Start up Flow with Velocity slip in the Entrance Region of a Porous Circular Tube Start up Flow with Velocity slip in the Entrance Region of a Porous Circular Tube

1980 ◽  
Vol 30 (1) ◽  
pp. 1-8
Author(s):  
Om Prakash ◽  
S. C. Rajvanshi
Keyword(s):  
Circular Tube ◽  
Velocity Slip ◽  
Entrance Region ◽  
Start Up

Fluid flow in the entrance region of a circular tube

1968 ◽  
Vol 15 (1) ◽  
pp. 635-637 ◽  
Author(s):  
V. E. Gubin ◽  
V. S. Levin
Keyword(s):  
Fluid Flow ◽  
Circular Tube ◽  
Entrance Region

scholarly journals Heat transfer in the thermal entrance region of a flat duct

1975 ◽  
Vol 19 (2) ◽  
pp. 146-160 ◽  
Author(s):  
A. S. Jones
Keyword(s):  
Heat Transfer ◽  
Circular Tube ◽  
Fluid Velocity ◽  
Axial Direction ◽  
Entrance Region ◽  
Heat Transfer Mechanism ◽  
Axial Diffusion ◽  
Axial Temperature ◽  
Thermal Entrance Region ◽  
Thermal Entrance

AbstractThe problem of heat transfer in a duct or tube for large values of the Péclet number has traditionally been solved by assuming that diffusion in the axial direction is negligible. This approach was used by Graetz [2] for the circular tube and by Prins et al [5] for the flat duct to obtain a series solution for downstream temperature field.Since these series converge very slowly in the neighbourhood of the origin, some other approach is necessary in the thermal entrance region. This was supplied by Lévêque [3] and extended by Mercer [4] who matched the Lévêque solution to the eigenfunction expansion.In all these solutions it was assumed that the axial diffusion of heat was negligible, but this assumption is invalid close to the discontinuity, since in this region the axial temperature gradient is large and the fluid velocity is small, so that axial diffusion plays an important role.In this paper, the assumptions implicit in Lévêque's solution are re-examined, and the correct approximation in the neighbourhood of the discontinuity as well as the solution which matches this into Lévêque's solution are presented. In the first of these solutions, diffusion is the only heat-transfer mechanism, while in the matching solution diffusion and convection are in balance.The corresponding solutions for the case of prescribed flux on the boundary are also considered.

Pressure Drop and Flow Development in the Entrance Region of Microchannels With Second-Order Velocity Slip Condition and the Requirement for Development Length

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Baibhab Ray ◽  
Franz Durst ◽  
Subhashis Ray
Keyword(s):  
Shear Stress ◽  
Pressure Drop ◽  
Parallel Plate ◽  
Velocity Slip ◽  
Second Order ◽  
Entrance Region ◽  
Slip Condition ◽  
Local Velocity ◽  
Flow Development ◽  
Developing Region

Abstract In this investigation, Lfd* and Δp in the entrance region of circular and parallel plate microchannels have been determined for 10−2≤Re≤104 and 10−4≤Kn≤0.2, employing the second-order velocity slip condition at the wall with C1=1 and 0≤C2≤0.5. Results indicate that although local velocity slip at the wall is always higher than that for the fully developed section, local wall shear stress for higher Kn and C2 could be lower than its fully developed value, which is also more prominent for lower Re. Therefore, depending upon the operating condition, K(x) and Kfd could assume negative values, implying that pressure gradient in the developing region could even be less than that in the fully developed section. It has been further observed that both Lfd* and Kfd are characterized by the low and the high Re asymptotes, using which extremely accurate correlations have been proposed for both geometries.

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