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A B C D E F G H I J K L M N O P Q R
Rabas and Taborek correlation, for heat transfer in banks of low fin tubes, Rackett equation (modified) for liquid density Radiation: Radiation shields, in radiation heat transfer, Radiation source analysis, Radiative heat transfer: Radiators, automotive, construction, Radiometers, application in gas radiation property measurement, Radiosity, Stephan's law for, Radiosity-irradiation formulations in radiative heat transfer, Rankine cycle in refrigeration, Rao, B K Raoult's law for partial pressure, Rating of heat exchangers, Rayleigh instability, in free convection, Rayleigh number Reay, D Reboilers: Reciprocal mode integrating sphere, for reflection and transmission measurements in radiation, Rectangles: Rectangular ducts: Rectangular enclosures, free convective heat transfer in: Rectangular fins, for plate fin exchangers Reduced pressure, correlations for pool boiling using, Reference temperature: Refinery processes, fouling in, Reflection, of thermal radiation, from solid surfaces: Reflectivity, of solid surfaces, Reflectometer, heated cavity, Reflux condensers, Refractories, density of, Refractory surfaces, Refrigerants: Refrigerant 11 (Trichlorofluoromethane): Refrigerant 12 (Dichlorodifluoromethane): Refrigerant 13 (Chlorotrifluoromethane): Refrigerant 21 (Dichlorofluoromethane): Refrigerant 22 (Chlorodifluoromethane): Refrigerant 116: Refrigerant plant, entropy generation in, Refrigeration, heat transfer in, Regenerators and thermal energy storage, Regimes of heat transfer, in ducts, single phase flow,
Forced Convection in Ducts
Reidel method, for predicting enthalpy of vaporisation, Reinforcing rings, for expansion bellows, Relaminarization, of turbulent flow, Reichenberg method, for effect of pressure on gas viscosity, Relief system design for shell-and-tube heat exchangers with tube side failure, Removal of fouling deposits: Renewable fuels, properties of, Renotherm, heat transfer medium, Repair, of expansion bellows, Residence times, in dryers: Resistance network analysis, Resistance (thermal) due to fouling: Reversible (minimum) work, in Reynolds number, Reynolds stress models, for turbulence, Rheologically complex materials, properties of: Rheological properties of drag reducing agents Rheology, shear flow experiments used in, Rhine, J M, Ribatski, G, Riblets for drag reduction, Richardson number, Richie, J M, Ring cells, in free convection, RODbaffles, in tube bundles with longitudinal flow, Rod bundles: Rohsenow correlation, for nucleate boiling, Roll cells, in free convection, Roller expansion, of tubes into tube sheets, Rose, J W, Rossby number, Rotary dryer, Rotating drums, heat transfer to particle bed in, Rotating surface, in an annular duct Rotation, as device for heat transfer augmentation, Roughness, surface: Rough walled passages, radiative heat transfer down, Rubber (sponge) balls, in fouling mitigation, Ryznar index for water quality,
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R Regimes of heat transfer, in ducts, single phase flow,
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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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