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.

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.

scholarly journals Boundary layer flow of air over water on a flat plate

1995 ◽  
Vol 284 ◽  
pp. 159-169 ◽  
Author(s):  
John J. Nelson ◽  
Amy E. Alving ◽  
Daniel D. Joseph
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Initial Conditions ◽  
Leading Edge ◽  
Water Layer ◽  
Large Reynolds Number ◽  
Boundary Layer Equations ◽  
Numerical Studies ◽  
Air Blowing ◽  
Layer Flow

A non-similar boundary layer theory for air blowing over a water layer on a flat plate is formulated and studied as a two-fluid problem in which the position of the interface is unknown. The problem is considered at large Reynolds number (based on x), away from the leading edge. We derive a simple non-similar analytic solution of the problem for which the interface height is proportional to x1/4 and the water and air flow satisfy the Blasius boundary layer equations, with a linear profile in the water and a Blasius profile in the air. Numerical studies of the initial value problem suggest that this asymptotic non-similar air–water boundary layer solution is a global attractor for all initial conditions.

A theoretical investigation of disturbance amplification in external laminar natural convection

1968 ◽  
Vol 34 (3) ◽  
pp. 551-564 ◽  
Author(s):  
R. P. Dring ◽  
B. Gebhart
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Natural Convection ◽  
Amplitude Ratio ◽  
Low Frequency ◽  
Leading Edge ◽  
Convection Boundary Layer ◽  
Uniform Heat Flux ◽  
Laminar Natural Convection ◽  
Sommerfeld Equation

The nature of instability and disturbance amplification in the laminar natural convection boundary layer over a vertical flat surface with uniform heat flux has been theoretically investigated. The coupled Orr-Sommerfeld equation has been numerically integrated for a Prandtl number of 6·7, with the boundary condition that the disturbance heat flux be zero at the surface. The spatial amplification characteristics of disturbances convected downstream were analyzed, and constant amplification rate contours were determined. The relative amplification has been calculated from these contours and is presented in the form of amplitude ratio contours. An important feature of these results is that the low frequency disturbances, which become unstable first, amplify very slowly and also have wavelengths which are much longer than the distance to the leading edge. The higher frequency, shorter wavelength, disturbances amplify much faster and are, therefore, presumed to be the dominant ones in stability considerations. The nature of the velocity and temperature amplitudes and phase profiles across the boundary layer has also been examined.

Experimental study of heat transfer in the boundary layer of a flat plate with the impact of weak shock waves on the leading edge

2020 ◽  
Author(s):  
V. L. Kocharin ◽  
A. A. Yatskikh ◽  
D. S. Prishchepova ◽  
A. V. Panina ◽  
Yu. G. Yermolaev ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Experimental Study ◽  
Shock Waves ◽  
Flat Plate ◽  
Leading Edge ◽  
Weak Shock ◽  
The Impact
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