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Taborek, J, xlv-lvi Taitel and Dukler flow regime map, for horizontal and inclined gas- liquid flows, Tamura et al correlation, for surface tension of mixtures, Taylor Forge method, for mechanical design of flanges, comparison with EN13445 method, Taylor series expansion, Teflon, use in heat transfer enhancement: TEMA (Tubular Exchanger Manufacturers Association): Temperature distribution: Tenders for heat exchangers, Terminal free fall velocity, in fluidization, Testing and inspection of heat exchangers: Tetrabromomethane: 1,1,2,2-Tetrachloroethane: Tetrachloroethylene: Tetradecane: Tetradecene: Tetrachlorodifluoroethane (Refrigerant 112): 1,1,1,2-Tetrafluoroethane (Refrigerant R134a): Tetrafluoromethane (Refrigerant 14): Tetrahydrofuran: 1,2,3,4-Tetramethylbenzene: 1,2,3,5-Tetramethylbenzene: 1,2,4,5-Tetramethylbenzene: Thermal conductivity: Thermal contact conductance (TCC), Thermal contact resistance (TCR), Thermal design, constructional features affecting, in shell-and-tube heat exchangers Thermal diffusivity: Thermal expansion coefficient: Thermal leakage in F-type shell-and-tube heat exchangers, Thermal mixing in plate heat exchangers, Thermal stress: Thermocal, heat transfer media, Thermodynamic cycles in refrigeration, Thermodynamic properties: Thermodynamic surface in radiative heat transfer, Thermoexel surface, for enhancement of boiling, Thermofluids, heat transfer medium, Thermosiphon Theta-NTU method: Thickness of boundary layers (displacement, momentum, energy, density, temperature), Thin-wall-type expansion bellows, Thiophene: Thome, J R Three-phase flows: Tie rods in shell-and-tube heat exchangers, Tinker method for shell-side heat transfer in shell-and-tube heat exchangers, Titanium and titanium alloys, T-junctions, loss coefficients in, Tolerances Toluene: m-Toluidine: Tong F-factor method, for critical heat flux with nonuniform heating, Tooth, A S, Total emissivity in gases, Transcendental equations in transient conduction, Transient behavior: Transition boiling: Transition flow, heat transfer in free convective flow over vertical surfaces in, Transitional flow, in combined free and forced convection, Transmission of thermal radiation in solids: Transmissivity of solids: Transport properties: Transverse flow, combined free and forced convection in, Treated surfaces, for augmentation of heat transfer, Triangular duct: Triangular fins, in plate fin exchangers, Triangular relationship, in annular gas-liquid flow, Tribromomethane: 1,1,1-Trichloroethane (Refrigerant 140a): Trichloroethylene: Trichlorofluoromethane (Refrigerant 11) Trichloromethane (Chloroform) (Refrigerant 20): 1,1,2-Trichlorotrifluoroethane (Refrigerant 113): Tridecane: Tridecene: Triethylamine: 1,1,1-Trifluoroethane (Refrigerant 143a): Trifluoromethane (Refrigerant 23): Trimethylamine: 1,2,3-Trimethylbenzene: 1,2,4-Trimethylbenzene: 1,3,5-Trimethylbenzene: 2,2,4-Trimethylpentane (Isooctane): Triphenylmethane: Triple interface (gas/solid/liquid), True temperature difference, in double pipe exchangers, Truelove, J S, Tsotsas, E Tube-baffle damage, in heat exchangers, Tube banks, finned: Tube banks, plain: Tube banks, roughened tubes, effect of roughness on Euler number in, Tube bundles: Tube counts, in shell-and-tube heat exchangers: Tube end attachment, in shell-and-tube heat exchangers, Tube inserts, heat exchangers with, Tube-in-plate extended surface configurations, fin efficiency of, Tube plates, in shell-and-tube heat exchangers: Tube rupture in shell-and-tube heat exchangers, Tube-to-tubesheet attachment, in shell-and-tube heat exchangers, Tubes: Tucker, R J, Tunnel dryer, Turbine exhaust condensers: Turbines, lost work in Turbulence: Turbulent boundary layers: Turbulent buffeting, as source of tube vibration, Turbulent energy, integral equation for, Turbulent flow: Turnarounds, in heat exchangers, Turner, C W, Twisted tapes: Twisted tube heat exchangers, Twisted tubes Two-equation models, for turbulent boundary layers, Two-phase loop with capillary pump, Two-phase flows:
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Forced Convection in Ducts

DOI 10.1615/hedhme.a.000168

2.5.1 Forced convection in ducts

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 = uρd /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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