Non-Newtonian Natural Convection Along a Vertical Flat Plate With Uniform Surface Temperature

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
S. Ghosh Moulic ◽  
L. S. Yao
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Shear Rate ◽  
Newtonian Fluid ◽  
Power Law ◽  
Similarity Solution ◽  
Leading Edge ◽  
Boundary Layer Equations ◽  
Shear Thinning Fluid ◽  
Vertical Flat Plate

Natural-convection boundary-layer flow of a non-Newtonian fluid along a heated semi-infinite vertical flat plate with uniform surface temperature has been investigated using a four-parameter modified power-law viscosity model. In this model, there are no physically unrealistic limits of zero or infinite viscosity that are encountered in the boundary-layer formulation for two-parameter Ostwald–de Waele power-law fluids. The leading-edge singularity is removed using a coordinate transformation. The boundary-layer equations are solved by an implicit finite-difference marching technique. Numerical results are presented for the case of a shear-thinning fluid. The results indicate that a similarity solution exists locally in a region near the leading edge of the plate, where the shear rate is not large enough to induce non-Newtonian effects; this similarity solution is identical to the similarity solution for a Newtonian fluid. The size of this region depends on the Prandtl number. Downstream of this region, the solution of the boundary-layer equations is nonsimilar. As the shear rate increases beyond a threshold value, the viscosity of the shear-thinning fluid is reduced. This leads to a decrease in the wall shear stress compared with that for a Newtonian fluid. The reduction in the viscosity accelerates the fluid in the region close to the wall, resulting in an increase in the local heat transfer rate compared with the case of a Newtonian fluid.

Non-Newtonian Natural Convection Along a Vertical Heated Wavy Surface Using a Modified Power-Law Viscosity Model

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
M. M. Molla ◽  
L. S. Yao
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Shear Rate ◽  
Power Law ◽  
Leading Edge ◽  
Numerical Results ◽  
Wavy Surface ◽  
Viscosity Model ◽  
Length Scale ◽  
Modified Power Law

Natural convection of non-Newtonian fluids along a vertical wavy surface with uniform surface temperature has been investigated using a modified power-law viscosity model. An important parameter of the problem is the ratio of the length scale introduced by the power-law and the wavelength of the wavy surface. In this model there are no physically unrealistic limits in the boundary-layer formulation for power-law, non-Newtonian fluids. The governing equations are transformed into parabolic coordinates and the singularity of the leading edge removed; hence, the boundary-layer equations can be solved straightforwardly by marching downstream from the leading edge. Numerical results are presented for the case of shear-thinning as well as shear-thickening fluid in terms of the viscosity, velocity, and temperature distribution, and for important physical properties, namely, the wall shear stress and heat transfer rates in terms of the local skin-friction coefficient and the local Nusselt number, respectively. Also results are presented for the variation in surface amplitude and the ratio of length scale to surface wavelength. The numerical results demonstrate that a Newtonian-like solution for natural convection exists near the leading edge where the shear-rate is not large enough to trigger non-Newtonian effects. After the shear-rate increases beyond a threshold value, non-Newtonian effects start to develop.

Mixed Convection Along a Semi-Infinite Vertical Flat Plate With Uniform Surface Heat Flux

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
S. Ghosh Moulic ◽  
L. S. Yao
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Leading Edge ◽  
Surface Heat ◽  
Convection Boundary Layer ◽  
Edge Region ◽  
Local Skin ◽  
Convection Boundary ◽  
Local Skin Friction ◽  
Vertical Flat Plate

Mixed-convection boundary-layer flow over a heated semi-infinite vertical flat plate with uniform surface heat flux, placed in a uniform isothermal upward freestream, has been investigated. Near the leading edge, the effect of natural convection can be treated as a small perturbation term. The effects of natural convection are accumulative and increase downstream. In the second region, downstream of the leading-edge region, natural convection eventually becomes as important as forced convection. The boundary-layer equations have been solved by an adaptive finite-difference marching technique. The numerical solution indicates that the series solution of the leading-edge region is included in that of the second region. This property is shared by many developing flows. However, the series solutions of local similarity or local nonsimilarity are only valid for very small distances from the leading edge. Numerical results for the local skin-friction factor, wall temperature, and local Nusselt number are presented for Pr=1 for a wide range of Grx*∕Rex5∕2, where Grx* is a local modified Grashof number and Rex is a local Reynolds number. The results indicate that cfxRex1∕2 and NuxRex–1∕2 increase monotonically with distance from the leading edge, where cfx is the local skin-friction factor and Nux is the local Nusselt number, and approach the free-convection limit at large values of Grx*∕Rex5∕2, although the velocity distribution differs from the velocity distribution in a free-convection boundary layer.

The Flow of Non-Newtonian Fluids on a Flat Plate With a Uniform Heat Flux

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
M. M. Molla ◽  
L. S. Yao
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Flat Plate ◽  
Power Law ◽  
Shear Thickening ◽  
Leading Edge ◽  
Newtonian Fluids ◽  
Uniform Heat Flux ◽  
Shear Stresses ◽  
Boundary Layer Equations

Forced convective heat transfer of non-Newtonian fluids on a flat plate with the heating condition of uniform surface heat flux has been investigated using a modified power-law viscosity model. This model does not restrain physically unrealistic limits; consequently, no irremovable singularities are introduced into a boundary-layer formulation for power-law non-Newtonian fluids. Therefore, the boundary-layer equations can be solved by marching from leading edge to downstream as any Newtonian fluids. For shear-thinning and shear-thickening fluids, non-Newtonian effects are illustrated via velocity and temperature distributions, shear stresses, and local temperature distribution. Most significant effects occur near the leading edge, gradually tailing off far downstream where the variation in shear stresses becomes smaller.

Viscous boundary layers in reversing flow

1976 ◽  
Vol 74 (1) ◽  
pp. 59-79 ◽  
Author(s):  
T. J. Pedley
Keyword(s):  
Boundary Layer ◽  
Shear Rate ◽  
Leading Edge ◽  
Wall Shear Rate ◽  
Viscous Boundary Layer ◽  
Large Molecules ◽  
Displacement Thickness ◽  
The Mean ◽  
Wall Shear ◽  
Viscous Boundary

The viscous boundary layer on a finite flat plate in a stream which reverses its direction once (at t = 0) is analysed using an improved version of the approximate method described earlier (Pedley 1975). Long before reversal (t < −t1), the flow at a point on the plate will be quasi-steady; long after reversal (t > t2), the flow will again be quasi-steady, but with the leading edge at the other end of the plate. In between (−t1 < t < t2) the flow is governed approximately by the diffusion equation, and we choose a simple solution of that equation which ensures that the displacement thickness of the boundary layer remains constant at t = −t1. The results of the theory, in the form of the wall shear rate at a point as a function of time, are given both for a uniformly decelerating stream, and for a sinusoidally oscillating stream which reverses its direction twice every cycle. The theory is further modified to cover streams which do not reverse, but for which the quasi-steady solution breaks down because the velocity becomes very small. The analysis is also applied to predict the wall shear rate at the entrance to a straight pipe when the core velocity varies with time as in a dog's aorta. The results show positive and negative peak values of shear very much larger than the mean. They suggest that, if wall shear is implicated in the generation of atherosclerosis because it alters the permeability of the wall to large molecules, then an appropriate index of wall shear at a point is more likely to be the r.m.s. value than the mean.

scholarly journals Two-Phase Dusty Fluid Flow Along a Rotating Axisymmetric Round-Nosed Body

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
Sadia Siddiqa ◽  
Naheed Begum ◽  
M. A. Hossain ◽  
Rama Subba Reddy Gorla
Keyword(s):  
Boundary Layer ◽  
Flow Characteristics ◽  
Leading Edge ◽  
Solid Particles ◽  
Dust Particles ◽  
Computational Domain ◽  
Two Phase ◽  
Carrier Fluid ◽  
Boundary Layer Equations ◽  
Implicit Finite Difference

This article is concerned with the class of solutions of gas boundary layer containing uniform, spherical solid particles over the surface of rotating axisymmetric round-nosed body. By using the method of transformed coordinates, the boundary layer equations for two-phase flow are mapped into a regular and stationary computational domain and then solved numerically by using implicit finite difference method. In this study, a rotating hemisphere is used as a particular example to elucidate the heat transfer mechanism near the surface of round-nosed bodies. We will investigate whether the presence of dust particles in carrier fluid disturbs the flow characteristics associated with rotating hemisphere or not. A comprehensive parametric analysis is presented to show the influence of the particle loading, the buoyancy ratio parameter, and the surface of rotating hemisphere on the numerical findings. In the absence of dust particles, the results are graphically compared with existing data in the open literature, and an excellent agreement has been found. It is noted that the concentration of dust particles’ parameter, Dρ, strongly influences the heat transport rate near the leading edge.

Trailing-edge stall

1970 ◽  
Vol 42 (3) ◽  
pp. 561-584 ◽  
Author(s):  
S. N. Brown ◽  
K. Stewartson
Keyword(s):  
Boundary Layer ◽  
Complete Solution ◽  
Leading Edge ◽  
Asymptotic Solutions ◽  
Angle Of Incidence ◽  
Trailing Edge ◽  
Boundary Layer Equations ◽  
Order Of Magnitude ◽  
Stall Angle ◽  
Fundamental Equations

A study is made of the laminar flow in the neighbourhood of the trailing edge of an aerofoil at incidence. The aerofoil is replaced by a flat plate on the assumption that leading-edge stall has not taken place. It is shown that the critical order of magnitude of the angle of incidence α* for the occurrence of separation on one side of the plate is$\alpha^{*} = O(R^{\frac{1}{16}})$, whereRis a representative Reynolds number, for incompressible flow, and α* =O(R−¼) for supersonic flow. The structure of the flow is determined by the incompressible boundary-layer equations but with unconventional boundary conditions. The complete solution of these fundamental equations requires a numerical investigation of considerable complexity which has not been undertaken. The only solutions available are asymptotic solutions valid at distances from the trailing edge that are large in terms of the scaled variable of orderR−⅜, and a linearized solution for the boundary layer over the plate which gives the antisymmetric properties of the aerofoil at incidence. The value of α* for which separation occurs is the trailing-edge stall angle and an estimate is obtained from the asymptotic solutions. The linearized solution yields an estimate for the viscous correction to the circulation determined by the Kutta condition.

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