In this paper,the mechanism of thermal energy transport in swirling flow of the Maxwell nanofluid induced by a stretchable rotating cylinder is studied.The rotation of the cylinder is kept constant in order to avoid t...In this paper,the mechanism of thermal energy transport in swirling flow of the Maxwell nanofluid induced by a stretchable rotating cylinder is studied.The rotation of the cylinder is kept constant in order to avoid the induced axially secondary flow.Further,the novel features of heat generation/absorption,thermal radiation,and Joule heating are studied to control the rate of heat transfer.The effects of Brownian and thermophoretic forces exerted by the Maxwell nanofluid to the transport of thermal energy are investigated by utilizing an effective model for the nanofluid proposed by Buongiorno.The whole physical problem of fluid flow and thermal energy transport is modelled in the form of partial differential equations(PDEs)and transformed into nonlinear ordinary differential equations(ODEs)with the help of the suitable flow ansatz.Numerically acquired results through the technique bvp4c are reported graphically with physical explanation.Graphical analysis reveals that there is higher transport of heat energy in the Maxwell nanoliquid for a constant wall temperature(CWT)as compared with the prescribed surface temperature(PST).Both thermophoretic and Brownian forces enhance the thermal energy transport in the flowing Maxwell nanofluid.Moreover,the temperature distribution increases with increasing values of the radiation parameter and the Eckert number.It is also noted that an increase in Reynolds number reduces the penetration depth,and as a result the flow and transport of energy occur only near the surface of the cylinder.展开更多
A nanofluid is composed of a base fluid component and nanoparticles, in which the nanoparticles are dispersed in the base fluid. The addition of nanoparticles into a base fluid can remarkably improve the thermal condu...A nanofluid is composed of a base fluid component and nanoparticles, in which the nanoparticles are dispersed in the base fluid. The addition of nanoparticles into a base fluid can remarkably improve the thermal conductivity of the nanofluid, and such an increment of thermal conductivity can play an important role in improving the heat transfer rate of the base fluid. Further, the dynamics of non-Newtonian fluids along with nanoparticles is quite interesting with numerous industrial applications. The present predominately predictive modeling studies the flow of the viscoelastic Oldroyd-B fluid over a rotating disk in the presence of nanoparticles. A progressive amendment in the heat and concentration equations is made by exploiting the Cattaneo-Christov heat and mass flux expressions. The characteristic of the Lorentz force due to the magnetic field applied normal to the disk is studied. The Buongiorno model together with the Cattaneo-Christov theory is implemented in the Oldroyd-B nanofluid flow to investigate the heat and mass transport mechanism. This theory predicts the characteristics of the fluid thermal and solutal relaxation time on the boundary layer flow. The von K′arm′an similarity functions are utilized to convert the partial differential equations(PDEs) into ordinary differential equations(ODEs). A homotopic approach for obtaining the analytical solutions to the governing nonlinear problem is carried out. The graphical results are obtained for the velocity field, temperature, and concentration distributions. Comparisons are made for a limiting case between the numerical and analytical solutions, and the results are found in good agreement. The results reveal that the thermal and solutal relaxation time parameters diminish the temperature and concentration distributions, respectively. The axial flow decreases in the downward direction for higher values of the retardation time parameter. The impact of the thermophoresis parameter boosts the temperature distribution.展开更多
This research paper analyzes the transport of thermal and solutal energy in the Maxwell nanofluid flow induced above the disk which is rotating with a constant angular velocity.The significant features of thermal and ...This research paper analyzes the transport of thermal and solutal energy in the Maxwell nanofluid flow induced above the disk which is rotating with a constant angular velocity.The significant features of thermal and solutal relaxation times of fluids are studied with a Cattaneo-Christov double diffusion theory rather than the classical Fourier’s and Fick’s laws.A novel idea of a Buongiorno nanofluid model together with the Cattaneo-Christov theory is introduced for the first time for the Maxwell fluid flow over a rotating disk.Additionally,the thermal and solutal distributions are controlled with the impacts of heat source and chemical reaction.The classical von Karman similarities are used to acquire the non-linear system of ordinary differential equations(ODEs).The analytical series solution to the governing ODEs is obtained with the well-known homotopy analysis method(HAM).The validation of results is provided with the published results by the comparison tables.The graphically presented outcomes for the physical problem reveal that the higher values of the stretching strength parameter enhance the radial velocity and decline the circumferential velocity.The increasing trend is noted for the axial velocity profile in the downward direction with the higher values of the stretching strength parameter.The higher values of the relaxation time parameters in the Cattaneo-Christov theory decrease the thermal and solutal energy transport in the flow of Maxwell nanoliquids.The higher rate of the heat transport is observed in the case of a larger thermophoretic force.展开更多
The present research article is devoted to studying the characteristics of Cattaneo-Christov heat and mass fluxes in the Maxwell nanofluid flow caused by a stretching sheet with the magnetic field properties.The Maxwe...The present research article is devoted to studying the characteristics of Cattaneo-Christov heat and mass fluxes in the Maxwell nanofluid flow caused by a stretching sheet with the magnetic field properties.The Maxwell nanofluid is investigated with the impact of the Lorentz force to examine the consequence of a magnetic field on the flow characteristics and the transport of energy.The heat and mass transport mechanisms in the current physical model are analyzed with the modified versions of Fourier’s and Fick’s laws,respectively.Additionally,the well-known Buongiorno model for the nanofluids is first introduced together with the Cattaneo-Christov heat and mass fluxes during the transient motion of the Maxwell fluid.The governing partial differential equations(PDEs)for the flow and energy transport phenomena are obtained by using the Maxwell model and the Cattaneo-Christov theory in addition to the laws of conservation.Appropriate transformations are used to convert the PDEs into a system of nonlinear ordinary differential equations(ODEs).The homotopic solution methodology is applied to the nonlinear differential system for an analytic solution.The results for the time relaxation parameter in the flow,thermal energy,and mass transport equations are discussed graphically.It is noted that higher values of the thermal and solutal relaxation time parameters in the Cattaneo-Christov heat and mass fluxes decline the thermal and concentration fields of the nanofluid.Further,larger values of the thermophoretic force enhance the heat and mass transport in the nanoliquid.Moreover,the Brownian motion of the nanoparticles declines the concentration field and increases the temperature field.The validation of the results is assured with the help of numerical tabular data for the surface velocity gradient.展开更多
This paper investigates the boundary layer flow of the Maxwell fluid around a stretchable horizontal rotating cylinder under the influence of a transverse magnetic field.The constitutive flow equations for the current...This paper investigates the boundary layer flow of the Maxwell fluid around a stretchable horizontal rotating cylinder under the influence of a transverse magnetic field.The constitutive flow equations for the current physical problem are modeled and analyzed for the first time in the literature.The torsional motion of the cylinder is considered with the constant azimuthal velocity E.The partial differential equations(PDEs)governing the torsional motion of the Maxwell fluid together with energy transport are simplified with the boundary layer concept.The current analysis is valid only for a certain range of the positive Reynolds numbers.However,for very large Reynolds numbers,the flow becomes turbulent.Thus,the governing similarity equations are simplified through suitable transformations for the analysis of the large Reynolds numbers.The numerical simulations for the flow,heat,and mass transport phenomena are carried out in view of the bvp4c scheme in MATLAB.The outcomes reveal that the velocity decays exponentially faster and reduces for higher values of the Reynolds numbers and the flow penetrates shallower into the free stream fluid.It is also noted that the phenomenon of stress relaxation,described by the Deborah number,causes to decline the flow fields and enhance the thermal and solutal energy transport during the fluid motion.The penetration depth decreases for the transport of heat and mass in the fluid with the higher Reynolds numbers.An excellent validation of the numerical results is assured through tabular data with the existing literature.展开更多
文摘In this paper,the mechanism of thermal energy transport in swirling flow of the Maxwell nanofluid induced by a stretchable rotating cylinder is studied.The rotation of the cylinder is kept constant in order to avoid the induced axially secondary flow.Further,the novel features of heat generation/absorption,thermal radiation,and Joule heating are studied to control the rate of heat transfer.The effects of Brownian and thermophoretic forces exerted by the Maxwell nanofluid to the transport of thermal energy are investigated by utilizing an effective model for the nanofluid proposed by Buongiorno.The whole physical problem of fluid flow and thermal energy transport is modelled in the form of partial differential equations(PDEs)and transformed into nonlinear ordinary differential equations(ODEs)with the help of the suitable flow ansatz.Numerically acquired results through the technique bvp4c are reported graphically with physical explanation.Graphical analysis reveals that there is higher transport of heat energy in the Maxwell nanoliquid for a constant wall temperature(CWT)as compared with the prescribed surface temperature(PST).Both thermophoretic and Brownian forces enhance the thermal energy transport in the flowing Maxwell nanofluid.Moreover,the temperature distribution increases with increasing values of the radiation parameter and the Eckert number.It is also noted that an increase in Reynolds number reduces the penetration depth,and as a result the flow and transport of energy occur only near the surface of the cylinder.
文摘A nanofluid is composed of a base fluid component and nanoparticles, in which the nanoparticles are dispersed in the base fluid. The addition of nanoparticles into a base fluid can remarkably improve the thermal conductivity of the nanofluid, and such an increment of thermal conductivity can play an important role in improving the heat transfer rate of the base fluid. Further, the dynamics of non-Newtonian fluids along with nanoparticles is quite interesting with numerous industrial applications. The present predominately predictive modeling studies the flow of the viscoelastic Oldroyd-B fluid over a rotating disk in the presence of nanoparticles. A progressive amendment in the heat and concentration equations is made by exploiting the Cattaneo-Christov heat and mass flux expressions. The characteristic of the Lorentz force due to the magnetic field applied normal to the disk is studied. The Buongiorno model together with the Cattaneo-Christov theory is implemented in the Oldroyd-B nanofluid flow to investigate the heat and mass transport mechanism. This theory predicts the characteristics of the fluid thermal and solutal relaxation time on the boundary layer flow. The von K′arm′an similarity functions are utilized to convert the partial differential equations(PDEs) into ordinary differential equations(ODEs). A homotopic approach for obtaining the analytical solutions to the governing nonlinear problem is carried out. The graphical results are obtained for the velocity field, temperature, and concentration distributions. Comparisons are made for a limiting case between the numerical and analytical solutions, and the results are found in good agreement. The results reveal that the thermal and solutal relaxation time parameters diminish the temperature and concentration distributions, respectively. The axial flow decreases in the downward direction for higher values of the retardation time parameter. The impact of the thermophoresis parameter boosts the temperature distribution.
文摘This research paper analyzes the transport of thermal and solutal energy in the Maxwell nanofluid flow induced above the disk which is rotating with a constant angular velocity.The significant features of thermal and solutal relaxation times of fluids are studied with a Cattaneo-Christov double diffusion theory rather than the classical Fourier’s and Fick’s laws.A novel idea of a Buongiorno nanofluid model together with the Cattaneo-Christov theory is introduced for the first time for the Maxwell fluid flow over a rotating disk.Additionally,the thermal and solutal distributions are controlled with the impacts of heat source and chemical reaction.The classical von Karman similarities are used to acquire the non-linear system of ordinary differential equations(ODEs).The analytical series solution to the governing ODEs is obtained with the well-known homotopy analysis method(HAM).The validation of results is provided with the published results by the comparison tables.The graphically presented outcomes for the physical problem reveal that the higher values of the stretching strength parameter enhance the radial velocity and decline the circumferential velocity.The increasing trend is noted for the axial velocity profile in the downward direction with the higher values of the stretching strength parameter.The higher values of the relaxation time parameters in the Cattaneo-Christov theory decrease the thermal and solutal energy transport in the flow of Maxwell nanoliquids.The higher rate of the heat transport is observed in the case of a larger thermophoretic force.
文摘The present research article is devoted to studying the characteristics of Cattaneo-Christov heat and mass fluxes in the Maxwell nanofluid flow caused by a stretching sheet with the magnetic field properties.The Maxwell nanofluid is investigated with the impact of the Lorentz force to examine the consequence of a magnetic field on the flow characteristics and the transport of energy.The heat and mass transport mechanisms in the current physical model are analyzed with the modified versions of Fourier’s and Fick’s laws,respectively.Additionally,the well-known Buongiorno model for the nanofluids is first introduced together with the Cattaneo-Christov heat and mass fluxes during the transient motion of the Maxwell fluid.The governing partial differential equations(PDEs)for the flow and energy transport phenomena are obtained by using the Maxwell model and the Cattaneo-Christov theory in addition to the laws of conservation.Appropriate transformations are used to convert the PDEs into a system of nonlinear ordinary differential equations(ODEs).The homotopic solution methodology is applied to the nonlinear differential system for an analytic solution.The results for the time relaxation parameter in the flow,thermal energy,and mass transport equations are discussed graphically.It is noted that higher values of the thermal and solutal relaxation time parameters in the Cattaneo-Christov heat and mass fluxes decline the thermal and concentration fields of the nanofluid.Further,larger values of the thermophoretic force enhance the heat and mass transport in the nanoliquid.Moreover,the Brownian motion of the nanoparticles declines the concentration field and increases the temperature field.The validation of the results is assured with the help of numerical tabular data for the surface velocity gradient.
文摘This paper investigates the boundary layer flow of the Maxwell fluid around a stretchable horizontal rotating cylinder under the influence of a transverse magnetic field.The constitutive flow equations for the current physical problem are modeled and analyzed for the first time in the literature.The torsional motion of the cylinder is considered with the constant azimuthal velocity E.The partial differential equations(PDEs)governing the torsional motion of the Maxwell fluid together with energy transport are simplified with the boundary layer concept.The current analysis is valid only for a certain range of the positive Reynolds numbers.However,for very large Reynolds numbers,the flow becomes turbulent.Thus,the governing similarity equations are simplified through suitable transformations for the analysis of the large Reynolds numbers.The numerical simulations for the flow,heat,and mass transport phenomena are carried out in view of the bvp4c scheme in MATLAB.The outcomes reveal that the velocity decays exponentially faster and reduces for higher values of the Reynolds numbers and the flow penetrates shallower into the free stream fluid.It is also noted that the phenomenon of stress relaxation,described by the Deborah number,causes to decline the flow fields and enhance the thermal and solutal energy transport during the fluid motion.The penetration depth decreases for the transport of heat and mass in the fluid with the higher Reynolds numbers.An excellent validation of the numerical results is assured through tabular data with the existing literature.