Analytical solutions for laminar flow in membrane channels with cylindrical symmetry: Single- and dual- membrane systems

2017 ◽  
Vol 523 ◽  
pp. 373-384 ◽  
Author(s):  
Sina Jahangiri Mamouri ◽  
Volodymyr V. Tarabara ◽  
André Bénard
Keyword(s):  
Laminar Flow ◽  
Analytical Solutions ◽  
Cylindrical Symmetry ◽  
Membrane Channels ◽  
Membrane Systems

Approximate analytical solution for the propagation of shock wave in a mixture of small solid particles and non-ideal gas: isothermal flow

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Gorakh Nath
Keyword(s):  
Shock Wave ◽  
Analytical Solutions ◽  
Order Approximation ◽  
Fluid Pressure ◽  
Strong Shock ◽  
Cylindrical Symmetry ◽  
Solid Particles ◽  
Approximate Analytical Solutions ◽  
Axis Of Symmetry ◽  
Physical Variables

Abstract This paper presents the development of mathematical model to obtain the approximate analytical solutions for isothermal flows behind the strong shock (blast) wave in a van der Waals gas and small solid particles mixture. The small solid particles are continuously distributed in the mixture and the equilibrium conditions for flow are maintained. To derive the analytical solutions, the physical variables such as density, pressure, and velocity are expanded using perturbation method in power series. The solutions are derived in analytical form for first approximation, and for second order approximation the set of differential equations are also obtained. The effects of an increase in the problem parameters value on the physical variables are investigated for first order approximation. A comparison is also, made between the solution of cylindrical shock and spherical shock. It is found that the fluid density and fluid pressure become zero near the point or axis of symmetry in spherical or cylindrical symmetry, respectively, and therefore a vacuum is created near the point or axis of symmetry which is in tremendous conformity with the physical condition in laboratory to generate the shock wave.

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.

scholarly journals Analytical solutions of heat transfer for laminar flow in rectangular channels

2014 ◽  
Vol 35 (4) ◽  
pp. 29-42 ◽  
Author(s):  
Witold Rybiński ◽  
Jarosław Mikielewicz
Keyword(s):  
Nusselt Number ◽  
Laminar Flow ◽  
Friction Factor ◽  
Cross Section ◽  
Constant Temperature ◽  
Analytical Solutions ◽  
Rectangular Cross Section ◽  
Temperature Profiles ◽  
Mathematical Form ◽  
Parallel Plates

Abstract The paper presents two analytical solutions namely for Fanning friction factor and for Nusselt number of fully developed laminar fluid flow in straight mini channels with rectangular cross-section. This type of channels is common in mini- and microchannel heat exchangers. Analytical formulae, both for velocity and temperature profiles, were obtained in the explicit form of two terms. The first term is an asymptotic solution of laminar flow between parallel plates. The second one is a rapidly convergent series. This series becomes zero as the cross-section aspect ratio goes to infinity. This clear mathematical form is also inherited by the formulae for friction factor and Nusselt number. As the boundary conditions for velocity and temperature profiles no-slip and peripherally constant temperature with axially constant heat flux were assumed (H1 type). The velocity profile is assumed to be independent of the temperature profile. The assumption of constant temperature at the channel’s perimeter is related to the asymptotic case of channel’s wall thermal resistance: infinite in the axial direction and zero in the peripheral one. It represents typical conditions in a minichannel heat exchanger made of metal.

scholarly journals Experimental evidence of velocity profile inversion in developing laminar flow using magnetic resonance velocimetry

2018 ◽  
Vol 851 ◽  
pp. 545-557 ◽  
Author(s):  
A. Reci ◽  
A. J. Sederman ◽  
L. F. Gladden
Keyword(s):  
Magnetic Resonance ◽  
Laminar Flow ◽  
Finite Difference ◽  
Velocity Profile ◽  
Experimental Evidence ◽  
Analytical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Magnetic Resonance Velocimetry

A discrepancy exists between the predictions of analytical solutions of approximate Navier–Stokes equations and numerical finite-difference solutions of the full Navier–Stokes equations regarding the development of laminar flow at the entrance to cylindrical pipes for Newtonian fluids. Starting from a uniform velocity profile at the entrance to the pipe, analytical solutions of approximate Navier–Stokes equations predict the velocity profile to have a maximum at the centre of the pipe at all times. In contrast, numerical finite-difference solutions of the full Navier–Stokes equations have suggested that the location of the velocity maximum moves from the wall towards the centre of the pipe at a short distance from the entrance, after which it remains at the centre of the pipe. This study presents the first experimental evidence of the moving velocity maximum from the wall towards the centre of the pipe. The initial uniform velocity profile was achieved by flowing the fluid through a monolith composed of narrow parallel channels and the flow development was investigated using magnetic resonance velocimetry. The experimentally observed variation of the position and size of the velocity maximum with the Reynolds number and the distance from the entrance to the pipe is shown to be in good agreement with the predictions of numerical finite-difference solutions of the full Navier–Stokes equations.

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