Laminar flow and convection

This is an important phenomenon in analyzing the morphology of crystals. 

Laminar flow, which is a directional flow, changes into turbulent flow when the critical Reynolds number (Re) exceeds 200. When there is a flow of solution around 

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Leal, L.G. (1992), Laminar Flow and Convective Transport Processes , Butterworth-Heinemann, Boston. 

A detailed discussion of this approximation and the asymptotic conditions required for it to be accepted may be found in Chap. 12, Section D, of the predecessor to this book L. G. Leal, Laminar Flow and Convective Transport Processes (Butterworth-Heinemami, Boston, 1992). 

Introductory Systems Analysis for Process Engineers E. Bruce Nauman Laminar Flow and Convective Transport Processes L. Gary Leal... 

Sedov LI (1993) Similarity and dimensional methods in mechanics, 10th edn. CRC, Boca Raton Shah RK, London AL (1978) Laminar flow forced convection in duct. Academic, New York Shapiro AK (1953) The dynamics and thermodynamics of compressible fluid flow. Wiley, New York... 

As is well known, fluid dynamics is the study of motion and transport in liquids and gases. It is primarily concerned with macroscopic phenomena in nonequilibrium fluids and covers such behavior as diffusion in quiescent fluids, convection, laminar flows, and fully developed turbulence. 

R.K. Shah and A.L. London, Laminar Flow Forced Convection in Ducts, Academic Press, New York, 1978. 

Shome, B. and Jensen M.K., Mixed Convection Laminar Flow and Heat Transfer of Liquids in Isothermal Horizontal Circular Ducts , Int. J. of Heat and Mass Transfer, Vol. 38, No. 11. pp. 1945-1956, 1995. 

Shah, R.K. and London, A.L. Laminar flow forced convection in ducts. Journal of Heat Transfer, 1974, 96, 159. 

S. Kakac and Y. Yener, Convective Heat Transfer (CRC Press, Florida, 1994). R.K. Shah and A.L. London, Laminar flow forced convection in ducts, Advances in Heat Transfer, edited by T.F.Jr. Irvine, and J.P. Hartnett (Academic Press, New York 1978), pp. 78-152. 

Bau H H and Wang Y-Z 1991 Chaos a heat transfer perspective Annual Reviews in Heat Transfer vol IV, ed C L Tien, pp 1-50 Ott E, Grebogi C and Yorke J A 1990 Controlling chaos Phys. Rev. Lett. 64 1196-9 Shah R K and London A L 1978 Laminar Flow Forced Convection in Ducts (New York Academic)... 

When symmetric membranes are used or when enzymes are fed to the spongy part of asymmetric membranes, enzyme immobilization results in either a uniform fixation of enzymes throughout the membrane wall, or in the formation of a carrier-enzyme insoluble network in the sponge of the membrane. Mass transfer through this solid phase must therefore be taken into account. A theoretical model neglecting radial convective transport and the dense layer in asymmetric membranes is available in the literature.81 The reacting solution is still assumed to be fed to the core of the hollow fibers. Steady state, laminar flow, and isothermal conditions are assumed. Moreover, the enzymes are assumed to be uniformly distributed and the membrane wall curvature is neglected. Differential dimensionless mass balance equations can be written as follows ... 

Convection. Stirring or hydrodynamic transport. Generally fluid flow occurs because of natural convection (convection caused by density gradients) md forced convection, and may be characterized by stagnant regions, laminar flow, and turbulent flow. 

H. H. Al-Ali, and M. S. Selim, Analysis of Laminar Flow Forced Convection Heat Transfer with Uniform Heating in the Entrance Region of a Circular Tube, Can. J. Chem. Eng., (70) 1101-1107, 1992. 

T. V. Nguyen, and I. L. MacLaine-Cross, Simultaneously Developing Laminar Flow, Forced Convection in the Entrance Region of Parallel Plates, / Heat Transfer, (113) 837-842,1991. 

In this section we consider what happens when two miscible liquids are contacted and mixed in a flow. The equilibrium for such a case is simply that of one phase uniformly distributed throughout the second, so any phenomena of interest are unsteady ones. The process whereby one phase is distributed in the second is termed miscible dispersion. In a laminar flow both convection and molecular diffusion will contribute to this dispersion. Other factors can also enter, including the geometry and any forced unsteadiness. 

Symmetrical growth and collapse curves of the sort pictured herein are difficult to obtain by a laminar-flow heat-convection model. This is because the heat equation is not symmetric with respect to time reversal. On the other hand, such symmetry is observed in the growth and collapse of cavitation bubbles, and indeed, is implied by the extended Rayleigh equation (Bll) ... 

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