Using the pressure gradient as the new variable instead of. the ordinary longitudinal coordinate x, Liu transformed the ordinary laminar boundary equations into a new form. On this base Liu obtained the frictional str...Using the pressure gradient as the new variable instead of. the ordinary longitudinal coordinate x, Liu transformed the ordinary laminar boundary equations into a new form. On this base Liu obtained the frictional stress factor by using the graphical method.In this paper the same variable replacement as in [1] is used and an approximate analytical solution of the laminar boundary layer equations by the series method is obtained. The author also obtains a formula of frictional stress factor. For the case of the main function without the term of constant, the author makes a further simplification. The error of the frictional stress factor obtained by the author is still less than 10%, compared with that of [1].展开更多
The exact similarity solutions of two dimensional laminar boundary layer were obtained by Blasius in 1908,however,for two dimensional turbulent boundary layers,no Blasius type similarity solutions(special exact soluti...The exact similarity solutions of two dimensional laminar boundary layer were obtained by Blasius in 1908,however,for two dimensional turbulent boundary layers,no Blasius type similarity solutions(special exact solutions)have ever been found.In the light of Blasius’pioneer works,we extend Blasius similarity transformation to the two dimensional turbulent boundary layers,and for a special case of flow modelled by Prandtl mixing-length,we successfully transform the two dimensional turbulent boundary layers partial differential equations into a single ordinary differential equation.The ordinary differential equation is numerically solved and some useful quantities are produced.For numerical calculations,a complete Maple code is provided.展开更多
The experimental investigation is conducted with LDV and hydrogen bubble technique in water flow. The shear layer thickness. the vorticity thickness. the maximulll value of turbulence intensities. the turbulent coher...The experimental investigation is conducted with LDV and hydrogen bubble technique in water flow. The shear layer thickness. the vorticity thickness. the maximulll value of turbulence intensities. the turbulent coherent structure. the variations of wall shear stress and the boundary layer shape factor are obtained. In the redevelopment region. the detailed analysis is first made for the streak structures in the near wall region and the turbulent boundary layer is formed at (x-xr) / h = 20.展开更多
The numerical analysis of heat transfer of laminar nanofluid flow over a fiat stretching sheet is presented. Two sets of boundary conditions （BCs） axe analyzed, i.e., a constant （Case 1） and a linear streamwise va...The numerical analysis of heat transfer of laminar nanofluid flow over a fiat stretching sheet is presented. Two sets of boundary conditions （BCs） axe analyzed, i.e., a constant （Case 1） and a linear streamwise variation of nanopaxticle volume fraction and wall temperature （Case 2）. The governing equations and BCs axe reduced to a set of nonlinear ordinary differential equations （ODEs） and the corresponding BCs, respectively. The dependencies of solutions on Prandtl number Pr, Lewis number Le, Brownian motion number Nb, and thermophoresis number Nt are studied in detail. The results show that the reduced Nusselt number and the reduced Sherwood number increase for the BCs of Case 2 compared with Case 1. The increases of Nb, Nt, and Le numbers cause a decrease of the reduced Nusselt number, while the reduced Sherwood number increases with the increase of Nb and Le numbers. For low Prandtl numbers, an increase of Nt number can cause to decrease in the reduced Sherwood number, while it increases for high Prandtl numbers.展开更多
文摘Using the pressure gradient as the new variable instead of. the ordinary longitudinal coordinate x, Liu transformed the ordinary laminar boundary equations into a new form. On this base Liu obtained the frictional stress factor by using the graphical method.In this paper the same variable replacement as in [1] is used and an approximate analytical solution of the laminar boundary layer equations by the series method is obtained. The author also obtains a formula of frictional stress factor. For the case of the main function without the term of constant, the author makes a further simplification. The error of the frictional stress factor obtained by the author is still less than 10%, compared with that of [1].
基金Xi’an University of Architecture and Technology(Grant no.002/2040221134).
文摘The exact similarity solutions of two dimensional laminar boundary layer were obtained by Blasius in 1908,however,for two dimensional turbulent boundary layers,no Blasius type similarity solutions(special exact solutions)have ever been found.In the light of Blasius’pioneer works,we extend Blasius similarity transformation to the two dimensional turbulent boundary layers,and for a special case of flow modelled by Prandtl mixing-length,we successfully transform the two dimensional turbulent boundary layers partial differential equations into a single ordinary differential equation.The ordinary differential equation is numerically solved and some useful quantities are produced.For numerical calculations,a complete Maple code is provided.
文摘The experimental investigation is conducted with LDV and hydrogen bubble technique in water flow. The shear layer thickness. the vorticity thickness. the maximulll value of turbulence intensities. the turbulent coherent structure. the variations of wall shear stress and the boundary layer shape factor are obtained. In the redevelopment region. the detailed analysis is first made for the streak structures in the near wall region and the turbulent boundary layer is formed at (x-xr) / h = 20.
文摘The numerical analysis of heat transfer of laminar nanofluid flow over a fiat stretching sheet is presented. Two sets of boundary conditions （BCs） axe analyzed, i.e., a constant （Case 1） and a linear streamwise variation of nanopaxticle volume fraction and wall temperature （Case 2）. The governing equations and BCs axe reduced to a set of nonlinear ordinary differential equations （ODEs） and the corresponding BCs, respectively. The dependencies of solutions on Prandtl number Pr, Lewis number Le, Brownian motion number Nb, and thermophoresis number Nt are studied in detail. The results show that the reduced Nusselt number and the reduced Sherwood number increase for the BCs of Case 2 compared with Case 1. The increases of Nb, Nt, and Le numbers cause a decrease of the reduced Nusselt number, while the reduced Sherwood number increases with the increase of Nb and Le numbers. For low Prandtl numbers, an increase of Nt number can cause to decrease in the reduced Sherwood number, while it increases for high Prandtl numbers.
