Noor Afzal - Profile on Academia.edu (original) (raw)
Papers by Noor Afzal
International Journal of Heat and Mass Transfer, Oct 1, 2010
The present work deals with the numerical study of temperature distribution in the laminar bounda... more The present work deals with the numerical study of temperature distribution in the laminar boundary layer driven by the stretching boundary surface subjected to pressure gradient. The similarity transformation obeying the same power law based on composite reference velocity (union of velocities of the stretching boundary and free stream) has been employed that leads to a single set of equations,
Fluid Mechanics and Its Applications, 1996
The turbulent boundary layer subjected to pressure gradient is analyzed at large Reynolds number,... more The turbulent boundary layer subjected to pressure gradient is analyzed at large Reynolds number, using the method of matched asymptotic expansions. It is shown that there exists a 'wake' limit, in which the governing equation is 'rich enough' to contain the equation of the ...
Bulletin of the American Physical Society, Nov 19, 2012
Submitted for the DFD12 Meeting of The American Physical Society Mesolayer analysis in a turbulen... more Submitted for the DFD12 Meeting of The American Physical Society Mesolayer analysis in a turbulent boundary layer and DNS data NOOR AFZAL, Retired Aligarh University, Aligarh 202002, India-The intermediate layer (mesolayer) in turbulent boundary layer has been analysed by the matched asymptotic expansions where matching is implemented by Izakson-Millikan-Kolmogorov hypothesis. The large-scale motions and very large scale motion are modifying the influences of the outer geometries, and most significantly near the locus of the peak in shear stress in the mesolayer. The mesolayer is formed by the interaction of inner and outer layer scales, whose length (time) scale is the geometric mean of the inner and outer length (time) scales, and is also proportional to Taylor micro length (time) scale. The mesolayer variable is proportional to inverse square root of appropriate friction Reynolds number, provided Reynolds number is large. It is shown that the shape factor and Reynolds shear maxima scale with mesolayer scale equivalent to Taylor micro length scale. Further, the turbulent bursting time period scales is shown to mesolayer time scale which is equivalent to Taylor micro time scale. The implications of mesolayer on higher order effects on skin friction law for lower Reynolds number have also been analyzed. The implications of shift origin are proposed by the Prandtl's transposition theorem, and consequently without any closure model.
Bulletin of the American Physical Society, Nov 23, 2014
Measurements in an axisymmetric turbulent boundary layer with weak and strong three-dimensional disturbances
Lecture Notes in Physics
Without Abstract
Reply by Author to A. Wortman
AIAA Journal, 1986
arXiv: Fluid Dynamics, 2020
The power laws in the overlap region of two layer theory of turbulent boundary layer have been ob... more The power laws in the overlap region of two layer theory of turbulent boundary layer have been obtained by Izakson-Millikan-Kolmogorov hypothesis. The solution of the open functional equation is not unique. The power laws for velocity \& skin friction have equivalence with log laws for velocity \& skin friction, for large Reynolds numbers.
arXiv: Fluid Dynamics, 2020
The power laws in the overlap region of two layer theory of turbulent boundary layer have been ob... more The power laws in the overlap region of two layer theory of turbulent boundary layer have been obtained by Izakson-Millikan-Kolmogorov hypothesis. The solution of the open functional equation is not unique. The power laws for velocity \\& skin friction have equivalence with log laws for velocity \\& skin friction, for large Reynolds numbers.
Bulletin of the American Physical Society, 2010
Turbulent energy production peak and its location from inner most log law or power law velocity in a turbulent channel/pipe and Couette flows
European Journal of Mechanics - B/Fluids
Abstract The present work deals with the inner most, log law velocity and inner most power law ve... more Abstract The present work deals with the inner most, log law velocity and inner most power law velocity, and the associated Reynolds shear stresses, for turbulent energy production in the buffer layer of a fully developed turbulent channel or pipe and Couette flow. The Reynolds momentum equations have been are analyzed with out any closure model of eddy viscosity, mixing length etc. The equivalence of power law solutions with log law solution is demonstrated for large Reynolds numbers. Turbulent energy production asymptotic theory is presented. In a fully developed turbulent channel/pipe flow the theory shows that the peak of production and its location are universal numbers for large friction Reynolds numbers, but for lower Reynolds number theory show dependence on inverse of friction Reynolds number R τ − 1 . For turbulent Couette flow peak of production and its location are universal numbers for all friction Reynolds numbers. The turbulent energy production theory predictions in the buffer layer are compared with experimental and DNS data which support the predictions, that in channel or pipe the prediction depend on friction Reynolds number dependence like R τ − 1 and for Couette flow the predictions are universal numbers.
J Eng Math, 1976
In this paper the heat transfer in the second order boundary layer flow of an incompressible flui... more In this paper the heat transfer in the second order boundary layer flow of an incompressible fluid with uniform oncoming stream is studied at low Prandtl numbers using the method of matched asymptotic expansions. The suction and injection are also included in first as well as second-order problems. For each of the second-order effects due to longitudinal curvature, transverse curvature, displacement and suction or injection the first five terms in an asymptotic expansion are obtained and compared with available exact results.
The period T between bursts in wall-bounded turbu lent shear flows has been studied; yet there is... more The period T between bursts in wall-bounded turbu lent shear flows has been studied; yet there is no agreement whether period scales with inner or outer variables'.
Wake layer in a thermal turbulent boundary layer with pressure gradient
Heat and Mass Transfer, 1999
Alternate Scales for Turbulent Boundary Layer on Transitional Rough Walls: Universal Log Laws
Journal of Fluids Engineering, 2008
The present work deals with four new alternate transitional surface roughness scales for descript... more The present work deals with four new alternate transitional surface roughness scales for description of the turbulent boundary layer. The nondimensional roughness scale ϕ is associated with the transitional roughness wall inner variable ζ=Z+∕ϕ, the roughness friction Reynolds number Rϕ=Rτ∕ϕ, and the roughness Reynolds number Reϕ=Re∕ϕ. The two layer theory for turbulent boundary layers in the variables, mentioned above, is presented by method of matched asymptotic expansions for large Reynolds numbers. The matching in the overlap region is carried out by the Izakson–Millikan–Kolmogorov hypothesis, which gives the velocity profiles and skin friction universal log laws, explicitly independent of surface roughness, having the same constants as the smooth wall case. In these alternate variables, just above the wall roughness level, the mean velocity and Reynolds stresses are universal and do not depend on surface roughness. The extensive experimental data provide very good support to our universal relations. There is no universality of scalings in traditional variables and different expressions are needed for inflectional type roughness, monotonic Colebrook–Moody roughness, k-type roughness, d-type roughness, etc. In traditional variables, the velocity profile and skin friction predictions for the inflectional roughness, k-type roughness, and d-type roughness are supported well by the extensive experimental data. The pressure gradient effect from the matching conditions in the overlap region leads to the universal composite laws, which for weaker pressure gradients yields log laws and for strong adverse pressure gradients provides the half-power laws for universal velocity profiles and in traditional variables the additive terms in the two situations depend on the wall roughness.
Roughness effects of commercial steel pipe in turbulent flow: universal scaling
Canadian Journal of Civil Engineering, 2013
The mean turbulent flow over a transitional rough commercial steel pipe is considered in terms of... more The mean turbulent flow over a transitional rough commercial steel pipe is considered in terms of alternate inner roughness variables. The matching of inner layer and outer layer in the overlap region leads to the universal log laws for velocity profile and friction factor, explicitly independent of surface roughness of all kinds. The roughness function, for commercial steel pipe differs from inflectional (sand grain) roughness. The traditional wall law and friction factor depends on type of surface roughness.
![Research paper thumbnail of Erratum: “Friction factor directly from transitional roughness in a turbulent pipe flow” [ASME Trans. J. Fluid Eng., 2007, 129, pp. 1255–1267]](https://attachments.academia-assets.com/66519407/thumbnails/1.jpg)
](Journal of Fluids Engineering, 2011
The minimum error solutions of boundary layer equations in the least square sense have been studi... more The minimum error solutions of boundary layer equations in the least square sense have been studied by employing the Euler-Lagrange equations. To test the method a class of problems, i.e., boundary layer on a flat platt:, Hiemenz flow, boundary layer on a moving sheet and boundary layer in non-Newtonian fl uids have been studied. The comparison of the results with approximate methods, like Karman-Pohlhuasen, local potential and other variational methods, shows that the present predictions are invariably better.
International Journal of Heat and Mass Transfer, Oct 1, 2010
The present work deals with the numerical study of temperature distribution in the laminar bounda... more The present work deals with the numerical study of temperature distribution in the laminar boundary layer driven by the stretching boundary surface subjected to pressure gradient. The similarity transformation obeying the same power law based on composite reference velocity (union of velocities of the stretching boundary and free stream) has been employed that leads to a single set of equations,
Fluid Mechanics and Its Applications, 1996
The turbulent boundary layer subjected to pressure gradient is analyzed at large Reynolds number,... more The turbulent boundary layer subjected to pressure gradient is analyzed at large Reynolds number, using the method of matched asymptotic expansions. It is shown that there exists a 'wake' limit, in which the governing equation is 'rich enough' to contain the equation of the ...
Bulletin of the American Physical Society, Nov 19, 2012
Submitted for the DFD12 Meeting of The American Physical Society Mesolayer analysis in a turbulen... more Submitted for the DFD12 Meeting of The American Physical Society Mesolayer analysis in a turbulent boundary layer and DNS data NOOR AFZAL, Retired Aligarh University, Aligarh 202002, India-The intermediate layer (mesolayer) in turbulent boundary layer has been analysed by the matched asymptotic expansions where matching is implemented by Izakson-Millikan-Kolmogorov hypothesis. The large-scale motions and very large scale motion are modifying the influences of the outer geometries, and most significantly near the locus of the peak in shear stress in the mesolayer. The mesolayer is formed by the interaction of inner and outer layer scales, whose length (time) scale is the geometric mean of the inner and outer length (time) scales, and is also proportional to Taylor micro length (time) scale. The mesolayer variable is proportional to inverse square root of appropriate friction Reynolds number, provided Reynolds number is large. It is shown that the shape factor and Reynolds shear maxima scale with mesolayer scale equivalent to Taylor micro length scale. Further, the turbulent bursting time period scales is shown to mesolayer time scale which is equivalent to Taylor micro time scale. The implications of mesolayer on higher order effects on skin friction law for lower Reynolds number have also been analyzed. The implications of shift origin are proposed by the Prandtl's transposition theorem, and consequently without any closure model.
Bulletin of the American Physical Society, Nov 23, 2014
Measurements in an axisymmetric turbulent boundary layer with weak and strong three-dimensional disturbances
Lecture Notes in Physics
Without Abstract
Reply by Author to A. Wortman
AIAA Journal, 1986
arXiv: Fluid Dynamics, 2020
The power laws in the overlap region of two layer theory of turbulent boundary layer have been ob... more The power laws in the overlap region of two layer theory of turbulent boundary layer have been obtained by Izakson-Millikan-Kolmogorov hypothesis. The solution of the open functional equation is not unique. The power laws for velocity \& skin friction have equivalence with log laws for velocity \& skin friction, for large Reynolds numbers.
arXiv: Fluid Dynamics, 2020
The power laws in the overlap region of two layer theory of turbulent boundary layer have been ob... more The power laws in the overlap region of two layer theory of turbulent boundary layer have been obtained by Izakson-Millikan-Kolmogorov hypothesis. The solution of the open functional equation is not unique. The power laws for velocity \\& skin friction have equivalence with log laws for velocity \\& skin friction, for large Reynolds numbers.
Bulletin of the American Physical Society, 2010
Turbulent energy production peak and its location from inner most log law or power law velocity in a turbulent channel/pipe and Couette flows
European Journal of Mechanics - B/Fluids
Abstract The present work deals with the inner most, log law velocity and inner most power law ve... more Abstract The present work deals with the inner most, log law velocity and inner most power law velocity, and the associated Reynolds shear stresses, for turbulent energy production in the buffer layer of a fully developed turbulent channel or pipe and Couette flow. The Reynolds momentum equations have been are analyzed with out any closure model of eddy viscosity, mixing length etc. The equivalence of power law solutions with log law solution is demonstrated for large Reynolds numbers. Turbulent energy production asymptotic theory is presented. In a fully developed turbulent channel/pipe flow the theory shows that the peak of production and its location are universal numbers for large friction Reynolds numbers, but for lower Reynolds number theory show dependence on inverse of friction Reynolds number R τ − 1 . For turbulent Couette flow peak of production and its location are universal numbers for all friction Reynolds numbers. The turbulent energy production theory predictions in the buffer layer are compared with experimental and DNS data which support the predictions, that in channel or pipe the prediction depend on friction Reynolds number dependence like R τ − 1 and for Couette flow the predictions are universal numbers.
J Eng Math, 1976
In this paper the heat transfer in the second order boundary layer flow of an incompressible flui... more In this paper the heat transfer in the second order boundary layer flow of an incompressible fluid with uniform oncoming stream is studied at low Prandtl numbers using the method of matched asymptotic expansions. The suction and injection are also included in first as well as second-order problems. For each of the second-order effects due to longitudinal curvature, transverse curvature, displacement and suction or injection the first five terms in an asymptotic expansion are obtained and compared with available exact results.
The period T between bursts in wall-bounded turbu lent shear flows has been studied; yet there is... more The period T between bursts in wall-bounded turbu lent shear flows has been studied; yet there is no agreement whether period scales with inner or outer variables'.
Wake layer in a thermal turbulent boundary layer with pressure gradient
Heat and Mass Transfer, 1999
Alternate Scales for Turbulent Boundary Layer on Transitional Rough Walls: Universal Log Laws
Journal of Fluids Engineering, 2008
The present work deals with four new alternate transitional surface roughness scales for descript... more The present work deals with four new alternate transitional surface roughness scales for description of the turbulent boundary layer. The nondimensional roughness scale ϕ is associated with the transitional roughness wall inner variable ζ=Z+∕ϕ, the roughness friction Reynolds number Rϕ=Rτ∕ϕ, and the roughness Reynolds number Reϕ=Re∕ϕ. The two layer theory for turbulent boundary layers in the variables, mentioned above, is presented by method of matched asymptotic expansions for large Reynolds numbers. The matching in the overlap region is carried out by the Izakson–Millikan–Kolmogorov hypothesis, which gives the velocity profiles and skin friction universal log laws, explicitly independent of surface roughness, having the same constants as the smooth wall case. In these alternate variables, just above the wall roughness level, the mean velocity and Reynolds stresses are universal and do not depend on surface roughness. The extensive experimental data provide very good support to our universal relations. There is no universality of scalings in traditional variables and different expressions are needed for inflectional type roughness, monotonic Colebrook–Moody roughness, k-type roughness, d-type roughness, etc. In traditional variables, the velocity profile and skin friction predictions for the inflectional roughness, k-type roughness, and d-type roughness are supported well by the extensive experimental data. The pressure gradient effect from the matching conditions in the overlap region leads to the universal composite laws, which for weaker pressure gradients yields log laws and for strong adverse pressure gradients provides the half-power laws for universal velocity profiles and in traditional variables the additive terms in the two situations depend on the wall roughness.
Roughness effects of commercial steel pipe in turbulent flow: universal scaling
Canadian Journal of Civil Engineering, 2013
The mean turbulent flow over a transitional rough commercial steel pipe is considered in terms of... more The mean turbulent flow over a transitional rough commercial steel pipe is considered in terms of alternate inner roughness variables. The matching of inner layer and outer layer in the overlap region leads to the universal log laws for velocity profile and friction factor, explicitly independent of surface roughness of all kinds. The roughness function, for commercial steel pipe differs from inflectional (sand grain) roughness. The traditional wall law and friction factor depends on type of surface roughness.
Journal of Fluids Engineering, 2011
The minimum error solutions of boundary layer equations in the least square sense have been studi... more The minimum error solutions of boundary layer equations in the least square sense have been studied by employing the Euler-Lagrange equations. To test the method a class of problems, i.e., boundary layer on a flat platt:, Hiemenz flow, boundary layer on a moving sheet and boundary layer in non-Newtonian fl uids have been studied. The comparison of the results with approximate methods, like Karman-Pohlhuasen, local potential and other variational methods, shows that the present predictions are invariably better.