Temperature different across film

Rayleigh number, Ra p L Cp AT k fl coefficient of thermal volume expansion AT temperature different across film L characteristic length dimension heat transfer by convection heat transfer by conduction Free convection... 

F, Factor, ratio of temperature difference across tube-side film to overall mean temperature difference Dimensionless Dimensionless... 

For turbulent flow of a fluid past a solid, it has long been known that, in the immediate neighborhood of the surface, there exists a relatively quiet zone of fluid, commonly called the Him. As one approaches the wall from the body of the flowing fluid, the flow tends to become less turbulent and develops into laminar flow immediately adjacent to the wall. The film consists of that portion of the flow which is essentially in laminar motion (the laminar sublayer) and through which heat is transferred by molecular conduction. The resistance of the laminar layer to heat flow will vaiy according to its thickness and can range from 95 percent of the total resistance for some fluids to about I percent for other fluids (liquid metals). The turbulent core and the buffer layer between the laminar sublayer and turbulent core each offer a resistance to beat transfer which is a function of the turbulence and the thermal properties of the flowing fluid. The relative temperature difference across each of the layers is dependent upon their resistance to heat flow. 

Figure 8 shows that increasing the heat flux at constant mass velocity causes the peak in wall temperature to increase and to move towards lower enthalpy or steam quality values. The increase in peak temperature is thus due not only to a higher heat flux, which demands a higher temperature difference across the vapor film at the wall, but to a lower flow velocity in the tube as the peaks move into regions of reduced quality. The latter effect of lower flow velocity is probably the dominant factor in giving fast burn-out its characteristically rapid and often destructive temperature rise, for, as stated earlier, fast burn-out is usually observed at conditions of subcooled or low quality boiling. 

A /)- = temperature difference across the outside (shell-side) film (K)... 

Commercially available heat flux sensors with thermopiles sandwiched at the interface were used to measure the local temperatures and heat fluxes that is. Omega Corporation, Model HFS-4 devices. The total thickness of the sensors was nominally less then 0.18 mm, and a schematic of the device is shown in Fig. 5.10. By measuring the temperature difference across the center film (AT) and assuming one-dimentional heat transfer, then the heat flux can be measured using the temperature difference and the thermal conductivity of the film. The local temperature is recorded using the thermocouple nearest the barrel. The senors were calibrated at ambient condition with zero heat flux. 

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 ... 

There are upper and lower limits of applicability of the equation above. The lower limit results because natural-convection heat transfer governs at low temperature differences between the surface and the fluid. The upper limit results because a transition to film boiling occurs at high temperature differences. In film boiling, a layer of vapor blankets the heat-transfer surface and no liquid reaches the surface. Heat transfer occurs as a result of conduction across the vapor film as well as by radiation. Film-boiling heat-transfer coefficients are much less than those for nucleate boiling. For further discussion of boiling heat transfer, see Refs. 5 and 6. 

Heal flux meters use a very sensitive device known as a thermopile lo measure the temperature difference across a thin, heat conducting film made of kapton (k = 0.345 W/m K). If the thermopile can delect temperature differences of 0.1 °C or more and the film thickness is 2 mm, what is the minimum heal flux this meter can detect Ansv/en 17.3 W/rrf... 

Heat transfer rates in falling film evaporators are relatively high even at low temperature differences across the liquid film thus, these evaporators are widely used for heat sensitive products because of uniform temperatures cuid short residence times. Generally, moderately viscous fluids and materials with mildly fouling characteristics can easily be handled in falling film evaporators in series for heavy evaporation loads, and part of the liquid can be pumped and recycled to the top of the unit. 

Rose [47,48] points out that when Eq. 14.78 is used in conjunction with an equation relating the heat transfer rate (i.e., condensation rate) to the temperature difference across the condensate film (an appropriate expression for a single tube might be Eq. 14.56), together with the interface equilibrium condition ... 

All of these factors are easily controlled in the design of such apparatus. Initial film thickness is controlled by hydrodynamic action of the blade, defined as that resulting from the balance of centrifugal force, water resistance, and a journal bearing type of lift. Rate of evaporation is controlled by the selection of the operating temperature difference across the heat transfer tube and the rate of film renewal is controlled by choice of output speed of the gear motor which drives the blade. 

Film boiling should be avoided in thermosiphon reboilers. A common rule of thumb (123, 124, 253, 254, 358) suggests that the temperature difference across the wall should not exceed 90 to 100 F. An alternative rule of thumb (187) suggests that maximum heat flux in thermosiphon reboilers should not exceed 12,000 and 30,000 Btu/h/ft for organics and aqueous solutions, respectively. Palen et al. (313) demonstrated that such rules of thumb are grossly oversimplified and fail to take physical properties and tube geometry... 

Typical thickness of passivation film in PbBi alloy is about 10 pm and 20 pm respectively for austenitic and perlitic steel, though scattering within the range fi om 10 pm to 100 pm. The film thermal conductivity is about 5 W/(mK). There is a good reason to believe that the film is not continuous because of its saturation with liquid metal. Thus, thermal resistance is rather low and temperature difference across the film is about 5K. 

The skin temperature is the process temperature inside the tube, plus the temperature differences across the film and metal resistances. The film resistance is usually larger than the metal resistance. It is calculated by taking the peak flux and dividing by the heat transfer coefficient. The heat transfer coefficient is usually 200-500 Btu/(hfit °F), which provides a typical film resistance of 45-80 °F. The metal resistanee is much smaller than the film resistance. It is calculated by taking the peak flux and dividing by the thermal conductivity of the metal. The thermal conductivity is usually 12-16 Btu/(h ft F), which results in a typical metal resistance of 15-20 °F (8-11 °C). The exception is for thick-walled tubes, which could have a metal resistance as high as 80 F (44 °C). 

The outer film heat transfer coefficient is almost a linear function of the temperature difference across this film. Tabulation of this parameter is shown in Fig. 5. 

Here AT is die maximum allowable temperature difference across the liquid film. 

Comparison of Eqs. (96) and (97) shows that the temperature difference across the film surrounding the catalyst pellet must be very low for a fully wetted particle, but could be important for a non-wetted particle. The design engineer must ensure that scale-up of reactor diameter for highly exothermic reactions does not diminish heat transfer from the reactor, or increase evaporation of liquid and generation of hot spots. To test for these effects, a pilot plant should be operated so that evaporation can occur leading to the development of dry zones. When this condition is found detailed axial temperature measurements should be taken. 

In view of the good agreement obtained between measured and theoretical temperature differences across the pellet-bulk fluid film (Butt et al. 1977), the temperature measurements may give accurate values of h under reaction conditions. 

In the above derivation the ATy refers to the temperature difference across a fluid film. If it is difficult to determine the individual film temperature difference, a similar derivation based on the over-all temperature difference results in... 

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