The Onset of Longitudinal Vortices in Mixed Convective Flow over an Inclined Surface in a Porous Medium

1980 ◽  
Vol 102 (3) ◽  
pp. 544-549 ◽  
Author(s):  
C. T. Hsu ◽  
P. Cheng
Keyword(s):  
Porous Medium ◽  
Convective Flow ◽  
Free Stream ◽  
Free Stream Velocity ◽  
Critical Parameters ◽  
Stream Velocity ◽  
Local Similarity ◽  
Mixed Convective Flow ◽  
Inclined Surface ◽  
Vortex Disturbances

The conditions marking the onset of vortex instability in mixed convective flow over an inclined surface in a saturated porous medium are investigated by means of a linear stability analysis. The basic state is assumed to be the steady two-dimensional boundary layer flow. The three-dimensional perturbation equations are simplified on the basis of a scaling argument whereby most of the streamwise derivatives of the disturbances are found to be negligible. For vortex disturbances, the resulting simplified equations in terms of the amplitude are solved approximately by the local similarity method. The eigenvalue problem is solved numerically for the cases of (1) an inclined surface at constant wall temperature with free stream velocity at zero angle of incidence with the inclined surface and (2) an inclined surface with constant heat flux with free stream velocity at 45 deg with respect to the inclined surface. Both aiding and opposing external flows are considered. The critical parameters and the critical wave numbers of disturbances for the two cases are obtained. It is found that the effect of the external flow is to suppress the growth of vortex disturbances in both aiding and opposing flows. At the same value of the mixed convection parameter, the opposing flow is found to be more unstable than the aiding flow.

scholarly journals SCALING GROUP OF TRANSFORMATIONS FOR BOUNDARY LAYER STAGNATION‐POINT FLOW THROUGH A POROUS MEDIUM TOWARDS A HEATED STRETCHING SHEET

2006 ◽  
Vol 11 (2) ◽  
pp. 187-197 ◽  
Author(s):  
G. C. Layek ◽  
S. Mukhopadhyay ◽  
SK. A. Samad
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Stagnation Point ◽  
Stretching Sheet ◽  
Free Stream ◽  
Free Stream Velocity ◽  
Stagnation Point Flow ◽  
Stream Velocity ◽  
Scaling Group Of Transformations ◽  
Scaling Group

An analysis is performed to investigate the structure of the boundary layer stagnation‐point flow and heat transfer of a fluid through a porous medium over a stretching sheet. A scaling group of transformations is applied to get the invariants. Using the invariants, a third and a second order ordinary differential equations corresponding to the momentum and energy equations are obtained respectively. The equations are then solved numerically. It is found that the horizontal velocity increases with the increasing value of the ratio of the free stream velocity (ax) and the stretching velocity (ax). The temperature decreases in this case. At a particular point of the stretching sheet, the fluid velocity decreases or increases with the increase of the permeability of the porous medium when the free stream velocity is less or grater than the stretching velocity.

scholarly journals Boundary-Layer Type Solutions for Initial Platelet Activation and Deposition

2002 ◽  
Vol 4 (2) ◽  
pp. 95-108 ◽  
Author(s):  
T. David ◽  
P. G. de Groot ◽  
P. G. Walker
Keyword(s):  
Platelet Activation ◽  
Peclet Number ◽  
Free Stream ◽  
Free Stream Velocity ◽  
Stream Velocity ◽  
Bulk Fluid ◽  
Péclet Number ◽  
Activated Platelets ◽  
Activation Rate ◽  
Initial Adhesion

This paper presents, on the basis of high Peclet number, a mathematical model for the activation and initial adhesion of flowing platelets onto a surface. In contrast to past work, the model is applicable to general 2D and axi-symmetric flows where the wall shear stress is knowna priori. Results indicate that for high activation reaction rates there exist two layers, one containing only activated platelets and the other both activated and non-activated platelets. Fundamental relationships are proposed between the adhesion rate of platelets to the surface and the characteristic parameters of Peclet number and Reynolds number. Activation in the bulk fluid (blood) is characterised by the Damkohler number, which is a function of activation rate and the free-stream velocity. It is shown that, as the free-stream velocity varies, there exists a maximum of activated platelet flux to the wall for particular values of the velocity. These values, at which the maximum occur, are themselves functions of the platelet activation rate. As the free-stream velocity increases the activation of platelets ceases altogether and adhesion is reduced to a very small value strengthening the hypothesis of the correlation between atherogenesis/thrombogenesis and areas of low shear.

Free Convective Couette flow1of1a1Dusty1Fluid1through1a Porous Medium1with1Periodic1Permeability1in1the1Absence1of Electrically Magneto Hydro Dynamic Model

2021 ◽  
Vol 58 (2) ◽  
pp. 6072-6083
Author(s):  
K. Rajesh, A. Govindarajan, M. Vidhya
Keyword(s):  
Flow Field ◽  
Dynamic Model ◽  
Analytical Solutions ◽  
Free Stream ◽  
Porous Plate ◽  
Free Stream Velocity ◽  
Dust Particles ◽  
Stream Velocity

“The purpose of this investigation stands to discuss the effects of periodic permeability on1the; free1convective flow of a dusty viscous; incompressible1fluid through a1highly1porous1channel. The porous1medium is confined by an infinite perpendicular porous plate supercilious the free stream velocity to be uniform. Analytical solutions are gained for the dusty flow field, the1temperature field, the1skin1friction and the rate1of heat1transfer. when there is an increase in mass concentration1of dust1particles, it is found that the1velocity profile of fluid and dust particles reduces.”

scholarly journals Mixed Convective Flow of Micropolar Nanofluid across a Horizontal Cylinder in Saturated Porous Medium

2019 ◽  
Vol 9 (23) ◽  
pp. 5241 ◽  
Author(s):  
Ahmed M. Rashad ◽  
Waqar A. Khan ◽  
Saber M. M. EL-Kabeir ◽  
Amal M. A. EL-Hakiem
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Convective Flow ◽  
Volume Fraction ◽  
Saturated Porous Medium ◽  
Titania Nanoparticles ◽  
Flow And Heat Transfer ◽  
Micropolar Nanofluid ◽  
Mixed Convective Flow ◽  
The Impact

The micropolar nanofluids are the potential liquids that enhance the thermophysical features and ability of heat transportation instead of base liquids. Alumina and Titania nanoparticles are mixed in a micropolar fluid. The impact of convective boundary condition is also examined with assisting and opposing flows of both nanofluids. The main objective of this study is to investigate mixed convective flow and heat transfer of micropolar nanofluids across a cylinder in a saturated porous medium. Non-similar variables are used to make the governing equations dimensionless. The local similar and non-similar solutions are obtained by using the Runge-Kutta-Fehlberg method of seventh order. The impacts of various embedded variables on the flow and heat transfer of micropolar nanofluids are investigated and interpreted graphically. It is demonstrated that the skin friction and heat transfer rates depend on solid volume fraction of nanoparticles, Biot number, mixed convection, and material parameters.

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