ARNOLD, K. (1999). Design of Gas-Handling Systems and Facilities (2nd ed.) Episode 1 Part 2 doc

Heat Transfer Theory 1 1

Multiple Transfer Mechanisms

Most heat transfer processes used in production facilities involve combi￾nations of conduction and convection transfer processes. For example, in

heat exchangers the transfer of heat energy from the hot fluid to the cold

fluid involves three steps. First, the heat energy is transferred from the hot

fluid to the exchanger tube, then through the exchanger tube wall, and

finally from the tube wall to the cold fluid. The first and third steps are

convection transfer processes, while the second step is conduction process,

To calculate the rate of heat transfer in each of the steps, the individual

temperature difference would have to be known. It is difficult to measure

accurately the temperatures at each boundary, such as at the surface of

the heat exchanger tube. Therefore, in practice, the heat transfer calcula￾tions are based on the overall temperature difference, such as the differ￾ence between the hot and cold fluid temperatures. The heat transfer rate

is expressed by the following equation, similar to the conductive/convec￾tive transfer process:

where q = overall heat transfer rate, Btu/hr

U = overall heat transfer coefficient, Btu/hr-ft2

-°F

A = heat transfer area, ft2

AT = overall temperature difference, °F

Examples of overall heat transfer coefficient and overall temperature

difference calculations are discussed in the following sections.

Overall Temperature Difference

The temperature difference may not remain constant throughout the

flow path. Plots of temperature vs. pipe length for a system of two concen￾tric pipes in which the annular fluid is cooled and the pipe fluid heated are

shown in Figures 2-2 and 2-3. When the two fluids travel in opposite direc￾tions, as in Figure 2-2, they are in countercurrent flow. When the fluids

travel in the same direction, as in Figure 2-3, they are in co-current flow.

The temperature of the inner pipe fluid in either case varies according

to one curve as it proceeds along the length of the pipe, and the tempera￾ture of the annular fluid varies according to another. The temperature dif￾ference at any point is the vertical distance between the two curves.

12 Design of GAS-HANDLING Systems and facilities

Figure 2-2. Change in AT over distance, counter-current flow of fluids.

Since the temperature of both fluids changes as they flow through the

exchanger, an "average" temperature difference must be used in Equation

2-3. Normally a log mean temperature difference is used and can be

found as follows:

where LMTD = log mean temperature difference, °F

ATj = larger terminal temperature difference, °F

AT2 = smaller terminal temperature difference, °F

Although two fluids may transfer heat in either counter-current or co￾current flow, the relative direction of the two fluids influences the value

of the LMTD, and thus, the area required to transfer a given amount of