Surface mean temperature difference

Fin efficiency is defined as the ratio of the mean temperature difference from surface to fluid divided by the temperature difference from fin to fluid at the base or root of the fin. Graphs of fin efficiency for extended surfaces of various types are given by Gardner [Tmn.s. Am. Soc. Mech. Eng., 67,621 (1945)]. 

ATni = mean temperature difference between fluid and surface (K),... 

The radiant section of an industrial boiler may typically contain only 10 per cent of the total heating surface, yet, because of the large temperature difference, it can absorb 30-50 per cent of the total heat exchange. The mean temperature difference available for heat transfer in the convective section is much smaller. To achieve a thermally efficient yet commercially viable design it is necessary to make full use of forced convection within the constraint of acceptable pressure drop. 

Example 1.11 A fluid evaporates at 3°C and cools water from 11.5°C to 6.4°C. What is the logarithmic mean temperature difference and what is the heat transfer if it has a surface area of 420 m and the thermal transmittance is 110 W/ (m K) ... 

U = overall heat transfer coefficient in Btu/hr ft2oF A = tube surface area in ft2 ATM = mean temperature difference in °F. For our... 

Although the result in Equation 15.45 applies to both countercurrent and cocurrent flow, in practice, cocurrent flow is almost never used as, given fixed fluid inlet and outlet temperatures, the logarithmic mean temperature difference for countercurrent flow is always larger. This in turn leads to smaller surface area requirements. Also, as shown in Figure 15.6a for countercurrent flow, the final temperature of the hot fluid can be lower than the final temperature of the cold fluid (sometimes known as temperature cross), whereas in Figure 15.6b, it is clear that there can never be a temperature cross. 

If the new increased heat duty and new log mean temperature difference are fixed, then the additional surface area above the existing area using a plain tube surface is given by9 ... 

As the mean temperature difference is 10 °C, the required surface area is... 

In units of BTU per hour per square foot of surface per °F mean temperature difference. U-values for steel pipe are quite high, but the addition of a thick concrete coating plus the effect of burying the pipe under several feet of bottom sediments could result in a very low U-value. Experimental data under controlled conditions is difficult If not impossible to obtain, but we can calculate U-values as low as 0.15. In actual practice we may experience average U-values as high as 1.0 to 2.0, particularly if some 1 sections of the pipeline do not remain completely buried. 

When processing is controlled by heat transfer variables, a log mean temperature difference (ATlmtd) and heat transfer surface area will predominate over the agitation variables. Provided it is sufficient to give a homogeneous process fluid temperature, increased agitation can only reduce the inside film resistance, which is one of a number of resistances that determines the overall heat transfer coefficient. 

A - surface area for heat transfer consistent with definition of U AT, = suitable mean temperature difference across heat exchanger... 

For vertical tubes, the superficial vapor velocity (based on the total heat-transfer surface) can be obtained by multiplying the value calculated from the preceding equation by 0.22. This assumes that there is adequate liquid circulating past the surface to satisfy the mass balance. For thermosiphon reboilers, a detailed analysis must be made to establish circulation rate, boiling pressure, sensible heat-transfer zone, boiling heat-transfer zone, and mean temperature difference. If hquid circulation rates are not adequate, ah hquid will be vaporized and superheating of the vapor wih occur with a resultant decrease in heat-transfer rates. 

Forced convection heat transfer is probably the most common mode in the process industries. Forced flows may be internal or external. This subsection briefly introduces correlations for estimating heat-transfer coefficients for flows in tubes and ducts flows across plates, cylinders, and spheres flows through tube banks and packed beds heat transfer to nonevaporating falling films and rotating surfaces. Section 11 introduces several types of heat exchangers, design procedures, overall heat-transfer coefficients, and mean temperature differences. 

For a cooler, select from Table 4.4 an approach temperature difference of 5.0 °C, which is an economic rule-of-thumb. This approach is selected rather than the upper limit of 50.0 C to conserve heat, but the surface area will be larger for the 5.0 C approach. From Equation 4.5.8, the exit raw-water temperature, tz, equals 29 °C, Because the raw water has a tendency to scale, it is located on the tube side. At a water temperature of about 50 °C and above, scale formation increases so that the exit water temperature should never exceed 50 °C (122 F). From Equation 4.5.5, the logarithmic-mean temperature difference is... 

The exchanger s coefficient of performance, Ua/Vd, can be monitored and is a measure of fouling. This ratio can readily be determined T,/will be known from design data, and Ua can be calculated by dividing the actual heat duty by the product of the surface area and the log mean temperature difference.,When /7a/by drops to, say, 80%, cleaning can be done to prevent further deterioration in performance. 

Weighted mean-temperature-difference for exchangers with phase changes Conserving steam Operating boilers intermittently Find the most compact surface condenser Does your surface condenser have spare capacity ... 

It Analyze heating and cooling of a fluid flowing in a tube under constant surface temperature and constant surface heat flux conditions, and work with the logarithmic mean temperature difference,... 

Note that the arithmetic mean temperature difference AT,j, is simply the average of the temperature differences between the surface and the fluid at the inlet and the exit of the tube. Inherent in this definition is the assumption that the mean fluid temperature varies linearly along the tube, which is hardly ever... 

C What does the logarithmic mean temperature differ-eiice represent for flow in a tube whose surface temperature is constant Why do we use the logarithmic mean temperature instead of the arithmetic mean temperature ... 

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