On the Skin Friction Coefficient for a Fully Rough Flat Plate

1983 ◽  
Vol 105 (3) ◽  
pp. 364-365 ◽  
Author(s):  
A. F. Mills ◽  
Xu Hang
Keyword(s):  
Experimental Data ◽  
Friction Coefficient ◽  
Velocity Profile ◽  
Skin Friction ◽  
Skin Friction Coefficient ◽  
Momentum Equation ◽  
Average Error ◽  
Friction Theory ◽  
Rough Plate ◽  
New Skin

A comparison of the Prandtl-Schlichting formula for skin friction of a fully rough plate with recently obtained experimental data shows an average error of 17.5 percent. It is suggested that the reason for this discrepancy is a failure to account for the wake component of the velocity profile. The integral momentum equation is used to derive a new skin friction theory which when compared to the same data gives an average error of 2.7 percent. A new skin friction formula is proposed which is valid over a wide parameter range.

A Simple, Accurate Integral Solution for Accelerating Turbulent Boundary Layers With Transpiration

1995 ◽  
Vol 117 (3) ◽  
pp. 535-538 ◽  
Author(s):  
James Sucec
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Skin Friction ◽  
Boundary Layers ◽  
Integral Form ◽  
Skin Friction Coefficient ◽  
Momentum Equation ◽  
Turbulent Boundary Layers ◽  
Integral Solution ◽  
Good Agreement

The inner law for transpired turbulent boundary layers is used as the velocity profile in the integral form of the x momentum equation. The resulting ordinary differential equation is solved numerically for the skin friction coefficient, as well as boundary layer thicknesses, as a function of position along the surface. Predicted skin friction coefficients are compared to experimental data and exhibit reasonably good agreement with the data for a variety of different cases. These include blowing and suction, with constant blowing fractions F for both mild and severe acceleration. Results are also presented for more complicated cases where F varies with x along the surface.

scholarly journals Unsteady Squeezing Flow of Casson Fluid with Magnetohydrodynamic Effect and Passing through Porous Medium

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Hamid Khan ◽  
Mubashir Qayyum ◽  
Omar Khan ◽  
Murtaza Ali
Keyword(s):  
Porous Medium ◽  
Friction Coefficient ◽  
Velocity Profile ◽  
Skin Friction ◽  
Opposite Effect ◽  
Casson Fluid ◽  
Skin Friction Coefficient ◽  
Squeezing Flow ◽  
Highly Nonlinear ◽  
Squeeze Number

An unsteady squeezing flow of Casson fluid having magnetohydrodynamic (MHD) effect and passing through porous medium channel is modeled and investigated. Similarity transformations are used to convert the partial differential equations (PDEs) of non-Newtonian fluid to a highly nonlinear fourth-order ordinary differential equation (ODE). The obtained boundary value problem is solved analytically by Homotopy Perturbation Method (HPM) and numerically by explicit Runge-Kutta method of order 4. For validity purpose, we compare the analytical and numerical results which show excellent agreement. Furthermore, comprehensive graphical analysis has been made to investigate the effects of various fluid parameters on the velocity profile. Analysis shows that positive and negative squeeze numberSqhave opposite effect on the velocity profile. It is also observed that Casson parameterβshows opposite effect on the velocity profile in case of positive and negative squeeze numberSq. MHD parameterMgand permeability constantMphave similar effects on the velocity profile in case of positive and negative squeeze numbers. It is also seen that, in case of positive squeeze number, similar velocity profiles have been obtained forβ,Mg, andMp. Besides this, analysis of skin friction coefficient has also been presented. It is observed that squeeze number, MHD parameter, and permeability parameter have direct relationship while Casson parameter has inverse relationship with skin friction coefficient.

Shape effect of Cu, Al2O3 and TiO2 nanoparticles on stagnation point nanofluid flow in a microgravity environment

2021 ◽  
Vol 2 (2) ◽  
pp. 01-13
Author(s):  
M.H.A. Kamal ◽  
A. Ali ◽  
Y.J. Lim ◽  
N.A. Rawi ◽  
S. Shafie
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Velocity Profile ◽  
Skin Friction ◽  
Stagnation Point ◽  
Skin Friction Coefficient ◽  
Microgravity Environment ◽  
Nanofluid Flow ◽  
Conservation Of Energy ◽  
Shaped Nanoparticles

The unsteady viscous nanofluid flow near a three-dimensional stagnation point was studied numerically under microgravity environment. g-Jitter is one of the effects occurs under microgravity environment that producing a fluctuating gravitational field. Three different types of nanoparticles were induced in the study that is copper (Cu), alumina (Al2O3), and titania (TiO2) which then produce a water-based typed of nanofluid. In addition, different shape of nanoparticle was applied on the study in analyzing the performance of each types of nanoparticle. The fluid system was then mathematically formulated into a system of partial differential equation based on physical law and principle such as conservation of mass, Newton’s second law and conservation of energy. The system of equation then undergoes semi-similar transformation technique in reducing the complexity of the problem into non dimensionless form. Keller box method was applied into the dimensionless system of equations in solving the problem numerically. The problem was analyzed in term of velocity and temperature profiles together with skin friction coefficient and Nusselt number. The results shown that temperature profile, skin friction coefficient and Nusselt number were increase while velocity profile decreased as nanoparticle volume fraction decreased. The results indicated that, the needle-shaped nanoparticles give the highest enhancement on the heat transfer of the nanofluid compared to sphere and disk-shaped nanoparticles with more than 14% significant different. In addition,  alumina hold the highest velocity profile while copper hold the lowest velocity profile.

Impact of viscosity variation on oblique flow of Cu–H2O nanofluid

2017 ◽  
Vol 232 (5) ◽  
pp. 622-631 ◽  
Author(s):  
R Tabassum ◽  
Rashid Mehmood ◽  
O Pourmehran ◽  
NS Akbar ◽  
M Gorji-Bandpy
Keyword(s):  
Heat Flux ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Volume Fraction ◽  
Variable Viscosity ◽  
Solid Volume Fraction ◽  
Local Heat ◽  
Skin Friction Coefficient ◽  
Viscosity Parameter ◽  
Local Heat Flux

The dynamic properties of nanofluids have made them an area of intense research during the past few decades. In this article, flow of nonaligned stagnation point nanofluid is investigated. Copper–water based nanofluid in the presence of temperature-dependent viscosity is taken into account. The governing nonlinear coupled ordinary differential equations transformed by partial differential equations are solved numerically by using fourth-order Runge–Kutta–Fehlberg integration technique. Effects of variable viscosity parameter on velocity and temperature profiles of pure fluid and copper–water nanofluid are analyzed, discussed, and presented graphically. Streamlines, skin friction coefficients, and local heat flux of nanofluid under the impact of variable viscosity parameter, stretching ratio, and solid volume fraction of nanoparticles are also displayed and discussed. It is observed that an increase in solid volume fraction of nanoparticles enhances the magnitude of normal skin friction coefficient, tangential skin friction coefficient, and local heat flux. Viscosity parameter is found to have decreasing effect on normal and tangential skin friction coefficients whereas it has a positive influence on local heat flux.

Low-Reynolds-Number Turbulent Boundary Layers in Zero and Favorable Pressure Gradients

1983 ◽  
Vol 27 (03) ◽  
pp. 147-157 ◽  
Author(s):  
A. J. Smits ◽  
N. Matheson ◽  
P. N. Joubert
Keyword(s):  
Friction Coefficient ◽  
Skin Friction ◽  
Boundary Layers ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Skin Friction Coefficient ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients ◽  
Mean Flow ◽  
Low Reynolds

This paper reports the results of an extensive experimental investigation into the mean flow properties of turbulent boundary layers with momentum-thickness Reynolds numbers less than 3000. Zero pressure gradient and favorable pressure gradients were studied. The velocity profiles displayed a logarithmic region even at very low Reynolds numbers (as low as Rθ = 261). The results were independent of the leading-edge shape, and the pin-type turbulent stimulators performed well. It was found that the shape and Clauser parameters were a little higher than the correlation proposed by Coles [10], and the skin friction coefficient was a little lower. The skin friction coefficient behavior could be fitted well by a simple power-law relationship in both zero and favorable pressure gradients.

Nanofluid flow past an impulsively started vertical plate with variable surface temperature

2016 ◽  
Vol 26 (1) ◽  
pp. 328-347 ◽  
Author(s):  
Rajesh Vemula ◽  
A J Chamkha ◽  
Mallesh M. P.
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Vertical Plate ◽  
Aluminium Oxide ◽  
Skin Friction Coefficient ◽  
Viscous Drag ◽  
Content Type ◽  
Variable Surface ◽  
Variable Surface Temperature

Purpose – The purpose of this paper is to focus on the numerical modelling of transient natural convection flow of an incompressible viscous nanofluid past an impulsively started semi-infinite vertical plate with variable surface temperature. Design/methodology/approach – The problem is governed by the coupled non-linear partial differential equations with appropriate boundary conditions. A robust, well-tested, Crank-Nicolson type of implicit finite-difference method, which is unconditionally stable and convergent, is used to solve the governing non-linear set of partial differential equations. Findings – The local and average values of the skin-friction coefficient (viscous drag) and the average Nusselt number (the rate of heat transfer) decreased, while the local Nusselt number increased for all nanofluids, namely, aluminium oxide-water, copper-water, titanium oxide-water and silver-water with an increase in the temperature exponent m. Selecting aluminium oxide as the dispersing nanoparticles leads to the maximum average Nusselt number (the rate of heat transfer), while choosing silver as the dispersing nanoparticles leads to the minimum local Nusselt number compared to the other nanofluids for all values of the temperature exponent m. Also, choosing silver as the dispersing nanoparticles leads to the minimum skin-friction coefficient (viscous drag), while selecting aluminium oxide as the dispersing nanoparticles leads to the maximum skin-friction coefficient (viscous drag) for all values of the temperature exponent m. Research limitations/implications – The Brinkman model for dynamic viscosity and Maxwell-Garnett model for thermal conductivity are employed. The governing boundary layer equations are written according to The Tiwari-Das nanofluid model. A range of nanofluids containing nanoparticles of aluminium oxide, copper, titanium oxide and silver with nanoparticle volume fraction range less than or equal to 0.04 are considered. Practical implications – The present simulations are relevant to nanomaterials thermal flow processing in the chemical engineering and metallurgy industries. This study also provides an important benchmark for further simulations of nanofluid dynamic transport phenomena of relevance to materials processing, with alternative computational algorithms (e.g. finite element methods). Originality/value – This paper is relatively original and illustrates the influence of variable surface temperature on transient natural convection flow of a viscous incompressible nanofluid and heat transfer from an impulsively started semi-infinite vertical plate.

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