Heat transfer local, defined

Individual Coefficient of Heat Transfer Because of the comphcated structure of a turbulent flowing stream and the impracti-cabifity of measuring thicknesses of the several layers and their temperatures, the local rate of beat transfer between fluid and solid is defined by the equations... 

In this table the parameters are defined as follows Bo is the boiling number, d i is the hydraulic diameter, / is the friction factor, h is the local heat transfer coefficient, k is the thermal conductivity, Nu is the Nusselt number, Pr is the Prandtl number, q is the heat flux, v is the specific volume, X is the Martinelli parameter, Xvt is the Martinelli parameter for laminar liquid-turbulent vapor flow, Xw is the Martinelli parameter for laminar liquid-laminar vapor flow, Xq is thermodynamic equilibrium quality, z is the streamwise coordinate, fi is the viscosity, p is the density, <7 is the surface tension the subscripts are L for saturated fluid, LG for property difference between saturated vapor and saturated liquid, G for saturated vapor, sp for singlephase, and tp for two-phase. 

When we want to look at the connection between the flow behavior and the amount of heat that is transferred into the fixed bed, the 3D temperature field is not the ideal tool. We can look at a contour map of the heat flux through the wall of the reactor tube. Fig. 19 actually displays a contour map of the global wall heat transfer coefficient, h0, which is defined by qw — h0(Tw-T0) where T0 is a global reference temperature. So, for constant wall temperature, qw and h0 are proportional, and their contour maps are similar. The map in Fig. 19 shows the local heat transfer coefficient at the tube wall and displays a level of detail that would be hard to obtain from experiment. The features found in the map are the result of the flow features in the bed and the packing structure of the particles. 

Kunii and Levenspiel (1991) identify two kinds of heat transfer coefficient to describe gas-particle heat transfer. The coefficient for a single particle, or local coefficient. If, is that pertaining to a single particle at high temperature Tj, introduced suddenly into a bed of cooler particles at a temperature and is defined by... 

The main difference between metals and polymers is related to the fact that transitions from one state to another in polymers occur (as a result of changing of environmental conditions, primarily temperature) not as jumps but continuously. This leads to the absence of a clearly defined line or transition front. Additionally, because of die low heat and temperature conductivity of polymeric materials, a change in material properties may take place over a large volume,or even simultaneously throughout the whole mass of an article, although the local transition rates and degrees of conversion may be different. Thus it is necessary to develop a macrokinetic model of the transition. This model must describe the combined effects of non-stationary heat transfer and reaction kinetics and is used to determine the temperature and conversion fields. 

Eq. (1.2) defined the local heat transfer coefficient, ht in terms of the local rate of heat transfer rate per unit area, the local wall temperature and, in those cases where it is changing, the local fluid temperature. In general, all of these quantities, i.e., h, q, Tw, and Tf, vary with position on the surface. For the majority of applications it is convenient to define, therefore, a mean or average heat transfer coefficient, h, such that if Q is the total heat transfer rate from the entire surface of area A then ... 

This can be written in terms of a local heat transfer coefficient which, since qx is the local heat rate from the film to the wall, is conventionally defined by ... 

Figure 7 shows the variation of the two-phase heat transfer coeffient (htp) as a function of the local subcooling parameter (Sc), for subcooled flow boiling. The subcooling parameter is defined as. 

The temperature of the fluid t F far away from the wall, appears in (1.23), the definition of the local heat transfer coefficient. If a fluid flows around a body, so called external flow, the temperature t F is taken to be that of the fluid so far away from the surface of the body that it is hardly influenced by heat transfer, i) F is called the free flow temperature, and is often written as diDC. However, when a fluid flows in a channel, (internal flow), e.g. in a heated tube, the fluid temperature at each point in a cross-section of the channel will be influenced by the heat transfer from the wall. The temperature profile for this case is shown in Figure 1.8. i) F is defined here as a cross sectional average temperature in such a way that t F is also a characteristic temperature for energy transport in the fluid along the channel axis. This definition of F links the heat flow from the wall characterised by a and the energy transported by the flowing fluid. 

The purpose of the study of irreversible thermodynamics is to extend classical thermodynamics to include systems in which irreversible processes (e.g., diffusion and heat transfer) are taking place. Such an extension is made possible by assuming that for systems not too far from equilibrium the postulate of local equilibrium applies Departures from local equilibrium are sufficiently small that all thermodynamic state quantities may be defined locally by the same relations as for systems at equilibrium. ... 

The diffusion cloud chamber has been widely used in the study of nucleation kinetics it is compact and produces a well-defined, steady supersaturation field. The chamber is cylindrical in shape, perhaps 30 cm in diameter and 4 cm high. A heated pool of liquid at the bottom of the chamber evaporates into a stationary carrier gas, usually hydrogen or helium. The vapor diffuses to the top of the chamber, where it cools, condenses, and drains back into the pool at the bottom. Because the vapor is denser than the carrier gas, the gas density is greatest at the bottom of the chamber, and the system is stable with respect to convection. Both diffusion and heat transfer are one-dimensional, with transport occurring from the bottom to the top of the chamber. At some position in the chamber, the temperature and vapor concentrations reach levels corre.sponding to supersaturation. The variation in the properties of the system are calculated by a computer solution of the onedimensional equations for heat conduction and mass diffusion (Fig. 10.2). The saturation ratio is calculated from the computed local partial pressure and vapor pressure. 

Vibrational modes perpendicular to the chain backbone arc only weakly coupled across neighboring chains by the various types of nonbonded interchain interactions. Heat transfer via backbone vibrations is therefore much more effective than heat transfer via vibrational modes perpendicular to the backbone. X is therefore a locally anisotropic property, as defined in Section 2.D. It is necessary to separate the connectivity indices into backbone and side group components because of this local anisotropy. 

Gy is the mass velocity (mass flnx) of the entering fluid, defined as the mass flow rate in kg/s (lb j/h) divided by the cross-sectional area of the tube or the flow channel. The snbscript i refers to the physical properties of the condensate and v to the vapor. Equation (6.86a) may be nsed to calcnlate the local condensing heat-transfer coefficient at any quality x by replacing the bracketed term by... 

Now, we wish to determine the local heat transfer from the boundary of the semiinfinite solid (or an inviscid fluid). In Chapter 1 we defined convection as... 

The quantity U, defined by Eq. (li.9) as a proportionality factor between dqfdA and A7 is called the local overall heat-transfer coefficient. 

To further characterize the laminar thin-layer heat transfer, it is helpful to introduce the idea of the local and average conduction layer thicknesses, and A, respectively A is defined... 

The authors of most experimental studies and analyses have focused their attention on the local values defined in Fig. 4.44. Churchill [55] fitted the local Nu values for assisting flow using Eq. 4.159 with m = 3 and with each average value on the right side of the equation replaced by its local value counterpart. Mucoglu and Chen [201] have solved the inclined flat plate problem for uniform wall temperature and heat flux and have presented local heat transfer results for mixed convection. 

The circumferentially averaged but axial local heat transfer coefficient hx is defined by... 

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