In the present paper, we have considered the steady fully developed laminar natural convective flow in open ended vertical concentric annuli in the presence of a ra- dial magnetic field. The induced magnetic field pro...In the present paper, we have considered the steady fully developed laminar natural convective flow in open ended vertical concentric annuli in the presence of a ra- dial magnetic field. The induced magnetic field produced by the motion of an electrically conducting fluid is taken into account. The transport equations concerned with the con- sidered model are first recast in the non-dimensional form and then unified analytical solutions for the velocity, induced magnetic field and temperature field are obtained for the cases of isothermal and constant heat flux on the inner cylin- der of concentric annuli. The effects of the various phys- ical parameters appearing into the model are demonstrated through graphs and tables. It is found that the magnitude of maximum value of the fluid velocity as well as induced magnetic field is greater in the case of isothermal condition compared with the constant heat flux case when the gap be- tween the cylinders is less or equal to 1.70 times the radius of inner cylinder, while reverse trend occurs when the gap between the cylinders is greater than 1.71 times the radius of inner cylinder. These fields are almost the same when the gap between the cylinders is equal to 1.71 times the radius of inner cylinder for both the cases. It is also found that as the Hartmann number increases, there is a flattening ten- dency for both the velocity and the induced magnetic field. The influence of the induced magnetic field is to increase the velocity profiles.展开更多
The present study concentrates on the analysis of MHD free convection flow past an inclined stretching sheet. The viscous dissipation and radiation effects are assumed in the heat equation. Approximation solutions hav...The present study concentrates on the analysis of MHD free convection flow past an inclined stretching sheet. The viscous dissipation and radiation effects are assumed in the heat equation. Approximation solutions have been derived for velocity, temperature, concentration, Nusselt number, skin friction and Sherwood number using Nachtsheim-Swigert shooting iteration technique along with the six-order Runge-Kutta iteration scheme. Graphs are plotted to find out the characteristics of different physical parameters. The variations of physical parameters on skin friction coefficient, Nusselt number and Sherwood number are displayed via table.展开更多
The aim of this research is the improvement towards the consumption of energy in the field of engineering and industry. The efforts have been paid to the enhancement of heat transmission and cooling process through a ...The aim of this research is the improvement towards the consumption of energy in the field of engineering and industry. The efforts have been paid to the enhancement of heat transmission and cooling process through a nanofluid coating of a nonlinear stretching disc. The combination of Water(H2 O) and multiple walled carbon nanotubes(MWCNT)/single walled carbon nanotubes(SWCNT) have been used as a nanofluid. The spreading of a thin nano-layer with variable thickness over a nonlinear and radially stretching surface has been considered. The estimated results of the problem have been accomplished using the Optimal Homotopy Analysis Method(OHAM). The residual errors of the OHAM method have been shown physically and numerically. The important physical parameters of skin friction and Nusselt number have been calculated and discussed. The other embedding parameters like generalized magnetic parameter, Prantl number, nanofluid volume fraction and Eckert number have been intended and discussed. The obtained results have been compared with the Numerical(ND-Solve) method for both sorts of CNTs. The closed agreement of both methods has been achieved.展开更多
文摘In the present paper, we have considered the steady fully developed laminar natural convective flow in open ended vertical concentric annuli in the presence of a ra- dial magnetic field. The induced magnetic field produced by the motion of an electrically conducting fluid is taken into account. The transport equations concerned with the con- sidered model are first recast in the non-dimensional form and then unified analytical solutions for the velocity, induced magnetic field and temperature field are obtained for the cases of isothermal and constant heat flux on the inner cylin- der of concentric annuli. The effects of the various phys- ical parameters appearing into the model are demonstrated through graphs and tables. It is found that the magnitude of maximum value of the fluid velocity as well as induced magnetic field is greater in the case of isothermal condition compared with the constant heat flux case when the gap be- tween the cylinders is less or equal to 1.70 times the radius of inner cylinder, while reverse trend occurs when the gap between the cylinders is greater than 1.71 times the radius of inner cylinder. These fields are almost the same when the gap between the cylinders is equal to 1.71 times the radius of inner cylinder for both the cases. It is also found that as the Hartmann number increases, there is a flattening ten- dency for both the velocity and the induced magnetic field. The influence of the induced magnetic field is to increase the velocity profiles.
文摘The present study concentrates on the analysis of MHD free convection flow past an inclined stretching sheet. The viscous dissipation and radiation effects are assumed in the heat equation. Approximation solutions have been derived for velocity, temperature, concentration, Nusselt number, skin friction and Sherwood number using Nachtsheim-Swigert shooting iteration technique along with the six-order Runge-Kutta iteration scheme. Graphs are plotted to find out the characteristics of different physical parameters. The variations of physical parameters on skin friction coefficient, Nusselt number and Sherwood number are displayed via table.
文摘The aim of this research is the improvement towards the consumption of energy in the field of engineering and industry. The efforts have been paid to the enhancement of heat transmission and cooling process through a nanofluid coating of a nonlinear stretching disc. The combination of Water(H2 O) and multiple walled carbon nanotubes(MWCNT)/single walled carbon nanotubes(SWCNT) have been used as a nanofluid. The spreading of a thin nano-layer with variable thickness over a nonlinear and radially stretching surface has been considered. The estimated results of the problem have been accomplished using the Optimal Homotopy Analysis Method(OHAM). The residual errors of the OHAM method have been shown physically and numerically. The important physical parameters of skin friction and Nusselt number have been calculated and discussed. The other embedding parameters like generalized magnetic parameter, Prantl number, nanofluid volume fraction and Eckert number have been intended and discussed. The obtained results have been compared with the Numerical(ND-Solve) method for both sorts of CNTs. The closed agreement of both methods has been achieved.
