The Overall Heat-Transfer Coefficient

Multiplying top and bottom of the right-hand side of equation (A8.29) by the outside diameter of the fuel pin cladding, 2d, gives  

Equation (A8.30) may be compared with the canonical form of the heat transfer equation, namely  

The heat transfer coefficient between pin cladding and coolant, Kcc, will vary with mass flow raised to the power of 0.8 as explained in Chapter 20, Section 20.6. 

When considering heat transfer by conduction, we have neglected the mechanism by which heat is transferred to and from the outer solid surfaces. In convective heat transfer, heat is transferred to and from flowing fluids. 

When a fluid is present in contact with each solid wall, there will be an additional resistance to heat transfer in each fluid boundary layer or film . The combined mechanism of heat transfer from a hot fluid through a dividing wall to a cold fluid has many similarities to conduction through a composite slab reviewed earlier. 

The boundary layers are often called films , and heat transfer by conduction predominates in them giving rise to significant resistances to heat transfer. We assume that all the resistance to heat transfer on the hot side is confined to the hot film and all that on the cold side is confined to the cold film. 

The associated heat transfer coefficients for these films are known as film heat transfer coefficients , /zh and hc for the hot and cold side, respectively. The heat flux through the hot film is given by q = hh(Th — T ), through the wall by q = (k lh )(Tx — T2) and through the cold film by q = hc(T2 — Tc). At steady state, the heat fluxes are constant and it is easy to show that 

U is known as the overall heat transfer coefficient and relates the heat flux to the overall temperature difference Th — Tc. 

Consider the plane wall shown in Fig. 2-5 exposed to a hot fluid A on one side and a cooler fluid B on the other side. The heat transfer is expressed by 

The heat-transfer process may be represented by the resistance network in Fig. 2-5b, and the overall heat transfer is calculated as the ratio of the overall temperature difference to the sum of the thermal resistances  

Observe that the value /hA is used to represent the convection resistance. The overall heat transfer by combined conduction and convection is frequently expressed in terms of an overall heat-transfer coefficient U, defined by the relation 

For a hollow cylintfer exposed to a convection environment on its inner and outer surfaces, the electric-resistance analogy would appear as in Fig. 2-6 where, again, 1A and TB are the two fluid temperatures. Note that the area for convection, is not the same for both fluids in this case, these areas depending on the inside tube diameter and wall thickness. In this case the overall heat transfer would be expressed by 

Calculations of the convection heat-transfer coefficients for use in the overall heat-transfer coefficient are made in accordance with the methods described in later chapters. Some typical values of the overall heat-transfer coefficient are given in Table 10-1. 

The following analysis is based on the situation shown in Fig. 1.12 A flat or curved wall separates a fluid at temperature 0 j from another with a temperature d. At steady state heat Q, flows from fluid 1 through the wall to fluid 2, as a result of the temperature difference th — d2. The heat flow Q is transferred from fluid 1 to the wall which has an area A1 and is at temperature dWi With as the heat transfer coefficient, it follows from section 1.1.3 that 

Here Am is the mean thermal conductivity of the wall according to (1.11), 6 its thickness and Am the average area calculated from (1.15). Finally an analogous relationship to (1.68) exists for the heat transfer from the wall to fluid 2 

The unknown wall temperatures dwl and dW2, can be eliminated from the three equations for Q. This means that Q can be calculated by knowing only the fluid temperatures d, and d2. This results in 

(1/kA) represents the resistance to overall heat transfer. It is made up of the single resistances of each transfer process in the series the resistance to convective transfer between fluid 1 and the wall, (l/cqhlj), the conduction resistance in the wall, ( J/Am.i4m) and the resistance to convective transfer between the wall and fluid 2, (l/o 22l2). This series approach for overall heat transfer resistance is analogous to that in electrical circuits, where the total resistance to the current is found by the addition of all the single resistances in series. Therefore, the three resistances which the heat flow Q must pass through, are added together. These three are the resistance due to the boundary layer in fluid 1, the conduction resistance in the wall and the resistance to transfer associated with the boundary layer in fluid 2. 

The temperature drop due to these thermal resistances behaves in exactly the same manner as the voltage drop in an electrical resistor, it increases as the resistance goes up and as the current becomes stronger. From (1.68) to (1.72) it follows that 

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The problem with Eq. (7.5) is that the overall heat transfer coefficient is not constant throughout the process. Is there some way to extend this model to deal with the individual heat transfer coefficients ... 

Now consider the heat transfer area required by enthalpy interval k, in which the overall heat transfer coefficient is allowed to vary... 

If solvent recovery is maximized by minimizing the temperature approach, the overall heat-transfer coefficient in the condenser will be reduced. This is due to the fact that a large fraction of the heat transfer area is now utilized for cooling a gas rather than condensing a Hquid. Depending on the desired temperature approach the overall heat-transfer coefficients in vent condensers usually range between 85 and 170 W/m K (ca 15 and 30 Btu/h-ft. °F). 

For the purpose of network synthesis, the overall heat-transfer coefficient is usually idealized as a constant value. This iadependence of the heat-transfer coefficient makes possible the iterations necessary to solve the network problem. Usually, the overall heat-transfer coefficient for each exchanger (match) is defined as... 

The rate of heat-transfer q through the jacket or cod heat-transfer areaM is estimated from log mean temperature difference AT by = UAAT The overall heat-transfer coefficient U depends on thermal conductivity of metal, fouling factors, and heat-transfer coefficients on service and process sides. The process side heat-transfer coefficient depends on the mixing system design (17) and can be calculated from the correlations for turbines in Figure 35a. 

FIG. 11 91 Effect of circulation ratio on the overall heat-transfer coefficient of an air-cooling coil. 

The overall heat-transfer coefficient U is eonstant throughout the heat exchanger. 

The overall heat transfer coefficient, U, is a measure of the conductivity of all the materials between the hot and cold streams. For steady state heat transfer through the convective film on the outside of the exchanger pipe, across the pipe wall and through the convective film on the inside of the convective pipe, the overall heat transfer coefficient may be stated as ... 

The only information available are the inlet temperatures of the hot and cold fluids and estimates for the overall heat transfer coefficient U and the heat transfer surface A. The flows are fixed and the specific heats of the fluids known. 

The overall heat transfer coefficient U. varies inversely with the anchor-to-wall clearance. Anchor to wall clearance is less than 1 m. 

Consider a single-zone jacket where there is an increase in the jacket flow, and a corresponding increase in the outside film coefficient because hj =f(Njjg, G). Therefore, a two-fold increase in the jacket flow results in an increase in hjj by 2 h . The overall heat transfer coefficient U = l/[FpoL + 1/hj], and a larger outside coefficient subsequently increases the overall heat transfer coefficient. The overall heat flux will increase due to the combined effects of the increased flow and lower jacket outlet temperature. The net result is an increase in the pressure drop. 

The cost of condensers/heat exchangers ( ) is taken as l,500 (heat transfer area in m ). The overall heat-transfer coefficients for the dehumidification, the... 

The fouling factors are applied as part of the overall heat transfer coefficient to both the inside and outside of the... 

Figure 10-44. Keep track of fouling by monitoring the overall heat transfer coefficient as a function of flow rate. (Used by permission Ganapa-thy, V., Chemical Engineering, Aug. 6,1984, p. 94. McGraw-Hill, Inc. All rights reserved.)...

The outer and inner tubes extend from separate stationary tube sheets. The process fluid is heated or cooled by heat transfer to/from the outer tube s outside surface. The overall heat transfer coefficient for the O.D. of the inner tube is found in the same manner as for the double-pipe exchanger. The equivalent diameter of the annulus uses the perimeter of the O.D. of the inner tube and the I.D. of the inner tube. Kem presents calculation details. 

The overall heat transfer coefficient for the insulation and the ambient air is ... 

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