Heat transfer number Definition

The value of tire heat transfer coefficient of die gas is dependent on die rate of flow of the gas, and on whether the gas is in streamline or turbulent flow. This factor depends on the flow rate of tire gas and on physical properties of the gas, namely the density and viscosity. In the application of models of chemical reactors in which gas-solid reactions are caiTied out, it is useful to define a dimensionless number criterion which can be used to determine the state of flow of the gas no matter what the physical dimensions of the reactor and its solid content. Such a criterion which is used is the Reynolds number of the gas. For example, the characteristic length in tire definition of this number when a gas is flowing along a mbe is the diameter of the tube. The value of the Reynolds number when the gas is in streamline, or linear flow, is less than about 2000, and above this number the gas is in mrbulent flow. For the flow... 

Equations (8) are based on the assumption of plug flow in each phase but one may take account of any axial mixing in each liquid phase by replacing the molecular thermal conductivities fc, and ku with the effective thermal conductivities /c, eff and kn eff in the definition of the Peclet numbers. The evaluation of these conductivity terms is discussed in Section II,B,1. The wall heat-transfer terms may be defined as... 

Under certain assumptions (discussed below), the cost per transfer unit Yx is independent of the number of transfer units x, as shown following Eqn. (20) below. Figure 4 displays the minimum of this dimensionless total cost for a feedwater heater with constant parameters Yx, y, Xu, Tc, M, cp, and U. Similar curves result for condensers and boilers. The values used for the dimensionless parameters y and Yx/XfjTQ are shown in the figure. From the definition x = UA/Mcp, it is seen that x is directly proportional to the heat transfer area A (since U, M, and Cp are constant). 

The heat transfer rate, q, is taken as positive in the direction wall-to-fluid so that it will have the same sign as(Tw -T/) and h will always, therefore, be positive. A number of names have been applied to h including convective heat transfer coefficient , heat transfer coefficient , film coefficient , film conductance , and unit thermal convective conductance . The heat transfer coefficient, h, has the units W/m2-K or, since its definition only involves temperature differences, W/m2oC, in the SI system of units. In the imperial system of units, h has the units Btu/ft2-hr-°F. 

Heat exchange in fully developed laminar flow of fluids in tubes of various cross-sections was studied in many papers (e.g., see [80, 253, 341]). In what follows, we present some definitive results for the limit Nusselt numbers corresponding to the region of heat stabilization in the flow in the case of high Peclet numbers (when the molecular heat transfer can be neglected). 

The difference between the exponent on the Schmidt number and the usual value of I may not be significant, but the exponent for the Reynolds number is definitely greater than 0.80. Other studies of heat transfer with large Prandtl numbers have also shown an exponent of about 0.9 for the Reynolds number. Various empirical equations that cover the entire range of Nsc or Vp, with good accuracy are available. "... 

In Table 1.10 those dimensionless groups that appear frequently in the heat and mass transfer literature have been listed. The list includes groups already mentioned above as well as those found in special fields of heat transfer. Note that, although similar in form, the Nus-selt and Biot numbers differ in both definition and interpretation. The Nusselt number is defined in terms of thermal conductivity of the fluid the Biot number is based on the solid thermal conductivity. 

Correlation. Definitions and a typical flow pattern for this problem are shown in Fig. 4.12. The heat transfer relations given here assume that the downward-facing surface is substantially all heated if the heated surface is set into a larger surface, the heat transfer will be reduced. Since the buoyancy force is mainly into the surface, laminar flow prevails up to very high Rayleigh numbers. The following equation can be used for 103 < Ra < 1010 ... 

Calculate the Reynolds number Re = GZVp and/or any other pertinent dimensionless groups (from the basic definitions) needed to determine the nondimensional heat transfer and flow friction characteristics (e.g.,/ or Nu and/) of heat transfer surfaces on each side of the exchanger. Subsequently, compute j or Nu and /factors. Correct Nu (or j) for variable fluid property effects [100] in the second and subsequent iterations from the following equations. 

The experimental heat-transfer correlation given does not include the effect of changing the Prandtl number. The jH factor will satisfactorily describe the effect of Prandtl on the heat-transfer coefficient. Combining the given correlation with the definitions of jH and Stw from Table 2.1 yields... 

Preliminary analysis of heat transfer from a vibrating surface indicated that the Nusselt and Reynolds numbers, with the amplitude and frequency of the impressed vibration, were the significant parameters. Since the flow when vibration is present is definitely a superposition or combination of the axial flow and vibration influences, it was considered appropriate to consider some combination parameter rather than separate parameters to represent the flow with vibration. It was therefore necessary to define a Reynolds number having significance for the combined axial and oscillatory cross flow envisioned. 

To adopt a common procedure here, the external film coefficient is expressed in terms of the Nusselt number. The internal coefficients, however, are given indirectly by the transfer efficiency, E , representing the fractional approach to the maximum possible heat transfer. Thus, by definition. 

Equation 12.5.b-8 is the same as Eq. I2.5.b-4 except for the term in the latter with D 2, representing direct effective particle-to-particle transport. For several types of situations, this term may be of definite importance mass transfer in highly porous solids at low Reynolds numbers (Wakao [63]) and the heat transfer situation discussed by Littman and Barile [61], which is analogous to the model for radial heat transfer proposed by De Wasch and Froment [62]. 

Nusselt s numbers, which are functions of numbers Re and Pr, are used for definitions of heat transfer and mass transfer coeffidents. 

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