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Lamella heat exchangers, Laminar flow: Laminar flow control, of boundary layers, Lancaster, J F, Langelier index for water quality, Large eddy simulation, in prediction of turbulent boundary layers, Laws for turbulent flows: Layers of fluid, free convection heat transfer in, Le Fevre equations for free convective heat transfer, Leakage between streams, in shell-and-tube heat exchangers Leakage effects, on heat transfer and pressure drop in shell-and-tube heat exchangers, Leaks, in heat exchanger, sealing by explosive welding, Lebedev, M E, Lee and Kesler equation, for vapour pressure, L-footed fins, Lessing rings, characteristic of, as packings for fixed beds, Li equation, for critical temperature of mixtures, Lienhard and Dhir analysis of critical heat flux in pool boiling, Lienhard and Eichhorn criterion, for transition in critical heat flux mechanism in crossflow over single tube, Lift force: Liley, P E, Limb, D, Limpet coils: Linnhoff, B, Liquefaction, exergy analysis of, Liquid fluidized beds, Liquid fuels, properties of, Liquid hold-up, Liquid-liquid-gas flow, Liquid-liquid flow, Liquid metals: Liquid sheets, in direct contact heat transfer, Liquid-solid interfaces, fouling at, Liquids: Lister, D H, Local conditions hypothesis, for critical heat flux in flow boiling, Lockhart and Martinelli correlations: Lodge's rubberlike liquid (non-Newtonian), Logarithmic law region, Logarithmic mean temperature difference
Balance equations applied to complete equipment Forced Convection in Ducts
Longitudinal flow and heat transfer in tube banks, Long-tube vertical evaporator, Loss coefficient, Lost work in unit operations/exergy analysis, Louvered fins, in plate fin exchangers, Low-alloy steels: Low-finned tubes: Low-nickel steels, Lubricants, physical properties: Lucas methods

Index

HEDH
A B C D E F G H I J K L
Lamella heat exchangers, Laminar flow: Laminar flow control, of boundary layers, Lancaster, J F, Langelier index for water quality, Large eddy simulation, in prediction of turbulent boundary layers, Laws for turbulent flows: Layers of fluid, free convection heat transfer in, Le Fevre equations for free convective heat transfer, Leakage between streams, in shell-and-tube heat exchangers Leakage effects, on heat transfer and pressure drop in shell-and-tube heat exchangers, Leaks, in heat exchanger, sealing by explosive welding, Lebedev, M E, Lee and Kesler equation, for vapour pressure, L-footed fins, Lessing rings, characteristic of, as packings for fixed beds, Li equation, for critical temperature of mixtures, Lienhard and Dhir analysis of critical heat flux in pool boiling, Lienhard and Eichhorn criterion, for transition in critical heat flux mechanism in crossflow over single tube, Lift force: Liley, P E, Limb, D, Limpet coils: Linnhoff, B, Liquefaction, exergy analysis of, Liquid fluidized beds, Liquid fuels, properties of, Liquid hold-up, Liquid-liquid-gas flow, Liquid-liquid flow, Liquid metals: Liquid sheets, in direct contact heat transfer, Liquid-solid interfaces, fouling at, Liquids: Lister, D H, Local conditions hypothesis, for critical heat flux in flow boiling, Lockhart and Martinelli correlations: Lodge's rubberlike liquid (non-Newtonian), Logarithmic law region, Logarithmic mean temperature difference
Balance equations applied to complete equipment Forced Convection in Ducts
Longitudinal flow and heat transfer in tube banks, Long-tube vertical evaporator, Loss coefficient, Lost work in unit operations/exergy analysis, Louvered fins, in plate fin exchangers, Low-alloy steels: Low-finned tubes: Low-nickel steels, Lubricants, physical properties: Lucas methods
M N O P Q R S T U V W X Y Z
L Logarithmic mean temperature difference
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Forced Convection in Ducts

DOI 10.1615/hedhme.a.000168

2.5.1 Forced convection in ducts

Volker Gnielinski

A. Introduction

When fluids flow at very low velocities, all the individual particles are flowing in parallel lines. This type of flow is called laminar flow. If a fluid stream enters a duct with a uniform velocity a velocity profile develops as the fluid moves down the tube, with the velocity at the duct wall being zero. At a sufficient distance downstream from the inlet, the velocity pattern becomes fixed. The shape of the velocity distribution curve is parabolic for flow in a tube or between parallel plates.

If the velocity of the fluid is gradually increased, there will be a point at which the fluid no longer flows in parallel lines, but by a series of eddies that result in a complete mixing of all parts of the flow except those immediately adjacent to the wall. This type of flow is called turbulent flow. The Reynolds number at which the flow changes from laminar to turbulent is the "critical Reynolds number" Re, where Re = u ρ d /η where u is the fluid average velocity, ρ its density, η its viscosity and d the channel equivalent diameter. The value of the critical Reynolds number in round tubes is between 2,100 and 2,300. In long rectangular ducts and annular spaces, the transition from laminar to turbulent flow also starts at a Reynolds number of 2,100 when the hydraulic diameter of the duct is used as the characteristic geometric dimension in calculating the Reynolds number.

At Reynolds numbers greater than 104, the flow is fully turbulent. Between the lower and upper limits lies the zone of transition from laminar to turbulent flow. These limits are affected by the type of entry, initial disturbances in the fluid, roughness, and so on.

If the duct wall is at a temperature different from that of the fluid, heat will be transferred and a temperature profile will develop in the fluid. At a sufficient distance from the beginning of heating or cooling, the temperature profile becomes fully developed and therefore the heat transfer coefficient is constant. The rate of heat transfer is always greater in turbulent flow.

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