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A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Lamella heat exchangers, Laminar flow:
in circular pipes, combined free and forced convective heat transfer in condensation in vertical surfaces, in ducts, characteristic of plate fin heat exchangers,
Laminar Flow Surfaces
heat transfer in ducts in heat transfer in free convection on a vertical surface in, in cross flow, in longitudinal flow, in noncircular pipes,
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 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:
in circular pipes, combined free and forced convective heat transfer in condensation in vertical surfaces, in ducts, characteristic of plate fin heat exchangers,
Laminar Flow Surfaces
heat transfer in ducts in heat transfer in free convection on a vertical surface in, in cross flow, in longitudinal flow, in noncircular pipes,
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 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 Laminar flow: in ducts, characteristic of plate fin heat exchangers,
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Laminar Flow Surfaces

DOI 10.1615/hedhme.a.000300



3.9.5 Laminar flow in plain surface geometries

It was previously noted that very compact surfaces (small hydraulic diameter) may operate at Reynolds numbers well within the laminar flow region. In the laminar regime, surface geometries designed to produce boundary layer interruptions may be of little benefit. Therefore, plain fin surfaces are likely candidates for very compact designs operating in the laminar regime. Laminar flow plate-fin geometries are also used in rotary regenerators, discussed in Section 3.15. For fully developed laminar flow, Nu and f Re are independent of Reynolds number. But Nu and f Re are dependent on the cross-sectional shape of the flow channel. Because of the small hydraulic diameter of the flow channels, their L /Dh may be sufficiently large that fully developed laminar flow solutions are applicable. For most channel shapes. the mean Nusselt number and friction factor will be within 10% of the fully developed for gases if L /Dh > 0.2 Re.

Table 1 [from Webb and Kim (2005)] gives fully developed laminar flow solutions for 11 channel shapes of interest in compact heat exchanger design. The tables give NuH  (constant heat input per unit length with uniform peripheral temperature) and NuT  (constant wall temperature). The ratio j /f (for Pr = 0.7) is proportional to the required flow channel frontal area for a specified α A and friction power. The hydraulic entrance length Lhy+ = (X /Dh) /Re is the dimensionless length required for the centerline velocity to attain 99% of its fully developed value. The constant K(∞) defines the pressure drop increment to be added to account for the increased friction in the flow development region. The pressure drop, accounting for the flow development region, is

\[\label{eq1} \Delta p=\left[\frac{4f_{fd}L}{D_{h}}+K(\infty)\right]\frac{G^{2}_{c}}{2\rho} \tag{1}\]

Table 1 Fully developed laminar flow solutions a

a jH and jT for Pr = 0.7. T ≈ constant temperature. H ≈ heat flux, ≈ heat flux with uniform peripheral temperature.
GeometryNuHNuTf ReK(∞)jH /fjT /fLhy+
     8.2357.541240.6860.3860.3540.0056
  6.4905.59720.5850.8790.3550.3060.0094
  6.0495.13719.7020.9450.3460.2940.0110
  5.3314.43918.2331.0760.3290.2740.0147
      4.3643.65716.001.240.3070.2580.038
  4.1233.39115.5481.3830.2990.2450.0255
  3.6083.09114.2271.5520.2860.2360.0324
  3.1112.4713.3331.8180.2630.2090.0398
  3.0142.3912.6301.7390.2690.2140.0408
  2.882.2213.0261.9910.2490.1920.0443
2.601.9912.6222.2360.2320.1780.0515

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