Heat transfer coefficients, film equations

Calculation of the overall heat transfer coefficient from Equation 15.13 requires knowledge of the film transfer coefficients. Although Table 15.1 presents typical values,... 

Heat transfer coefficients, film convection and radiation, 189 equations, 189-192 Heat transfer coefficients, overall, 170... 

Nusselt equation = a method for predicting forced convection heat transfer coefficients (film coefficients). (See sec. 2.5.2.)... 

Vertical Tubes For the following cases Reynolds number < 2100 and is calculated by using F = Wp/ KD. The Nusselt equation for the heat-transfer coefficient for condensate films may be written in the following ways (using liquid physical properties and where L is the cooled lengm and At is — t,) ... 

Of these special surfaces, only the double-fluted tube has seen extended services. Most of the gain in heat-transfer coefficient is due to the condensing side the flutes tend to collect the condensate and leave the lauds bare [Caruavos, Proc. First Int. Symp. Water Desalination, 2, 205 (1965)]. The coudeusiug-film coefficient (based on the actual outside area, which is 28 percent greater than the nominal area) may be approximated from the equation... 

The preceding equations are reported to predict actual heat transfer coefficients only about 15% lower than experimental values—the difference can be attributed to the rippling of the film and early turbulence and drainage instabilities on the bottom side of the tube. ... 

H = heat transfer coefficient ratio, h /hN h i = effective heat transfer film coefficient, Btu/hr-ff-°F hNu condensing film coefficient by Nusselt equation Btu/hr-ff-°F... 

The calculation of heat transfer film coefficients in an air-lift bioreactor is more complex, as small reactors may operate under laminar flow conditions whereas large-scale vessels operate under turbulent flow conditions. It has been found that under laminar flow conditions, the fermentation broths show non-Newtonian behaviour, so the heat transfer coefficient can be evaluated with a modified form of the equation known as the Graetz-Leveque equation 9... 

From both of these equations, it will be noted that the heat transfer coefficient is noi a function of the temperature difference. Here Re" — (d N pj x-) and Re = (udvp/n), where dv is the tube diameter and u is the average velocity of the liquid in the film in the axial direction. 

Below a Reynolds number of about 2000 the flow in pipes will be laminar. Providing the natural convection effects are small, which will normally be so in forced convection, the following equation can be used to estimate the film heat-transfer coefficient ... 

The presence of waves will increase the heat-transfer coefficient, so the use of equation 12.51 above a Reynolds number of 30 will give conservative (safe) estimates. The effect of waves on condensate film on heat transfer is discussed by Kutateladze (1963). 

The equation given by Bromley (1950) can be used to estimate the heat-transfer coefficient for film boiling on tubes. Heat transfer in the film-boiling region will be controlled by conduction through the film of vapour, and Bromley s equation is similar to the Nusselt equation for condensation, where conduction is occurring through the film of condensate. 

The analysis was later modified to include some of the factors neglected by Nusselt1213. One of these is the effect of buoyancy forces acting on the liquid film. This results in the pl term in Equation 15.80 being replaced by Pl(pl — Pv ) Such buoyancy forces are usually only important close to the critical point. In most cases, the two most important factors that cause a significant deviation from Equation 15.80 are the presence of vapor shear forces and noncondensable gases in the vapor. Vapor shear forces act to increase the heat transfer coefficient, whereas noncondensable gases act to decrease it. 

The boiling film coefficient for a kettle reboiler can be estimated from the correlation for pool boiling. Equation 15.96 gives one such method due to Palen15. However, the correlation requires the heat flux to be known, and therefore the heat transfer area to be known. Hence the calculation will need to be iterative. An initial estimate of the overall heat transfer coefficient of 2000 W-m 2-K 1 gives ... 

However, one other issue that needs to be included in the assessment often helps mitigate the uncertainties in the assessment of the film heat transfer coefficient. A fouling allowance needs to be added to the film transfer coefficient according to Equation 15.13. 

Equation H.l shows that each stream makes a contribution to total heat transfer area defined only by its duty, position in the composite curves and its film transfer coefficient. This contribution to area means a contribution to capital cost also. If, for example, a corrosive stream requires special materials of construction, it will have a greater contribution to capital cost than a similar noncorrosive stream. If only one cost law is to be used for a network comprising mixed materials of construction, the area contribution of streams requiring special materials must somehow increase. One way of doing this is by weighting the heat transfer coefficient to reflect the cost of the material the stream requires. 

Dukler and Taitel, 1991b). The simplest configuration of annular flow is a vertical falling film with concurrent downward flow. Given information on interfacial shear and considering the film to be smooth, the film thickness and heat transfer coefficient between the wall and the liquid film can be predicted from the following basic equations (Dukler, 1960) ... 

The results for the heat transfer coefficient were satisfactorily correlated by equation 6.68 as shown in Figure 6.30. Since the resistance to heat transfer in the solid could be neglected compared with that in the gas, the coefficients which were calculated were gas-film coefficients, correlated by ... 

This represents the lowest possible value of the film heat transfer coefficient when no natural or forced convection currents are present. When there is a relative velocity between the sphere and the surrounding fluid the heat transfer coefficient will increase and heat transfer will improve. Thus for heat transfer to and from spherical particles, correlations take the form of equation 2.8... 

Dukler (D12), 1959 Theoretical analysis of turbulent film flow (with and without downward cocurrent gas stream) with extension to film heat transfer. Interfacial disturbances are neglected basic equations are solved by computer giving film thicknesses, velocity profiles, local and mean heat transfer coefficients. Interfacial shear is shown to be of great importance. 

In writing the energy balance (Equation 5.17) we slipped another fast one by the reader by assuming h to be the same as ho, the heat transfer coefficient from the liquid film-air film interface to the air. If a significant resistance is associated with the liquid film, h is better expressed by the overall heat transfer coefficient (U), which consists of both he andhL. Note that hL is the convection coefficient from the liquid film to the interface [7], When appreciable liquid film resistance exists, our energy balance should be written as... 

Having established all of these added variables for the shell-side h0 film heat-transfer coefficients D and Gs, Eq. (5.3) is expanded here, since these variables must be determined for this equation. 

Equation (5.40) is good and applicable for film heat-transfer coefficients for gas-phase, vapor-phase, and condensing fluids. The Cp, K, and U isc input values should be accurate for the tube-side fluid being cooled. 

The convective heat transfer coefficients hi and h0 must be calculated from equations that involve the geometry of the system, the physical properties of the fluid, and the velocity with which it is flowing. These equations are obtained variously by more or less fundamental analysis of the heat transfer and fluid flow mechanisms, or by correlation of experimental data, or by combinations of these methods. A few typical values of the film coefficients are... 

We again see that the reciprocal of the overall heat transfer coefficient is equivalent to the overall resistance to heat transfer, which is equal to the sum of resistances in the hot film (1 //zG), the wall [r0 n(r0/ri)]/kw and the cold film (r0 r- ), as shown in Equation (22). However in this case, the expressions for the resistances in the wall and the cold film are modified to take the curvature into account. No such modification is required for the outside film resistance, as the overall heat transfer coefficient is defined based on the outside surface area of the cylinder. 

Viscosity Correction for the Dirty Exchanger. These overall coefficients are based upon the uncorrected film heat transfer coefficients, i.e. those without the viscosity correction parameter (gfgw)014. As the temperature difference across a layer is proportional to the layer s thermal resistance (see Equations (2) and (10)), the relative resistances, above, allow estimation of the mean tube wall temperature, and hence evaluation of the viscosity corrections (jib/hw)° 14 to the film coefficients. Mean bulk temperature difference ... 

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