An improved shooting method was presented for solving the natural convention boundary layer equations, with a coupling of the velocity field to the temperature field. The numerical results are consistent with the appr...An improved shooting method was presented for solving the natural convention boundary layer equations, with a coupling of the velocity field to the temperature field. The numerical results are consistent with the approximate solution obtained by former researchers.展开更多
The classical power law non-Newtonian fluids energy boundary layer equation is proved improper to describe the self-similar heat transfer. A theoretical analysis for momentum and energy boundary layer transfer behavio...The classical power law non-Newtonian fluids energy boundary layer equation is proved improper to describe the self-similar heat transfer. A theoretical analysis for momentum and energy boundary layer transfer behavior is made and the full similarity heat boundary layer equation is developed, which may be characterized by a power law relationship between shear stress and velocity gradient with the Falkner-Skan equation as a special case. Both analytical and numerical solutions are presented for momentum and energy boundary layer equations by using the similarity transformation and shooting technique and the associated transfer characteristics are discussed.展开更多
This paper studies flow and heat transfer of nanofluids over a rotating disk with uniform stretching rate.Three types of nanopaiticles-Cu,Al_(2)O_(3) and CuO-with water-based nanofluids are considered.The governing eq...This paper studies flow and heat transfer of nanofluids over a rotating disk with uniform stretching rate.Three types of nanopaiticles-Cu,Al_(2)O_(3) and CuO-with water-based nanofluids are considered.The governing equations are reduced by Von Karman transformation and then solved by the homotopy analysis method(HAM),which is in close agreement with numerical results.Results indicate that with increasing in stretching strength parameter,the skin friction and the local Nusselt number,the velocity in radial and axial directions increase,whereas the velocity in tangential direction and the thermal boundary'layer thickness decrease,respectively.Moreover,the effects of volume fraction and types of nanofluids on velocity and temperature fields are also analyzed.展开更多
A theoretical investigation was done for the generalized Berman problem, which arises in steady laminar flow of an incompressible viscous fluid along a channel with accelerating rigid porous walls. The existence of mu...A theoretical investigation was done for the generalized Berman problem, which arises in steady laminar flow of an incompressible viscous fluid along a channel with accelerating rigid porous walls. The existence of multiple solutions and its conditions were established by taking into account exponentially small terms in matched asymptotic expansion. The correctness of the analytical predictions was verified by numerical results.展开更多
This paper investigates flow and heat transfer of power law fluids on a continuous moving surface. The temperature distribution is obtained numerically by considering the effect of the power law viscosity on thermal d...This paper investigates flow and heat transfer of power law fluids on a continuous moving surface. The temperature distribution is obtained numerically by considering the effect of the power law viscosity on thermal diffusivity and the characteristics of the flow and heat transfer are analyzed. The results show that the distribution of the thermal boundary layer depends not only on the velocity ratio parameter of the plate, but also on the power law index and Prandtl number of fluids.展开更多
The effects of the second-order velocity slip and temperature jump boundary conditions on the magnetohydrodynamic （MHD） flow and heat transfer in the presence of nanoparticle fractions are investigated. In the model...The effects of the second-order velocity slip and temperature jump boundary conditions on the magnetohydrodynamic （MHD） flow and heat transfer in the presence of nanoparticle fractions are investigated. In the modeling of the water-based nanofluids containing Cu and A1203, the effects of the Brownian motion, thermophoresis, and thermal radiation are considered. The governing boundary layer equations are transformed into a system of nonlinear differential equations, and the analytical approximations of the solutions axe derived by the homotopy analysis method （HAM）. The reliability and efficiency of the HAM solutions are verified by the residual errors and the numerical results in the literature. Moreover, the effects of the physical factors on the flow and heat transfer are discussed graphically.展开更多
This paper presents a theoretical analysis of the heat transfer for the boundary layer flow on a continuous moving surface in power law fluid. The expressions of the thermal boundary layer thickness with the different...This paper presents a theoretical analysis of the heat transfer for the boundary layer flow on a continuous moving surface in power law fluid. The expressions of the thermal boundary layer thickness with the different heat conductivity coefficients are obtained according to the theory of the dimensional analysis of fluid dynamics and heat transfer. And the numerical results of CFD agree well with the proposed expressions. The estimate formulas can be successfully applied to giving the thermal boundary layer thickness.展开更多
Analytical and numerical solutions are established for momentum and energy laminar boundary layer induced by a shock wave. The results indicated that skin friction σ decreases with increasing in velocity ratio ξ(1...Analytical and numerical solutions are established for momentum and energy laminar boundary layer induced by a shock wave. The results indicated that skin friction σ decreases with increasing in velocity ratio ξ(1≤ξ【 6). For each specified ξ(1≤ξ【 6), temperature w(t) increases with increasing of Tw but decreases with Te , and for a range of t ∈[1,ξ], w(t) decreases with the increasing of t. Thermal diffusion increases with increasing of uw but decreases with increasing Ue.展开更多
The heat transfer of a magnetohydrodynamics nanofluid inside an annulus considering the second-order slip condition and nanoparticle migration is theoret-ically investigated. A second-order slip condition, which appro...The heat transfer of a magnetohydrodynamics nanofluid inside an annulus considering the second-order slip condition and nanoparticle migration is theoret-ically investigated. A second-order slip condition, which appropriately represents the non-equilibrium region near the interface, is prescribed rather than the no-slip condition and the linear Navier slip condition. To impose different temperature gradients, the outer wall is subjected to q2, the inner wall is subjected to q1, and q1 〉 q2. A modified two-component four-equation non-homogeneous equilibrium model is employed for the nanofiuid, which have been reduced to two-point ordinary boundary value differential equations in the consideration of the thermally and hydrodynamically fully developed flow. The homotopy analysis method （HAM） is employed to solve the equations, and the h-curves are plotted to verify the accuracy and efficiency of the solutions. Moreover, the effects of the physical factors on the flow and heat transfer are discussed in detail, and the semi-analytical relation between NUB and NBT is obtained.展开更多
An efficient Adomian analytical decomposition technique for studying the momentum and heat boundary layer equations with exponentially stretching surface conditions was presented and an approximate analytical solution...An efficient Adomian analytical decomposition technique for studying the momentum and heat boundary layer equations with exponentially stretching surface conditions was presented and an approximate analytical solution was obtained, which can be represented in terms of a rapid convergent power series with elegantly computable terms. The reliability and efficiency of the approximate solution were verified using numerical solutions in the literature. The approximate solution can be successfully applied to provide the values of skin friction and the temperature gradient coefficient.展开更多
The behavior for a class of initial, boundary value problems of generalized diffusion equations was studied utilizing the similarity transformation and shooting technique. Numerical solutions are presented fork(s) = S...The behavior for a class of initial, boundary value problems of generalized diffusion equations was studied utilizing the similarity transformation and shooting technique. Numerical solutions are presented fork(s) = SM exponent M 1.0 to 5.0, and power law parameter N (N = 0.3 to 3.0). The results shown that for each fixed M, the temperature distribution e decreases with increasing in power law parameter N, and for each fixed N, the temperature distribution 6 increases with the decreasing of M.展开更多
An analysis is carried out to study the steady flow characteristics from a continuous flat surface moving in a parallel free stream of non-Newtonian power law fluid. The constitutive equations of the fluid are transfo...An analysis is carried out to study the steady flow characteristics from a continuous flat surface moving in a parallel free stream of non-Newtonian power law fluid. The constitutive equations of the fluid are transformed into dimensionless ones. The velocity field is measured by Particle Image Velocimetry. Experimental results are obtained for the distribution of velocity. The influence of wall velocity ratio parameter on boundary layer flow field is observed in the experiment. Dimensionless velocity distribution and shearing stress distribution are obtained by post-processing experimental results. The effects of various physical parameters like velocity ratio parameter and similarity variable on various momentum transfer characteristics are discussed in detail and shown graphically. It is indicated that dimensionless velocity increases with velocity ratio parameter and similarity variable, and that dimensionless shearing stress decreases with velocity ratio parameter and similarity variable.展开更多
Nanoparticle-mediated drug delivery is recognized as a promising option for targeted treatment of atherosclerosis. In this paper, the Eulerian-Lagrangian technique is adopted to simulate the delivery of drug-loaded na...Nanoparticle-mediated drug delivery is recognized as a promising option for targeted treatment of atherosclerosis. In this paper, the Eulerian-Lagrangian technique is adopted to simulate the delivery of drug-loaded nanoparticles to patient-specific atherosclerotic plaque with the aid of an external magnetic field. Plaques and vascular walls are introduced as porous media formulated by the Darcy-Forchheimer model in this targeted transport process. The results demonstrate that the delivery efficiency of particles to atherosclerosis depends on the external magnetic field, such as configuration and intensity, in which the configuration angle of the current wire is a key factor and the double current wires have advantages over the single current wire. Meanwhile, the delivery efficiency gradually decreases as the distance between the plaque cap and the current wire increases. Further, although augmenting the current or magnetic susceptibility can generally improve the delivery efficiency of nanoparticles, this increase is not apparent when small-sized nanoparticles are employed as drug transport particles. The results obtained can potentially serve as the guideline to optimize regimens for the targeted therapy of atherosclerosis.展开更多
The convection of a Maxwell fluid over a stretching porous surface with a heat source/sink in the presence of nanoparticles is investigated. The Lie symmetry group transformations are used to convert the boundary laye...The convection of a Maxwell fluid over a stretching porous surface with a heat source/sink in the presence of nanoparticles is investigated. The Lie symmetry group transformations are used to convert the boundary layer equations into coupled nonlinear ordinary differential equations. The ordinary differential equations are solved numerically by the Bvp4c with MATLAB, which is a collocation method equivalent to the fourth-order mono-implicit Runge-Kutta method. Furthermore, more attention is paid to the effects of the physical parameters, especially the parameters related to nanoparticles, on the temperature and concentration distributions with consideration of permeability and the heat source/sink.展开更多
The specific problem to be considered here concerns the boundary layer problem of a non-Newtonian fluid on a flat plate in length, whose surface has a constant velocity opposite in the direction to that of the mainstr...The specific problem to be considered here concerns the boundary layer problem of a non-Newtonian fluid on a flat plate in length, whose surface has a constant velocity opposite in the direction to that of the mainstream with Uw 〉〉 U∞, or alternatively when the plate surface velocity is kept fixed but the stream speed is reduced to zero. A theoretical analysis for a boundary layer flow is made and the self-similar equation is determined. Solutions are presented numerically for special power index and the associated transfer behavior is discussed.展开更多
Fractional boundary layer flow of Maxwell fluid on an unsteady stretching surface was investigated. Time-space dependent fractional derivatives are introduced into the constitutive equations of the fluid. We developed...Fractional boundary layer flow of Maxwell fluid on an unsteady stretching surface was investigated. Time-space dependent fractional derivatives are introduced into the constitutive equations of the fluid. We developed and solved the governing equations using explicit finite difference method and the L1- algorithm as well as shifted Grunwald-Letnikov formula. The effects of fractional parameters, relaxation parameter, Reynolds number, and unsteadiness parameter on the velocity behavior and characteristics of boundary layer thickness and skin friction were analyzed. Results obtained indicate that the behavior of boundary layer of viscoelastic fluid strongly depends on time-space fractional parameters. Increases of time fractional derivative parameter and relaxation parameter cause a decrease of velocity while boundary layer thickness increase, but the space fractional derivative parameter and fractional Reynolds number have the opposite effects.展开更多
Flow and heat transfer of a pseudo-plastic power-law fluid over a stretching permeable surface with the magnetic effect is investigated. In the boundary conditions,the nonlinear temperature jump and the velocity slip ...Flow and heat transfer of a pseudo-plastic power-law fluid over a stretching permeable surface with the magnetic effect is investigated. In the boundary conditions,the nonlinear temperature jump and the velocity slip are considered. Semi-similarity equations are obtained and solved by bvp4c with MATLAB. The problem can be considered as an extension of the previous work done by Mahmoud(Mahmoud, M. A. A. Slip velocity effect on a non-Newtonian power-law fluid over a moving permeable surface with heat generation. Mathematical and Computer Modelling, 54, 1228–1237(2011)). Efforts are made to discuss the effects of the power-law number, slip velocity, and temperature jump on the dimensionless velocity and temperature distribution.展开更多
An efficient analytical decomposition technique was presented for solving the singular nonlinear boundary value problem arising in viscous flow when the Crocco variable was introduced. The approximate analytical solut...An efficient analytical decomposition technique was presented for solving the singular nonlinear boundary value problem arising in viscous flow when the Crocco variable was introduced. The approximate analytical solution may be represented in terms of a rapid convergent power series with elegantly computable terms. The reliability and efficiency of the approximate solutions were verified by numerical ones in the literature. The approximate analytical solutions can be successfully applied to give the values of skin friction coefficient.展开更多
基金The work is financially supported by the National Natural Science Foundations of China (No.50476083).
文摘An improved shooting method was presented for solving the natural convention boundary layer equations, with a coupling of the velocity field to the temperature field. The numerical results are consistent with the approximate solution obtained by former researchers.
文摘The classical power law non-Newtonian fluids energy boundary layer equation is proved improper to describe the self-similar heat transfer. A theoretical analysis for momentum and energy boundary layer transfer behavior is made and the full similarity heat boundary layer equation is developed, which may be characterized by a power law relationship between shear stress and velocity gradient with the Falkner-Skan equation as a special case. Both analytical and numerical solutions are presented for momentum and energy boundary layer equations by using the similarity transformation and shooting technique and the associated transfer characteristics are discussed.
基金supported by National Natural Science Foundations of China(Nos.51276014,51476191).
文摘This paper studies flow and heat transfer of nanofluids over a rotating disk with uniform stretching rate.Three types of nanopaiticles-Cu,Al_(2)O_(3) and CuO-with water-based nanofluids are considered.The governing equations are reduced by Von Karman transformation and then solved by the homotopy analysis method(HAM),which is in close agreement with numerical results.Results indicate that with increasing in stretching strength parameter,the skin friction and the local Nusselt number,the velocity in radial and axial directions increase,whereas the velocity in tangential direction and the thermal boundary'layer thickness decrease,respectively.Moreover,the effects of volume fraction and types of nanofluids on velocity and temperature fields are also analyzed.
基金This work was financially supported by the National Natural Science Foundations of China (No.50476083).
文摘A theoretical investigation was done for the generalized Berman problem, which arises in steady laminar flow of an incompressible viscous fluid along a channel with accelerating rigid porous walls. The existence of multiple solutions and its conditions were established by taking into account exponentially small terms in matched asymptotic expansion. The correctness of the analytical predictions was verified by numerical results.
基金The work is supported by the National Natural Science Foundation of China （No. 50476083）.
文摘This paper investigates flow and heat transfer of power law fluids on a continuous moving surface. The temperature distribution is obtained numerically by considering the effect of the power law viscosity on thermal diffusivity and the characteristics of the flow and heat transfer are analyzed. The results show that the distribution of the thermal boundary layer depends not only on the velocity ratio parameter of the plate, but also on the power law index and Prandtl number of fluids.
基金Project supported by the National Natural Science Foundation of China(Nos.51276014 and51476191)the Fundamental Research Funds for the Central Universities(No.FRF-BR-12-004)
文摘The effects of the second-order velocity slip and temperature jump boundary conditions on the magnetohydrodynamic （MHD） flow and heat transfer in the presence of nanoparticle fractions are investigated. In the modeling of the water-based nanofluids containing Cu and A1203, the effects of the Brownian motion, thermophoresis, and thermal radiation are considered. The governing boundary layer equations are transformed into a system of nonlinear differential equations, and the analytical approximations of the solutions axe derived by the homotopy analysis method （HAM）. The reliability and efficiency of the HAM solutions are verified by the residual errors and the numerical results in the literature. Moreover, the effects of the physical factors on the flow and heat transfer are discussed graphically.
基金the National Natural Science Foundation of China (No.50476083)
文摘This paper presents a theoretical analysis of the heat transfer for the boundary layer flow on a continuous moving surface in power law fluid. The expressions of the thermal boundary layer thickness with the different heat conductivity coefficients are obtained according to the theory of the dimensional analysis of fluid dynamics and heat transfer. And the numerical results of CFD agree well with the proposed expressions. The estimate formulas can be successfully applied to giving the thermal boundary layer thickness.
基金The authors express their thanks for the support by "Cross-Century Talents Projects of Educational Ministry of China" the "973" key foundation under the contract No.G1998061510
文摘Analytical and numerical solutions are established for momentum and energy laminar boundary layer induced by a shock wave. The results indicated that skin friction σ decreases with increasing in velocity ratio ξ(1≤ξ【 6). For each specified ξ(1≤ξ【 6), temperature w(t) increases with increasing of Tw but decreases with Te , and for a range of t ∈[1,ξ], w(t) decreases with the increasing of t. Thermal diffusion increases with increasing of uw but decreases with increasing Ue.
基金Project supported by the National Natural Science Foundation of China(Nos.51476191 and51406008)
文摘The heat transfer of a magnetohydrodynamics nanofluid inside an annulus considering the second-order slip condition and nanoparticle migration is theoret-ically investigated. A second-order slip condition, which appropriately represents the non-equilibrium region near the interface, is prescribed rather than the no-slip condition and the linear Navier slip condition. To impose different temperature gradients, the outer wall is subjected to q2, the inner wall is subjected to q1, and q1 〉 q2. A modified two-component four-equation non-homogeneous equilibrium model is employed for the nanofiuid, which have been reduced to two-point ordinary boundary value differential equations in the consideration of the thermally and hydrodynamically fully developed flow. The homotopy analysis method （HAM） is employed to solve the equations, and the h-curves are plotted to verify the accuracy and efficiency of the solutions. Moreover, the effects of the physical factors on the flow and heat transfer are discussed in detail, and the semi-analytical relation between NUB and NBT is obtained.
基金This work was financially supported by the National Natural Science Foundation of China (No.50476083).
文摘An efficient Adomian analytical decomposition technique for studying the momentum and heat boundary layer equations with exponentially stretching surface conditions was presented and an approximate analytical solution was obtained, which can be represented in terms of a rapid convergent power series with elegantly computable terms. The reliability and efficiency of the approximate solution were verified using numerical solutions in the literature. The approximate solution can be successfully applied to provide the values of skin friction and the temperature gradient coefficient.
基金Cross-Century Talents Proects of Ministry of Education of China the "973" Key Foundation under the contractNo.G l99806l5l0.
文摘The behavior for a class of initial, boundary value problems of generalized diffusion equations was studied utilizing the similarity transformation and shooting technique. Numerical solutions are presented fork(s) = SM exponent M 1.0 to 5.0, and power law parameter N (N = 0.3 to 3.0). The results shown that for each fixed M, the temperature distribution e decreases with increasing in power law parameter N, and for each fixed N, the temperature distribution 6 increases with the decreasing of M.
基金supported by the National Natural Science Foundation of China (No. 50476083)
文摘An analysis is carried out to study the steady flow characteristics from a continuous flat surface moving in a parallel free stream of non-Newtonian power law fluid. The constitutive equations of the fluid are transformed into dimensionless ones. The velocity field is measured by Particle Image Velocimetry. Experimental results are obtained for the distribution of velocity. The influence of wall velocity ratio parameter on boundary layer flow field is observed in the experiment. Dimensionless velocity distribution and shearing stress distribution are obtained by post-processing experimental results. The effects of various physical parameters like velocity ratio parameter and similarity variable on various momentum transfer characteristics are discussed in detail and shown graphically. It is indicated that dimensionless velocity increases with velocity ratio parameter and similarity variable, and that dimensionless shearing stress decreases with velocity ratio parameter and similarity variable.
基金Project supported by the National Natural Science Foundation of China(Nos.11772046 and 81870345)。
文摘Nanoparticle-mediated drug delivery is recognized as a promising option for targeted treatment of atherosclerosis. In this paper, the Eulerian-Lagrangian technique is adopted to simulate the delivery of drug-loaded nanoparticles to patient-specific atherosclerotic plaque with the aid of an external magnetic field. Plaques and vascular walls are introduced as porous media formulated by the Darcy-Forchheimer model in this targeted transport process. The results demonstrate that the delivery efficiency of particles to atherosclerosis depends on the external magnetic field, such as configuration and intensity, in which the configuration angle of the current wire is a key factor and the double current wires have advantages over the single current wire. Meanwhile, the delivery efficiency gradually decreases as the distance between the plaque cap and the current wire increases. Further, although augmenting the current or magnetic susceptibility can generally improve the delivery efficiency of nanoparticles, this increase is not apparent when small-sized nanoparticles are employed as drug transport particles. The results obtained can potentially serve as the guideline to optimize regimens for the targeted therapy of atherosclerosis.
基金supported by the National Natural Science Foundation of China(No.11302024)the Fundamental Research Funds for the Central Universities(No.FRF-TP-15-036A3)+1 种基金the Beijing Higher Education Young Elite Teacher Project(No.YETP0387)the Foundation of the China Scholarship Council in 2014(No.154201406465041)
文摘The convection of a Maxwell fluid over a stretching porous surface with a heat source/sink in the presence of nanoparticles is investigated. The Lie symmetry group transformations are used to convert the boundary layer equations into coupled nonlinear ordinary differential equations. The ordinary differential equations are solved numerically by the Bvp4c with MATLAB, which is a collocation method equivalent to the fourth-order mono-implicit Runge-Kutta method. Furthermore, more attention is paid to the effects of the physical parameters, especially the parameters related to nanoparticles, on the temperature and concentration distributions with consideration of permeability and the heat source/sink.
基金This work is supported by the National Natural Science Foundation of China (No.50476083) and the Cross-Century Talents Projectsby the Ministry Education of China.
文摘The specific problem to be considered here concerns the boundary layer problem of a non-Newtonian fluid on a flat plate in length, whose surface has a constant velocity opposite in the direction to that of the mainstream with Uw 〉〉 U∞, or alternatively when the plate surface velocity is kept fixed but the stream speed is reduced to zero. A theoretical analysis for a boundary layer flow is made and the self-similar equation is determined. Solutions are presented numerically for special power index and the associated transfer behavior is discussed.
基金supported by the National Natural Science Foundation of China (51476191 and 51406008)
文摘Fractional boundary layer flow of Maxwell fluid on an unsteady stretching surface was investigated. Time-space dependent fractional derivatives are introduced into the constitutive equations of the fluid. We developed and solved the governing equations using explicit finite difference method and the L1- algorithm as well as shifted Grunwald-Letnikov formula. The effects of fractional parameters, relaxation parameter, Reynolds number, and unsteadiness parameter on the velocity behavior and characteristics of boundary layer thickness and skin friction were analyzed. Results obtained indicate that the behavior of boundary layer of viscoelastic fluid strongly depends on time-space fractional parameters. Increases of time fractional derivative parameter and relaxation parameter cause a decrease of velocity while boundary layer thickness increase, but the space fractional derivative parameter and fractional Reynolds number have the opposite effects.
基金Project supported by the National Natural Science Foundation of China(No.11302024)the Fundamental Research Funds for the Central Universities(No.FRF-TP-12-108A)the Foundation of the China Scholarship Council in 2014(No.154201406465041)
文摘Flow and heat transfer of a pseudo-plastic power-law fluid over a stretching permeable surface with the magnetic effect is investigated. In the boundary conditions,the nonlinear temperature jump and the velocity slip are considered. Semi-similarity equations are obtained and solved by bvp4c with MATLAB. The problem can be considered as an extension of the previous work done by Mahmoud(Mahmoud, M. A. A. Slip velocity effect on a non-Newtonian power-law fluid over a moving permeable surface with heat generation. Mathematical and Computer Modelling, 54, 1228–1237(2011)). Efforts are made to discuss the effects of the power-law number, slip velocity, and temperature jump on the dimensionless velocity and temperature distribution.
基金The work was financially supported by the National Natural Science Foundation of China (No.50476083) and the Cross-CenturyTalents Projects of the Educational Ministry of China.
文摘An efficient analytical decomposition technique was presented for solving the singular nonlinear boundary value problem arising in viscous flow when the Crocco variable was introduced. The approximate analytical solution may be represented in terms of a rapid convergent power series with elegantly computable terms. The reliability and efficiency of the approximate solutions were verified by numerical ones in the literature. The approximate analytical solutions can be successfully applied to give the values of skin friction coefficient.
