In this study,we examine the effects of various shapes of nanoparticles in a steady flow of hybrid nanofluids between two stretchable rotating disks.The steady flow of hybrid nanofluids with transformer oil as the bas...In this study,we examine the effects of various shapes of nanoparticles in a steady flow of hybrid nanofluids between two stretchable rotating disks.The steady flow of hybrid nanofluids with transformer oil as the base fluid and Fe_(3)O_(4)+TiO_(2)as the hybrid nanofluid is considered.Several shapes of Fe_(3)O_(4)+TiO_(2)hybrid nanofluids,including sphere,brick,blade,cylinder,and platelet,are studied.Every shape exists in the same volume of a nanoparticle.The leading equations(partial differential equations(PDEs))are transformed to the nonlinear ordinary differential equations(ODEs)with the help of similarity transformations.The system of equations takes the form of ODEs depending on the boundary conditions,whose solutions are computed numerically by the bvp4c MATLAB solver.The outputs are compared with the previous findings,and an intriguing pattern is discovered,such that the tangential velocity is increased for the rotation parameter,while it is decreased by the stretching values because of the lower disk.For the reaction rate parameter,the concentration boundary layer becomes shorter,and the activation energy component increases the rate at which mass transfers come to the higher disk but have the opposite effect on the bottom disk.The ranges of various parameters taken into account are Pr=6.2,Re=2,M=1.0,φ_(1)=φ_(2)=0.03,K=0.5,S=-0.1,Br=0.3,Sc=2.0,α_(1)=0.2,γ=0.1,E_(n)=2.0,and q=1.0,and the rotation factor K is within the range of 0 to 1.展开更多
Cone-disk systems find frequent use such as conical diffusers,medical devices,various rheometric,and viscosimetry applications.In this study,we investigate the three-dimensional flow of a water-based Ag-Mg O hybrid na...Cone-disk systems find frequent use such as conical diffusers,medical devices,various rheometric,and viscosimetry applications.In this study,we investigate the three-dimensional flow of a water-based Ag-Mg O hybrid nanofluid in a static cone-disk system while considering temperature-dependent fluid properties.How the variable fluid properties affect the dynamics and heat transfer features is studied by Reynolds's linearized model for variable viscosity and Chiam's model for variable thermal conductivity.The single-phase nanofluid model is utilized to describe convective heat transfer in hybrid nanofluids,incorporating the experimental data.This model is developed as a coupled system of convective-diffusion equations,encompassing the conservation of momentum and the conservation of thermal energy,in conjunction with an incompressibility condition.A self-similar model is developed by the Lie-group scaling transformations,and the subsequent self-similar equations are then solved numerically.The influence of variable fluid parameters on both swirling and non-swirling flow cases is analyzed.Additionally,the Nusselt number for the disk surface is calculated.It is found that an increase in the temperature-dependent viscosity parameter enhances heat transfer characteristics in the static cone-disk system,while the thermal conductivity parameter has the opposite effect.展开更多
The magnetohydrodynamic （MHD） flow of the third grade fluid between two permeable disks with heat transfer is investigated. The governing partial differential equa- tions are converted into the ordinary differential...The magnetohydrodynamic （MHD） flow of the third grade fluid between two permeable disks with heat transfer is investigated. The governing partial differential equa- tions are converted into the ordinary differential equations by suitable transformations. The transformed equations are solved by the homotopy analysis method （HAM）. The expressions for square residual errors are defined, and the optimal values of convergence- control parameters are selected. The dimensionless velocity and temperature fields are examined for various dimensionless parameters. The skin friction coefficient and the Nus- selt number are tabulated to analyze the effects of dimensionless parameters.展开更多
Laminar heat transfer problem is analyzed for a disk rotating with the angular speed ωin a co-rotating fluid (with the angular speed Ω). The fluid is swirled in accordance with a forced-vortex law, it rotates as a s...Laminar heat transfer problem is analyzed for a disk rotating with the angular speed ωin a co-rotating fluid (with the angular speed Ω). The fluid is swirled in accordance with a forced-vortex law, it rotates as a solid body at β= Ω/ω= const. Radial variation of the disk’s surface temperature follows a power law. An exact numerical solution of the problem is obtained basing on the self-similar profiles of the local temperature of fluid, its static pressure and velocity components. Numerical computations were done at the Prandtl numbers Pr = 1(?)0.71. It is shown that with increasing βboth radial and tangential components of shear stresses decrease, and to zero value at β= 1. Nusselt number is practically constant at β= 0(?) 0.3 (and even has a point of a maximum in this region); Nu decrease noticeably for larger βvalues.展开更多
An exact solution of laminar heat transfer problem for a uniform flow perpendicular to a rotating disk was obtained. Radial velocity at the outer edge of the boundary layer increases linearly in the radial direction, ...An exact solution of laminar heat transfer problem for a uniform flow perpendicular to a rotating disk was obtained. Radial velocity at the outer edge of the boundary layer increases linearly in the radial direction, while the temperature difference between the disk and outer flow follows a power law. The problem is solved using self-similar velocity and temperature profiles. Nusselt numbers were computed for the Prandtl numbers Pr=1 and 0.71 at different values of parameters affecting flow and heat transfer. Special flow regime was identified where rotating disk heat transfer is determined only by peculiarities of the impinging flow. Results of predictions agree well with known experiments in the vicinity of the stagnation point.展开更多
The three-dimensional random packing of particles has attracted physicists, chemists, sedimentologists, materials scientists and mathematicians for more than a century. The study focuses on the packing density, porosi...The three-dimensional random packing of particles has attracted physicists, chemists, sedimentologists, materials scientists and mathematicians for more than a century. The study focuses on the packing density, porosity, the packing concentration, coordination number and the effect of the particle’s shape, density on the packing etc. For the metals and crystallized rocks with equigranular texture without porosity, there exists the"triple-point junction" with an angle of 120掳 in two dimensions. Every particle is adjacent to another six particles. To explain this texture, scientists proposed the definition of"Voronoi polygon". J. A. Dodds tried to demonstrate this conclusion by展开更多
The paper presents results of simulation of turbulent heat transfer and hydrodynamics over a free rotating disk using an integral method based on power-law velocity and temperature profiles and three different laws fo...The paper presents results of simulation of turbulent heat transfer and hydrodynamics over a free rotating disk using an integral method based on power-law velocity and temperature profiles and three different laws for the tangent of the flow swirl angle tan. It appeared that a quadratic correlation of tan is the most proper one for a free rotating disk. Resulting equation for the Nusselt number is in a better agreement with experimental data of different authors than known Dorfman formula.展开更多
文摘In this study,we examine the effects of various shapes of nanoparticles in a steady flow of hybrid nanofluids between two stretchable rotating disks.The steady flow of hybrid nanofluids with transformer oil as the base fluid and Fe_(3)O_(4)+TiO_(2)as the hybrid nanofluid is considered.Several shapes of Fe_(3)O_(4)+TiO_(2)hybrid nanofluids,including sphere,brick,blade,cylinder,and platelet,are studied.Every shape exists in the same volume of a nanoparticle.The leading equations(partial differential equations(PDEs))are transformed to the nonlinear ordinary differential equations(ODEs)with the help of similarity transformations.The system of equations takes the form of ODEs depending on the boundary conditions,whose solutions are computed numerically by the bvp4c MATLAB solver.The outputs are compared with the previous findings,and an intriguing pattern is discovered,such that the tangential velocity is increased for the rotation parameter,while it is decreased by the stretching values because of the lower disk.For the reaction rate parameter,the concentration boundary layer becomes shorter,and the activation energy component increases the rate at which mass transfers come to the higher disk but have the opposite effect on the bottom disk.The ranges of various parameters taken into account are Pr=6.2,Re=2,M=1.0,φ_(1)=φ_(2)=0.03,K=0.5,S=-0.1,Br=0.3,Sc=2.0,α_(1)=0.2,γ=0.1,E_(n)=2.0,and q=1.0,and the rotation factor K is within the range of 0 to 1.
文摘Cone-disk systems find frequent use such as conical diffusers,medical devices,various rheometric,and viscosimetry applications.In this study,we investigate the three-dimensional flow of a water-based Ag-Mg O hybrid nanofluid in a static cone-disk system while considering temperature-dependent fluid properties.How the variable fluid properties affect the dynamics and heat transfer features is studied by Reynolds's linearized model for variable viscosity and Chiam's model for variable thermal conductivity.The single-phase nanofluid model is utilized to describe convective heat transfer in hybrid nanofluids,incorporating the experimental data.This model is developed as a coupled system of convective-diffusion equations,encompassing the conservation of momentum and the conservation of thermal energy,in conjunction with an incompressibility condition.A self-similar model is developed by the Lie-group scaling transformations,and the subsequent self-similar equations are then solved numerically.The influence of variable fluid parameters on both swirling and non-swirling flow cases is analyzed.Additionally,the Nusselt number for the disk surface is calculated.It is found that an increase in the temperature-dependent viscosity parameter enhances heat transfer characteristics in the static cone-disk system,while the thermal conductivity parameter has the opposite effect.
文摘The magnetohydrodynamic （MHD） flow of the third grade fluid between two permeable disks with heat transfer is investigated. The governing partial differential equa- tions are converted into the ordinary differential equations by suitable transformations. The transformed equations are solved by the homotopy analysis method （HAM）. The expressions for square residual errors are defined, and the optimal values of convergence- control parameters are selected. The dimensionless velocity and temperature fields are examined for various dimensionless parameters. The skin friction coefficient and the Nus- selt number are tabulated to analyze the effects of dimensionless parameters.
文摘Laminar heat transfer problem is analyzed for a disk rotating with the angular speed ωin a co-rotating fluid (with the angular speed Ω). The fluid is swirled in accordance with a forced-vortex law, it rotates as a solid body at β= Ω/ω= const. Radial variation of the disk’s surface temperature follows a power law. An exact numerical solution of the problem is obtained basing on the self-similar profiles of the local temperature of fluid, its static pressure and velocity components. Numerical computations were done at the Prandtl numbers Pr = 1(?)0.71. It is shown that with increasing βboth radial and tangential components of shear stresses decrease, and to zero value at β= 1. Nusselt number is practically constant at β= 0(?) 0.3 (and even has a point of a maximum in this region); Nu decrease noticeably for larger βvalues.
文摘An exact solution of laminar heat transfer problem for a uniform flow perpendicular to a rotating disk was obtained. Radial velocity at the outer edge of the boundary layer increases linearly in the radial direction, while the temperature difference between the disk and outer flow follows a power law. The problem is solved using self-similar velocity and temperature profiles. Nusselt numbers were computed for the Prandtl numbers Pr=1 and 0.71 at different values of parameters affecting flow and heat transfer. Special flow regime was identified where rotating disk heat transfer is determined only by peculiarities of the impinging flow. Results of predictions agree well with known experiments in the vicinity of the stagnation point.
基金Project supported by the National Natural Science Foundation of China.
文摘The three-dimensional random packing of particles has attracted physicists, chemists, sedimentologists, materials scientists and mathematicians for more than a century. The study focuses on the packing density, porosity, the packing concentration, coordination number and the effect of the particle’s shape, density on the packing etc. For the metals and crystallized rocks with equigranular texture without porosity, there exists the"triple-point junction" with an angle of 120掳 in two dimensions. Every particle is adjacent to another six particles. To explain this texture, scientists proposed the definition of"Voronoi polygon". J. A. Dodds tried to demonstrate this conclusion by
文摘The paper presents results of simulation of turbulent heat transfer and hydrodynamics over a free rotating disk using an integral method based on power-law velocity and temperature profiles and three different laws for the tangent of the flow swirl angle tan. It appeared that a quadratic correlation of tan is the most proper one for a free rotating disk. Resulting equation for the Nusselt number is in a better agreement with experimental data of different authors than known Dorfman formula.
