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A B C D E F G H I J K L M N O P
Packaged units, specification of, Packing characteristic, in cooling towers, Packings, for cooling towers Packings, for fixed beds: Packinox heat exchanger, Paints, spectral characteristics of reflectance of surfaces treated with, Palen, J W Panchal, C B, Paraffins, normal and isonormal: Paraldehyde: Parallel channel instability, in condensers, Partial boiling in subcooled forced convective heat transfer, Participating media, radiation interaction in, Particle convective component, in heat transfer from fluidized beds, Particle emissivity, Particle Reynolds number in fixed beds, Particles: Particulate fluidization, Particulate fouling, Pass arrangements, in plate heat exchangers, Passes, tube side, Passive methods, for augmentation of heat transfer, passive systems for: PD5500 mechanical design of shell-and-tube heat exchangers to, Peacock, D K, Pearson number, Peclet number Peng-Robinson equation of state, application to hydrocarbons, Penner's rule, in absorption of radiation by gases, Pentachloroethane (Refrigerant 120): Pentadecane: Pentadecene: Pentadiene 1, 2: Pentadiene 1, trans 3: Pentadiene 1, 4: Pentadiene 2-3: Pentafluoroethane (Refrigerant 125) Pentamethylbenzene: Pentane: Pentanoic acid: 1-Pentanol: 1-Pentene: cis-2-Pentene: trans-2-Pentene: Pentylacetate: Pentylbenzene: Pentylcyclohexane: Pentylcyclopentane: Pentylcyclopropane, liquid properties, Perforated fins, in plate fin heat exchangers, Perforated plates, loss coefficients in, Periodic operation, of regenerator, Periodic variations in temperature, thermal conduction in bodies with, PFR correlation, for heat transfer in high fin tube banks, Pharmaceutical industry, fouling of heat exchangers in, Phase change materials, in augmentation of heat transfer, Phase change number, Phase equilibrium: Phase inversion Phase separation, as source of corrosion problems, Phenol: Phenols: Phenylhydrazine: Phonons, in thermal conductivity of solids, Phosgene: Physical properties: Pi theorum, in dimensional analysis, Pinch analysis, for heat exchanger network design, Pioro, I L Pioro, LS, Pipe leads, Piperidine: Pipes, circular: Pipes, noncircular: Piping components: Pitting corrosion, in stainless steels, Planck's constant, Planck's law, for spectral distribution of blackbody radiation, Plane shells, steady-state thermal conduction in, Plastic deformation Plate fin heat exchangers Plate fins, efficiency, Plate heat exchangers: Plate evaporator Plates: Plug flow: Plug flow model, for furnaces, Pneumatic conveyance, Pneumatic conveying dryer, P-NTU method: Polarization, of thermal radiation, Polyglycols, as heat transfer media, Polymers: Pool boiling, Porous surfaces: Port arrangements, in plate heat exchangers, Portable fouling unit, Poskas, P, Postdryout heat transfer: Powders: Power law fluid (non-Newtonian), Power plant: Prandtl number Precipitation (crystallization) fouling, Precipitation hardening, of stainless steels, Pressure coefficient: Pressure control of condensers, Pressure drop: Pressure gradient: Pressure, specification of in mechanical design to EN13445, Pressure testing, Pressure vessels, principle codes for, Pressurised water reactor, fouling in, Printed circuit heat exchanger, Problem table algorithm, in pinch analysis, Process heaters: Progressive plastic deformation Prolate spheroids, free convective heat transfer from, Promoters, in dropwise condensation, Propadiene: Propane: 1-Propanol: 2-Propanol: Propeller agitator, Property ratio method, for temperature dependent physical property Propionaldehyde: Propionic acid: Propionic anhydride: Proprionitrile: Propyl acetate: Propylamine: Propylbenzene: Propylcyclohexane: Propylcyclopentane: Propylene: 1,3-Propylene glycol: Propylene oxide: Propyl formate: Propyl propionate: Pseudo-boiling in supercritical fluids, Pseudo-film boiling in supercritical fluids, Pseudocritical pressure, Pseudocritical tempertaure, Pugh, S F Pulp and paper industry, fouling of heat exchangers in, Pulsations, use in augmentation of heat transfer, Pulverized fuel water-tube boiler, Pumping, lost work in, Pushkina and Sorokin correlation, for flooding in vertical tubes, Pyramid, free convective heat transfer from, Pyridine:
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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 fRe are independent of Reynolds number. But Nu and fRe 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 αA 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

ajH and jT for Pr = 0.7. T constant temperature. H heat flux, heat flux with uniform peripheral temperature.
GeometryNuHNuTfReK(∞)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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