darcy relation which is usually determined from experimental results can always be described by a piecewise linear function, and the problem can be equivalently transformed to a multiphase implicit Stefan problem. The novel feature of this Stefan problem is that the phases of the porous media are divided by hydraulic gradients, not the excess pore water pressures. Using the similarity transformation technique, an exact solution for the situation that the external load increases in proportion to the square root of time is developed. The study on the existence and uniqueness of the solution leads to the requirement of a group of inequalities. A similar Stefan problem considering constant surface seepage velocity is also investigated, and the solution, which we indicate to be uniquely existent under all conditions, is established. Meanwhile, the relation between our Stefan problem and the traditional multiphase Stefan problem is demonstrated. In the end, computational examples of the solution are presented and discussed. The solution provides a useful benchmark for verifying the accuracy of general approximate algorithms of Stefan problems, and it is also attractive in the context of inverse problem analysis.
基金supported by grants from the National Natural Science Foundation of China (41671068, 41421061, and 41771040)the State Key Laboratory of Cryospheric Sciences (SKLCS-ZZ-2017)the Hundred Talents Program of the Chinese Academy of Sciences granted to Chang Wei Xie (51Y551831)
文摘The Stefan equation provides a useful and widely used method for predicting the depth of thawing and freezing in a soil where little site-specific information is available. The original Stefan equation was derived for only a homogeneous medium, and some algorithms have been developed for its use in a multilayered system. However, although the Stefan equation was derived more than 100 years ago, there is not a unified understanding for its use in a multilayered system. This paper examines the use of the Stefan equation in multilayered soil, based on comparing three algorithms(JL-algorithm, NM-algorithm, and XG-algorithm). We conclude that the JL and NM algorithms are incorrect, as they arose from flawed mathematical derivations. Both of these algorithms failed to recognize that the thawing depth in a multilayered soil is a piecewise function and not a continuous function of time. This work asserts that the XG-algorithm is a correct and rigorous method to determine the freezing–thawing fronts in multilayered soil.
文摘The study reveals analytically on the 3-dimensional viscous time-dependent gyrotactic bioconvection in swirling nanofluid flow past from a rotating disk.It is known that the deformation of the disk is along the radial direction.In addition to that Stefan blowing is considered.The Buongiorno nanofluid model is taken care of assuming the fluid to be dilute and we find Brownian motion and thermophoresis have dominant role on nanoscale unit.The primitive mass conservation equation,radial,tangential and axial momentum,heat,nano-particle concentration and micro-organism density function are developed in a cylindrical polar coordinate system with appropriate wall(disk surface)and free stream boundary conditions.This highly nonlinear,strongly coupled system of unsteady partial differential equations is normalized with the classical von Kármán and other transformations to render the boundary value problem into an ordinary differential system.The emerging 11th order system features an extensive range of dimensionless flow parameters,i.e.,disk stretching rate,Brownian motion,thermophoresis,bioconvection Lewis number,unsteadiness parameter,ordinary Lewis number,Prandtl number,mass convective Biot number,Péclet number and Stefan blowing parameter.Solutions of the system are obtained with developed semi-analytical technique,i.e.,Adomian decomposition method.Validation of the said problem is also conducted with earlier literature computed by Runge-Kutta shooting technique.
文摘This paper considers the quasi-stationary Stefan problem:△u(x,t)=0 in space-time domain,u=0 and Vv +(?)u/(?)u=0 on the free boundary.Under the natural conditions the existence of classical solution locally in time is proved bymaking use of the property of Frechet derivative operator and fixed point theorem. For thesake of simplicity only the one-phase problem is dealt with. In fact two-phase problem can bedealt with in a similar way with more complicated calculation.
基金supported by the National Natural Science Foundation (10871179) of China
文摘In this paper,the relaxation algorithm and two Uzawa type algorithms for solving discretized variational inequalities arising from the two-phase Stefan type problem are proposed.An analysis of their convergence is presented and the upper bounds of the convergence rates are derived.Some numerical experiments are shown to demonstrate that for the second Uzawa algorithm which is an improved version of the first Uzawa algorithm,the convergence rate is uniformly bounded away from 1 if τh^-2 is kept bounded,where τ is the time step size and h the space mesh size.
文摘There are many works (i.e. [1]) aiming to find out numerically how positive feedback affects the formation of invadopodia and invasion of cancer cells;however, studies on the cancer cell invasion model with free boundary are fairly rare. In this paper, we study modified cancer cell invasion model with free boundary, where, free boundary stands for cancer cell membrane, so that we can more precisely describe the positive feedback affects. Firstly, we simplized the model by means of characteristic curve and semi-groups’ property, and obtained the Stefan-like problem by introducing Gaussian Kernel and Green function. Secondly, based on the classical Stefan problem, we derived the integral solution of simplified model, which could lead us a further step to find the solution of modified cancer cell invasion model.
文摘In this paper, we prove the existence theorems of locbal or global classical solutions to Stefan problems with various kinetic conditions at the free boundary.
文摘The current mathematical model explains the influence of non-linear thermal radiation on the Casson liquid flow over a moving thin needle by considering Buongiorno’s nanofluid model.The influences of Stefan blowing,Dufour and Soret effects are also considered in the model.The equations which represent the described flow pattern are reduced to ordinary differential equations(ODEs)by using apt similarity transformations and then they are numerically solved with Runge–Kutta-Fehlberg’s fourth fifth-order method(RKF-45)with shooting process.The impacts of pertinent parameters on thermal,mass and velocity curves are deliberated graphically.Skin friction,rate of heat and mass transfer are also discussed graphically.Results reveal that,the increase in values of Brownian motion,thermophoresis,Dufour number,heating and radiative parameters improves the heat transfer.The increasing values of the Schmidt number deteriorates the mass transfer but a converse trend is seen for increasing values of the Soret number.Finally,the escalating values of the radiative parameter decays the rate of heat transfer.
基金Supported by National Natural Science Foundation of China (90410011)the Natural Science Foundation of the Education Department of Anhui Province (2005KJ316ZC).
文摘A Stefan problem with nonlinear boundary flux and internal convection of a material are considered. The existence, uniqueness and continuous dependence of globally weak solution of this problem are obtained. This paper extends the results of Fahuai Yi and T.M.Shih, relaxes restrictions that does not be to accord with reality very much on internal convection and boundary conditions in their articles.
文摘A one-phase Stefan problem for the nonhomogeneous heat equation with the source term depending on an unknown parameter p(t) is considered. The existence and uniqueness of the solution (p, s, u) are also demonstrated.
基金the National Natural Science Foundation of China and the Chinese Academy of Sciences
文摘A numerical analysis was carried out to study the moving boundary problem in the physical process of pulsed Nd-YAG laser surface melting prior to vaporization.The enthalpy method was applied to solve this two-phase axisymmetrical mehing problem.Computational results of tempera ture fields were obtained,which provide useful information to practical lair treatment processing. The validity of enthalpy method in solving such problems is presented.
文摘Reuse of abandoned or underused historic buildings and sites has become an increasing global trend within the built environment in the past two decades(Bullen and Love 2011;Gravagnuolo et al.2017).Bypassing the wasteful processes of demolition and new construction,adaptive reuse prolongs the lifespan of cultural heritage,contributes to environmental sustainability and enhances urban livability(Ikiz Kaya et al.2021).Focusing on three Asian global cities—Hong Kong,Shanghai and Singapore,the book of Asian Revitalization:Adaptive Reuse in Hong Kong,Shanghai,and Singapore,edited by Cummer and DiStefano,provides a needed analysis of adaptive reuse trends,policies and practices in Asian context.
