Circular tube, convection

Table 3. Correlations for Convective Heat-Transfer and Friction Coefficients for Circular Tube Flow ...

A variety of studies can be found in the literature for the solution of the convection heat transfer problem in micro-channels. Some of the analytical methods are very powerful, computationally very fast, and provide highly accurate results. Usually, their application is shown only for those channels and thermal boundary conditions for which solutions already exist, such as circular tube and parallel plates for constant heat flux or constant temperature thermal boundary conditions. The majority of experimental investigations are carried out under other thermal boundary conditions (e.g., experiments in rectangular and trapezoidal channels were conducted with heating only the bottom and/or the top of the channel). These experiments should be compared to solutions obtained for a given channel geometry at the same thermal boundary conditions. Results obtained in devices that are built up from a number of parallel micro-channels should account for heat flux and temperature distribution not only due to heat conduction in the streamwise direction but also conduction across the experimental set-up, and new computational models should be elaborated to compare the measurements with theory. 

Convective heat transfer to fluid inside circular tubes depends on three dimensionless groups the Reynolds number. Re = pdtu/ii, the Prandtl number, Pr = Cpiilk where k is the thermal conductivity, and the length-to-diameter ratio, L/D. These groups can be combined into the Graetz number, Gz = RePr4/L. The most commonly used correlations for the inside heat transfer coefficient are... 

A transparent gas flows into and out of a black circular tube of length L and diameter D. The gas has a mean velocity um, specific heat at constant pressure cp and density p. The wall of the tube is thin, and the outer surface is insulated. The tube wall is heated electrically and a uniform input of heat is provided per unit area, per unit time. Determine the local wall temperature distribution along the tube length. Assume that the convective heat transfer coefficient h between the gas and the inside of the tube is constant. 

A circumferential fin of rectangular profile is constructed of I percent carbon steel and attached to a circular tube maintained at I50°C. The diameter of the fin is 5 cm, and the length is also 5 cm with a thickness of 2 mm. The surrounding air is maintained at 20°C and the convection heat-transfer coefficient may be taken as 100 W/m2 °C. Calculate the heat lost from the fin. 

The dispersion of a non-reactive solute in a circular tube of constant cross-section in which the flow is laminar is described by the convective-diffusion equation... 

No. 67016 (1967) Forced convection heat transfer in circular tubes. Part I, turbulent flow. 

No. 68007 (1968) Forced convection in circular tubes. Part III, further data for turbulent flow. 

Heat transfer rate through the wall of a circular tube with convection acting on the outer surface is given per unit of its length by... 

Now consider a fluid at a uniform temperature entering a circular tube whose surface is maintained at a different temperature. This time, the fluid particles in the layer in contact with the surface of the tube assume the surface temperature. Tins initiates convection heat transfer in the tube and Ihe development of a thermal hoimdaiy layer along the tube. The thickness of this boundary layer also increases in tfle flow direction until Ihe boundary layer reaches the tube center and thus fills the entire tube, as sliown in Fig. 8-7. 

SOLUTION Water is healed by steam in a circular tube. The tube length required to heat the water to a specified temperature is to be determined. Assumptions 1 Steady operating conditions exist. 2 Fluid properties are constant. 3 The convection heat transfer coefficient is constant. 4 The conduction resistance of copper tube is negligible so that (he inner surface temperature of the tube is equal to the condensation temperature of steam. 

C Consider laminar forced convection in a circular tube. Will the heal flux be higher near the inlet of the tube or near the... 

Ameel, T.A., Wang, X., Barron, R.F. and Warrington, R.O., Laminar Forced Convection in a Circular Tube with Constant Heat Flux and Slip Flow, Mieroseale Ther-mophys. Eng, 1(4), 1997, 303-320. 

The correct solution of heat convection in circular tubes for slip flow, taking into account both - the velocity... 

Heat convection for gaseous flow in a circular tube in the slip flow regime with uniform temperature boundary condition was solved in [23]. The effects of the rarefaction and surface accommodation coefficients were considered. They defined a fictitious extrapolated boundary where the fluid velocity does not slip by scaling the velocity profile with a new variable, the shp radius, pj = l/(l + 4p.,Kn), where is a function of the momentum accommodation coefficient, and defined as p, =(2-F,j,)/F,j,. Therefore, the velocity profile is converted to the one used for the... 

Let us discuss qualitative specific features of convective heat and mass transfer in a turbulent flow through a circular tube and plane channel in the region of stabilized flow. Experimental evidence indicates that several characteristic regions with different temperature profiles can be distinguished. At moderate Prandtl numbers (0.5 < Pr < 2.0), the structure and sizes of these regions are similar to those of the wall layer and the core of the turbulent stream considered in Section 1.6. 

Let us briefly consider convective mass transfer accompanied by a surface reaction in a circular tube. Laminar steady-state fluid flow in a circular tube of radius a with Poiseuille velocity profile is outlined in Subsection 1.5-3. For... 

T.A. Ameel, R.F. Barron, X.M. Wang, and R.O. Warrington, Lantinar forced convection in a circular tube with constant heat flux and shp flow. Microscale Thermophysical Engineering 1, 303-320 (1997). 

Circular Isothermal Fins on a Horizontal Tube. Tsubouchi and Masuda [269] measured the heat transfer by natural convection in air from circular fins attached to circular tubes, as in the configuration shown in Fig. 4.23/ Correlations for the heat transfer from the tips of the fins (see the figure for definition), and from the cylinder plus vertical fin surfaces, were reported separately. 

J. A. Sabbagh, A. Aziz, A. S. El-Ariny, and G. Hamad, Combined Free and Forced Convection in Inclined Circular Tubes, J. Heat Transfer (98) 322-324,1976. 

H. H. Al-Ali, and M. S. Selim, Analysis of Laminar Flow Forced Convection Heat Transfer with Uniform Heating in the Entrance Region of a Circular Tube, Can. J. Chem. Eng., (70) 1101-1107, 1992. 

H. Miyazaki, Combined Free and Forced Convective Heat Transfer and Fluid Flow in a Rotating Curved Circular Tube, Int. J. Heat Mass Transfer (14) 1295-1309,1971. 

In regard to nonsteady tube flows. Mason et al. have observed both inward and outward radial migration of rigid, neutrally buoyant spheres in oscillatory (S9b, G9b) and pulsatile (Tl) flows in circular tubes at frequencies up to 3 cps, at which frequencies inertial effects are likely to be important. We refer here to inertial effects arising from the local acceleration terms in the Navier-Stokes equations, rather than from the convective acceleration terms. In the oscillatory case the spheres (a/R 0.10) attained equilibrium positions at about P = 0.85. Important Reynolds numbers here are those based upon mean tube velocity for one-half cycle and upon frequency. Nonneutrally buoyant spheres in oscillatory flow migrate permanently to the tube axis, irrespective of whether they are denser or lighter than the fluid (K4a). 

Ideally the output of a loop Injector used In liquid chromatography or flow Injection analysis would be a sharp concentration pulse. However, this Is unlikely to be the case because of various dispersive forces which act on the concentration plug. Convective flow under laminar conditions In a circular tube, such as the outlet tube of a loop Injector, tends to be much slower near the walls of the tube than In the center and this will distort the Initial shape of the Injected materials (8,9). In addition, radial and axial diffusion of material In the tube can alter its initial shape. The degree of dispersion can be evaluated (9) by the Peclet nusd>er (P,) and the reduced time (r). These values are defined as... 

The heating or cooling of process streams is frequently required. Chapter 6 discusses the fundamentals of convective heat transfer to non-Newtonian fluids in circular and non-circular tubes imder a range of boundary and flow conditions. Limited information on heat transfer from variously shaped objects - plates, cylinders and spheres - immersed in non-Newtonian fluids is also included here. 

Values of film transfer coefficients are usually obtained from correlations between dimensionless groups. For forced convection (turbulent flow) within circular tubes the relevant groups are ... 

T. A. Ameel, et at. Laminar forced convection in a circular tube with constant heat... 

In heat transfer in a fluid in laminar flow, the mechanism is one of primarily conduction. However, for low flow rates and low viscosities, natural convection effects can be present. Since many non-Newtonian fluids are quite viscous, natural convection effects are reduced substantially. For laminar flow inside circular tubes of power-law fluids, the equation of Metzner and Gluck (M2) can be used with highly viscous non-Newtonian fluids with negligible natural convection for horizontal or vertical tubes for the Graetz number Nq, > 20 and n > 0.10. 

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