An integral approach to the calculation of skin friction and heat transfer in the laminar flow of a high-Prandtl-number power-law non-Newtonian fluid past a wedge

1991 ◽  
Vol 69 (2) ◽  
pp. 83-89 ◽  
Author(s):  
G. Ramamurty ◽  
K. Narasimha Rao ◽  
K. N. Seetharamu
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Prandtl Number ◽  
Skin Friction ◽  
Layer Thickness ◽  
Power Law ◽  
Boundary Layer Thickness ◽  
Thermal Boundary Layer ◽  
Integral Approach ◽  
High Prandtl Number

An integral approach to the theoretical analysis for the skin friction of a non-Newtonian, power-law-fluid flow over a wedge is presented, when the inertia terms in the boundary-layer equations are small but need consideration. The method adopted for the solution of the equations considers an integrated average value of the inertia terms in the momentum equation. The values of the velocities and the boundary-layer thickness obtained from the hydrodynamic analysis are used for the calculation of the thermal-boundary-layer thickness. A linear velocity profile is assumed for the flow field within the thermal boundary layer as the fluids chosen for the analysis are high-Prandtl-number fluids. The results of the skin friction and the rates of the heat transfer are tabulated for a number of values of the flow behaviour index, n, varying from 0.05 to 5.0. This analysis is applicable to viscous polymer solutions having high Prandtl numbers.

A CFD Evaluation of Multiple RANS Turbulence Models for Prediction of Boundary Layer Flows on a Turbine Vane

2013 ◽  
Author(s):  
Thomas E. Dyson ◽  
David G. Bogard ◽  
Sean D. Bradshaw
Keyword(s):  
Boundary Layer ◽  
Prandtl Number ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Thermal Boundary Layer ◽  
Turbulence Models ◽  
Experimental Measurements ◽  
Thermal Boundary Layer Thickness ◽  
Mean Velocity ◽  
High Turbulence

There is a growing trend toward the use of conjugate CFD for use in prediction of turbine cooling performance. While many studies have evaluated the performance of RANS simulations relative to experimental measurements of the momentum boundary layer, no studies have evaluated their performance in prediction of the accompanying thermal boundary layer. This is largely due to the fact that, until recently, no appropriate experimental data existed to validate these models. This study compares several popular RANS models — including the realizable k-ε and k-ω SST models — with a four equation k-ω model (“Transition SST”) and experimental measurements at selected positions on the pressure and suction sides of a model C3X vane. Comparisons were made using mean velocity and temperature in the boundary layer without film cooling under conditions of high and low mainstream turbulence. The best performing model was evaluated using modification of the turbulent Prandtl number to attempt to better match the data for the high turbulence case. Overall, the models did not perform well for the low turbulence case; they greatly over-predicted the thermal boundary layer thickness. For the high turbulence case, their performance was better. The Transition SST model performed the best with an average thermal boundary layer thickness within 15% of the experimentally measured values. Prandtl number variation proved to be an inadequate means of improving the thermal boundary layer predictions.

Similarity Solution of Combined Convection Heat Transfer From a Rotating Cone or Disk to Non-Newtonian Fluids

1990 ◽  
Vol 112 (4) ◽  
pp. 939-944 ◽  
Author(s):  
T.-Y. Wang ◽  
C. Kleinstreuer
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Prandtl Number ◽  
Power Law ◽  
Similarity Solution ◽  
Boundary Layer Thickness ◽  
Viscosity Index ◽  
Convection Heat Transfer ◽  
Convection Heat ◽  
Rotating Cone

A powerful similarity solution of the highly nonlinear, coupled boundary-layer equations has been developed for steady laminar mixed convection heat transfer between a rotating cone/disk and power-law fluids. Of special interest are the effects of the power-law viscosity index, a generalized local Prandtl number, the buoyancy parameter, and the type of thermal wall condition on the velocity and temperature fields and hence the skin friction coefficient and the local Nusselt number. While the momentum boundary-layer thickness increases measurably with decreasing viscosity index n, the thermal boundary-layer thickness is less affected by changes in n. The magnitude and direction of the buoyancy force influence the upward velocity profile near the wall and the temperature profiles significantly. Both Prandtl number and buoyancy parameter have a more pronounced effect on the skin friction group, SFG ~ cf, than on the heat transfer group, HTG ~ Nu.

scholarly journals Magnetohydrodynamic free convection of non-Newtonian power-law fluids over a uniformly heated horizontal plate

2020 ◽  
Vol 24 (2 Part B) ◽  
pp. 1323-1334 ◽  
Author(s):  
Alireza Bahmani ◽  
Hadi Kargarsharifabad
Keyword(s):  
Boundary Layer ◽  
Nusselt Number ◽  
Prandtl Number ◽  
Skin Friction ◽  
Power Law ◽  
Thermal Boundary Layer ◽  
Hartmann Number ◽  
Viscosity Index ◽  
Thermal Boundary Layer Thickness ◽  
Power Law Fluids

The MHD free convection flow of non-Newtonian power-law fluids over a horizontal plate subjected to a constant heat flux is studied. The results are presented for various values of the three influential parameters, i. e. the generalized Hart?mann number, the generalized Prandtl number, and the non-Newtonian power-law viscosity index. Increasing the Hartmann number increases the thermal boundary-layer thickness and the surface temperature and consequently decreases the wall skin friction and Nusselt number. A lower generalized Prandtl number results in a larger skin friction coefficient and higher wall temperature as well as thicker thermal boundary-layer. The viscosity index is predicted to influence the flow conditions depending on the value of generalized Hartmann number. At high generalized Prandtl number numbers, by decreasing non-Newtonian power-law index, the wall skin friction, temperature scale, and thermal boundary-layer thickness are increased and the Nusselt number is decreased, while the opposite trend is observed for low generalized Prandtl number. A general correlation for the Nusselt number is derived using the numerical results

Effects of temperature-dependent viscosity and thermal conductivity on mixed convection flow along a magnetized vertical surface

2016 ◽  
Vol 26 (5) ◽  
pp. 1580-1592 ◽  
Author(s):  
Ashraf Muhammad ◽  
Ali J Chamkha ◽  
S Iqbal ◽  
Masud Ahmad
Keyword(s):  
Magnetic Field ◽  
Thermal Conductivity ◽  
Boundary Layer ◽  
Prandtl Number ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Thermal Boundary Layer ◽  
Content Type ◽  
Variation Parameter ◽  
Momentum Boundary Layer

Purpose – The purpose of this paper is to report a numerical solution for the problem of steady, two dimensional boundary layer buoyant flow on a vertical magnetized surface, when both the viscosity and thermal conductivity are assumed to be temperature-dependent. In this case, the motion is governed by a coupled set of three nonlinear partial differential equations, which are solved numerically by using the finite difference method (FDM) by introducing the primitive variable formulation. Calculations of the coupled equations are performed to investigate the effects of the different governing parameters on the profiles of velocity, temperature and the transverse component of magnetic field. The effects of the thermal conductivity variation parameter, viscosity variation parameter, magnetic Prandtl number Pmr, magnetic force parameter S, mixed convection parameter Ri and the Prandtl number Pr on the flow structure and heat transfer characteristics are also examined. Design/methodology/approach – FDM. Findings – It is noted that when the Prandtl number Pr is sufficiently large, i.e. Pr=100, the buoyancy force that driven the fluid motion is decreased that decrease the momentum boundary layer and there is no change in thermal boundary layer is noticed. It is also noted that due to slow motion of the fluid the magnetic current generates which increase the magnetic boundary layer thickness at the surface. It is observed that the momentum boundary layer thickness is increased, thermal and magnetic field boundary layers are decreased with the increase of thermal conductivity variation parameter =100. The maximum boundary layer thickness is increased for =100 and there is no change seen in the case of thermal boundary layer thickness but magnetic field boundary layer is deceased. The momentum boundary layer thickness shoot quickly for =40 but is very smooth for =50.There is no change is seen for the case of thermal boundary layer and very clear decay for =40 is noted. Originality/value – This work is original research work.

Boundary Layer Closure and Heat Transfer in Constant Base Pressure and Simple Wave Guns

1978 ◽  
Vol 100 (4) ◽  
pp. 690-696 ◽  
Author(s):  
A. D. Anderson ◽  
T. J. Dahm
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Method Of Characteristics ◽  
Simple Wave ◽  
Momentum Equation ◽  
Base Pressure ◽  
Two Dimensional ◽  
The Method Of Characteristics

Solutions of the two-dimensional, unsteady integral momentum equation are obtained via the method of characteristics for two limiting modes of light gas launcher operation, the “constant base pressure gun” and the “simple wave gun”. Example predictions of boundary layer thickness and heat transfer are presented for a particular 1 in. hydrogen gun operated in each of these modes. Results for the constant base pressure gun are also presented in an approximate, more general form.

Freestream Flow Effects on Film Effectiveness and Heat Transfer Coefficient Augmentation for Compound Angle Shaped Holes

2017 ◽  
Author(s):  
Joshua B. Anderson ◽  
John W. McClintic ◽  
David G. Bogard ◽  
Thomas E. Dyson ◽  
Zachary Webster
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Layer Thickness ◽  
Film Cooling ◽  
Gas Turbines ◽  
Boundary Layer Thickness ◽  
Adiabatic Effectiveness ◽  
Compound Angle

The use of compound-angled shaped film cooling holes in gas turbines provides a method for cooling regions of extreme curvature on turbine blades or vanes. These configurations have received surprisingly little attention in the film cooling literature. In this study, a row of laid-back fanshaped holes based on an open-literature design, were oriented at a 45-degree compound angle to the approaching freestream flow. In this study, the influence of the approach flow boundary layer thickness and character were experimentally investigated. A trip wire and turbulence generator were used to vary the boundary layer thickness and freestream conditions from a thin laminar boundary layer flow to a fully turbulent boundary layer and freestream at the hole breakout location. Steady-state adiabatic effectiveness and heat transfer coefficient augmentation were measured using high-resolution IR thermography, which allowed the use of an elevated density ratio of DR = 1.20. The results show adiabatic effectiveness was generally lower than for axially-oriented holes of the same geometry, and that boundary layer thickness was an important parameter in predicting effectiveness of the holes. Heat transfer coefficient augmentation was highly dependent on the freestream turbulence levels as well as boundary layer thickness, and significant spatial variations were observed.

Convection Heat Transfer of Power-Law Fluids Along the Inclined Nonuniformly Heated Plate With Suction or Injection

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Jize Sui ◽  
Liancun Zheng ◽  
Xinxin Zhang
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Skin Friction ◽  
Power Law ◽  
Inclination Angle ◽  
Convection Heat Transfer ◽  
Heated Plate ◽  
Convection Heat ◽  
Power Law Fluids ◽  
Suction Or Injection

A comprehensive analysis to convection heat transfer of power-law fluids along the inclined nonuniformly heated plate with suction or injection is presented. The effects of power-law viscosity on temperature field are taken into account in highly coupled velocity and temperature fields. Analytical solutions are established by homotopy analysis method (HAM), and the effects of pertinent parameters (velocity power-law exponent, temperature power index, suction/injection parameter, and inclination angle) are analyzed. Some new interesting phenomena are found, for example, unlike classical boundary layer problem in which the skin friction monotonically increases (decreases) with suction increases (injection increases), but there exists a special region where the skin friction is not monotonic, which is strongly bound up with Prandtl number, which have never been reported before. The nonmonotony occurs in suction region for Prandtl number Npr < 1 and injection region for Npr > 1. Results also illustrate that the velocity profile decreases but the heat convection is enhanced obviously with increasing in temperature power exponent m (generalized Prandtl number Npr has similar effects), the decreases in inclination angle lead to the reduction in convection and heat transfer efficiency.

Heat Transfer Around a Cylindrical Protuberance Mounted in a Plane Turbulent Boundary Layer

2005 ◽  
Vol 128 (2) ◽  
pp. 153-161 ◽  
Author(s):  
Takayuki Tsutsui ◽  
Masafumi Kawahara
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Aspect Ratio ◽  
Turbulent Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Reynolds Numbers ◽  
Heat Transfer Characteristics ◽  
Low Aspect Ratio ◽  
Maximum Value

Heat transfer characteristics around a low aspect ratio cylindrical protuberance placed in a turbulent boundary layer were investigated. The diameters of the protuberance, D, were 40 and 80mm, and the height to diameter aspect ratio H∕D ranged from 0.125 to 1.0. The Reynolds numbers based on D ranged from 1.1×104 to 1.1×105 and the thickness of the turbulent boundary layer at the protuberance location, δ, ranged from 26 to 120mm for these experiments. In this paper we detail the effects of the boundary layer thickness and the protuberance aspect ratio on heat transfer. The results revealed that the overall heat transfer for the cylindrical protuberance reaches a maximum value when H∕δ=0.24.

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