Logarithmic temperature difference

For a countercurrent heat exchanger, the logarithmic temperature difference is then... 

This is the logarithmic temperature difference for the counterflow hear exchanger. 

The logarithmic mean temperature difference is defined when AT, A7, Consider the case where AT2 = ATj. The logarithmic temperature difference is obtained by applying I lTopital s rule as AT2 —> AT, giving... 

When the condensation process is not exactly isothermal but the temperature change is small such as where there is a significant change in pressure, or where a narrow boiling range multicomponent mixture is being condensed the logarithmic temperature difference can still be used but the temperature correction factor will be needed for multipass condensers. The appropriate terminal temperatures should be used in the calculation. 

When the fluid being vaporised is a single component and the heating medium is steam (or another condensing vapour), both shell and tubes side processes will be isothermal and the mean temperature difference will be simply the difference between the saturation temperatures. If one side is not isothermal the logarithmic mean temperature difference should be used. If the temperature varies on both sides, the logarithmic temperature difference must be corrected for departures from true cross- or counter-current flow (see Section 12.6). 

Improved Flue-Gas Heat Recovery. The majority of the heat losses in cracking furnaces is contained in the flue gas which leaves the furnace. Today s cracking furnaces with integrated waste heat recovery are designed for thermal efficiencies between 90 and 93%, which correspond to flue-gas outlet temperatures of about 130° to 180°C. A further decrease of the flue-gas outlet temperature usually is not economic, as the heat-transfer surface of the upper bundles becomes too large because of the small mean logarithmic temperature difference. 

C The temperature difference between Ihe hot and cold fluids in a heat exchanger is given to be AT[ at one end and A / 2 at the other end. Can the logarithmic temperature difference ATia of this heat exchanger be greater than both Al and AT 2 Explain. 

In the above relation q, or are enthalpy variations over a temperature interval with a mean-logarithmic temperature difference The notation h, or /ij designates partial... 

Heat transfer in the exchanger is achieved mainly by convection and the surface area required for transfer to heat is given by the expression A = QIHT, where Q is the heat load in joules/hr., A is the area in m, H is the overall heat transfer coefficient in watts/m K, and T is the logarithmic temperature difference. 

Finally the overall heat transfer coefficient is obtained from equation 8. The global heat transferred for each tube is computed with equation 9. We call A7 / semi logarithmic temperature difference . It is the best compromise between pure logarithmic temperature difference that has no sense here (only one tube) and pure arithmetic temperature difference that does not allow to follow the evolution of water properties along the tube. The heat exchange diagram of the 0TB is presented in figure 3. 

Tc average temperature of the cooling medium, assuming that T-Tc (Tc,our-Tc m), otherwise one should use the logarithmic temperature difference. 

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