A Numerical Study of the Laminar Flow of Non-Newtonian Fluids Along a Vertical Wall

1973 ◽  
Vol 40 (1) ◽  
pp. 290-292 ◽  
Author(s):  
T. M. T. Yang ◽  
D. W. Yarbrough
Keyword(s):  
Boundary Layer ◽  
Steady State ◽  
Laminar Flow ◽  
Power Law ◽  
Analytical Solutions ◽  
Numerical Study ◽  
Vertical Wall ◽  
Newtonian Fluids ◽  
Momentum Integral ◽  
Accelerating Flow

The momentum integral technique is used to describe the steady-state, laminar, accelerating flow of a power-law liquid film along a vertical wall. Values for film thicknesses and boundary-layer thicknesses are obtained numerically and compared with existing analytical solutions for Newtonian fluids.

Laminar Flow Along a Vertical Wall

1968 ◽  
Vol 35 (4) ◽  
pp. 631-633 ◽  
Author(s):  
R. Haugen
Keyword(s):  
Thin Film ◽  
Boundary Layer ◽  
Laminar Flow ◽  
Film Thickness ◽  
Closed Form ◽  
Analytical Study ◽  
Vertical Wall ◽  
Mathematical Solution ◽  
Dimensionless Variables ◽  
Accelerating Flow

An analytical study is presented which describes the laminar accelerating flow of a thin film falling along a vertical wall. The approximate mathematical solution is given with emphasis on the growth and decrease of the boundary layer and film thickness, respectively. These resultant solutions are given in closed form and are found dependent upon two-dimensionless variables: φ2=3U0νgh02 and ζ2=1+2gh0x¯U02.

scholarly journals Free Convective MHD Flow Past a Vertical Cone with Variable Heat and Mass Flux

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
J. Prakash ◽  
S. Gouse Mohiddin ◽  
S. Vijaya Kumar Varma
Keyword(s):  
Boundary Layer ◽  
Power Law ◽  
Mass Flux ◽  
Numerical Study ◽  
Convection Boundary Layer ◽  
Vertical Cone ◽  
Local Skin ◽  
Surface Mass ◽  
Flow Past ◽  
Power Law Exponent

A numerical study of buoyancy-driven unsteady natural convection boundary layer flow past a vertical cone embedded in a non-Darcian isotropic porous regime with transverse magnetic field applied normal to the surface is considered. The heat and mass flux at the surface of the cone is modeled as a power law according to qwx=xm and qw*(x)=xm, respectively, where x denotes the coordinate along the slant face of the cone. Both Darcian drag and Forchheimer quadratic porous impedance are incorporated into the two-dimensional viscous flow model. The transient boundary layer equations are then nondimensionalized and solved by the Crank-Nicolson implicit difference method. The velocity, temperature, and concentration fields have been studied for the effect of Grashof number, Darcy number, Forchheimer number, Prandtl number, surface heat flux power-law exponent (m), surface mass flux power-law exponent (n), Schmidt number, buoyancy ratio parameter, and semivertical angle of the cone. Present results for selected variables for the purely fluid regime are compared with the published results and are found to be in excellent agreement. The local skin friction, Nusselt number, and Sherwood number are also analyzed graphically. The study finds important applications in geophysical heat transfer, industrial manufacturing processes, and hybrid solar energy systems.

Contribution of vertical advection to supergradient wind in tropical cyclone boundary layer: A numerical study

2021 ◽  
Author(s):  
Rong Fei ◽  
Yuqing Wang ◽  
Yuanlong Li
Keyword(s):  
Boundary Layer ◽  
Steady State ◽  
Wind Speed ◽  
Tropical Cyclone ◽  
Vertical Structure ◽  
Numerical Study ◽  
Substantial Reduction ◽  
Vertical Advection ◽  
Physics Model ◽  
Tropical Cyclone Boundary Layer

AbstractThe existence of supergradient wind in the interior of the boundary layer is a distinct feature of a tropical cyclone (TC). Although the vertical advection is shown to enhance supergradient wind in TC boundary layer (TCBL), how and to what extent the strength and structure of supergradient wind are modulated by vertical advection are not well understood. In this study, both a TCBL model and an axisymmetric full-physics model are used to quantify the contribution of vertical advection process to the strength and vertical structure of supergradient wind in TCBL. Results from the TCBL model show that the removal of vertical advection of radial wind reduces both the strength and height of supergradient wind by slightly more than 50%. The removal of vertical advection of agradient wind reduces the height of the supergradient wind core by ~30% but increases the strength of supergradient wind by ~10%. Results from the full-physics model show that the removal of vertical advection of radial wind or agradient wind reduces both the strength and height of supergradient wind but the removal of that of radial wind produces a more substantial reduction (52%) than the removal of that of agradient wind (35%). However, both the intensification rate and final intensity of the simulated TCs in terms of maximum 10-m wind speed show little differences in experiments with and without the vertical advection of radial or agradient wind, suggesting that supergradient wind contributes little to either the intensification rate or the steady-state intensity of the simulated TC.

Analysis of a Transient Asymmetrically Heated/Cooled Open Thermosyphon

1993 ◽  
Vol 115 (3) ◽  
pp. 621-630 ◽  
Author(s):  
G. F. Jones ◽  
J. Cai
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Vertical Plate ◽  
Numerical Study ◽  
Vertical Wall ◽  
Constant Heat Flux ◽  
Closed Form Expression ◽  
Transient Temperature ◽  
Large Reservoir ◽  
One Dimensional

We present a numerical study of transient natural convection in a rectangular open thermosyphon having asymmetric thermal boundary conditions. One vertical wall of the thermosyphon is either heated by constant heat flux (“warmup”) or cooled by convection to the surroundings (“cooldown”). The top of the thermosyphon is open to a large reservoir of fluid at constant temperature. The vorticity, energy, and stream-function equations are solved by finite differences on graded mesh. The ADI method and iteration with overrelaxation are used. We find that the thermosyphon performs quite differently during cooldown compared with warmup. In cooldown, flows are mainly confined to the thermosyphon with little momentum and heat exchange with the reservoir. For warmup, the circulation resembles that for a symmetrically heated thermosyphon where there is a large exchange with the reservoir. The difference is explained by the temperature distributions. For cooldown, the fluid becomes stratified and the resulting stability reduces motion. In contrast, the transient temperature for warmup does not become stratified but generally exhibits the behavior of a uniformly heated vertical plate. For cooldown and Ra > 104, time-dependent heat transfer is predicted by a closed-form expression for one-dimensional conduction, which shows that Nu → Bi1/2/A in the steady-state limit. For warmup, transient heat transfer behaves as one-dimensional conduction for early times and at steady state and for Ra* ≥ 105, can be approximated as that for a uniformly heated vertical plate.

A Numerical Study of Dean Instability in Non-Newtonian Fluids

2005 ◽  
Vol 128 (1) ◽  
pp. 34-41 ◽  
Author(s):  
H. Fellouah ◽  
C. Castelain ◽  
A. Ould El Moctar ◽  
H. Peerhossaini
Keyword(s):  
Aspect Ratio ◽  
Cross Section ◽  
Power Law ◽  
Numerical Study ◽  
Rectangular Cross Section ◽  
Newtonian Fluids ◽  
Dean Number ◽  
Bingham Number ◽  
Curved Channels ◽  
Power Law Index

We present a numerical study of Dean instability for non-Newtonian fluids in a laminar 180deg curved-channel flow of rectangular cross section. A methodology based on the Papanastasiou model (Papanastasiou, T. C., 1987, J. Rheol., 31(5), pp. 385–404) was developed to take into account the Bingham-type rheological behavior. After validation of the numerical methodology, simulations were carried out (using FLUENT CFD code) for Newtonian and non-Newtonian fluids in curved channels of square or rectangular cross section and for a large aspect and curvature ratios. A criterion based on the axial velocity gradient was defined to detect the instability threshold. This criterion was used to optimize the grid geometry. The effects of curvature and aspect ratio on the Dean instability are studied for all fluids, Newtonian and non-Newtonian. In particular, we show that the critical value of the Dean number decreases with increasing curvature ratio. The variation of the critical Dean number with aspect ratio is less regular. The results are compared to those for Newtonian fluids to emphasize the effect of the power-law index and the Bingham number. The onset of Dean instability is delayed with increasing power-law index. The same delay is observed in Bingham fluids when the Bingham number is increased.

Numerical Study on Pulsating Laminar Flow in Annular Space for Power-Law Fluid

2013 ◽  
Vol 394 ◽  
pp. 86-91
Author(s):  
Shan Bo Huang ◽  
Liang Gong ◽  
Zhao Min Li
Keyword(s):  
Laminar Flow ◽  
Power Law ◽  
Numerical Study ◽  
Simple Algorithm ◽  
Petroleum Engineering ◽  
Annular Space ◽  
Reciprocating Motion ◽  
Power Law Fluid ◽  
Liquidity Index ◽  
Axial Pressure Gradient

A mathematical model of pulsating laminar flow inside an annular space for power-law fluid was established basing on the background of petroleum engineering. The characteristic of pulsating flow was obtained by employed SIMPLE algorithm. The investigation result shows that the velocity profile and axial pressure gradient are affected by the frequency, amplitude, liquidity index and annular distance of reciprocating motion and the affection is violent near the inner wall.

Axial Laminar Flow of Non-Newtonian Fluids in Narrow Eccentric Annuli

1965 ◽  
Vol 5 (04) ◽  
pp. 277-280 ◽  
Author(s):  
Robert D. Vaughn
Keyword(s):  
Laminar Flow ◽  
Power Law ◽  
Flow Rate ◽  
Pressure Loss ◽  
Large Diameter ◽  
Experimental Studies ◽  
Small Diameter ◽  
Journal Bearings ◽  
Newtonian Fluids ◽  
Eccentric Annuli

Abstract The analysis of laminar flow of power-law non- Newtonian fluids in narrow, eccentric annuli is employed in this paper to discuss the problems of lubricant flow in journal bearings and of errors introduced by eccentricity in experimental studies with concentric annuli on extruders and wellbore annuli. The velocity profile and pressure loss-flow rate equations are developed for the laminar flow region. In addition, the expected error in flow rate and pressure-loss measurements for concentric annuli as a result of eccentricity is determined. For example, a 10 per cent displacement of the core of an almost concentric annulus would cause a 1.8 per cent decrease in the observed pressure loss for a fluid with a power-law exponent n of 0.25. The corresponding increase in the observed volumetric flow rate would be 7.5 per cent. Introduction Non-Newtonianism and eccentricity occur simultaneously in two engineering problems:flow of lubricants in journal-bearings and pressure-reducing bushings, andflow of non-Newtonian fluids in plastic extruders and wellbore annuli. The lubricants used for moving parts are often non-Newtonian in character - often they are plastic in behavior. A solution to the problem of flow of non-Newtonian fluids in narrow eccentric annuli is particularly pertinent to this problem. In all experimental studies of laminar flow of fluids in concentric annuli, such as in extruders and well casings, the error due to eccentricity must be estimated or studied. A number of publications have dealt with this problem for Newtonian fluids; however, I am not aware of work for non-Newtonian fluids. This work is directed to the non-Newtonian problem. Before the solution to the problem is given, the pertinent conclusions from the work on Newtonian fluids will be reviewed. Heyda and Redberger and Charles have published general solutions to the problem of the laminar flow of Newtonian fluids in eccentric annuli, apparently without knowing of the earlier work of Caldwell and Bairstow and Berry, which is reported by Dryden, et al. Although several mathematical routes are encompassed by the work of these authors, the results appear to be equivalent. Redberger and Charles show that the error caused by eccentricity in concentric annuli is negligible for small diameter ratios (K less than 0.5); however, for large diameter ratios (K - 1), the error in the predicted flow rate can be as great as 100 per cent or more. Partial solutions to the problem are available from the work of Dryden, Tao and Donovan and Piercy, et al. Tao and Donovan examined the case of flow in narrow, eccentric annuli (K - 1) with and without rotation of the annular core. These authors also reviewed previous work on this subject and verified their approach with experimental data. Dryden gives the solution for the limiting case of complete eccentricity or tangency. Piercy, et al. published an early solution to the problem of narrow eccentric annular flow. The conclusions of Redberger and Charles and the experimental proof of Tao and Donovans both suggest that the region of large diameter ratios (K - 1) is of main interest and that the parallel planes approximation to the solution in this region is satisfactory. This method will now be extended to the laminar flow of non-Newtonian fluids in narrow eccentric annuli. THEORETICAL SOLUTION The geometrical aspects of the problem are illustrated in Fig. 1. To represent the non-Newtonian fluid the power-law model was selected. (1) This model has many disadvantages which have been pointed out; nevertheless, As simplicity, its frequent and wide applicability justify its use in this work. Fredrickson and Birds and Savins have used it as a basis for a theoretical study of laminar flow of non-Newtonian fluids in concentric annuli. SPEJ P. 277ˆ

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