Thermal Design. LMTD Method

In this text we are mainly concerned with the thermal design of heat exchangers, a topic treated in the next section. An important related problem, the performance of an available heat exchanger under different conditions, is treated in Section 7.2. 

After neglecting the effect of axial conduction, the first law of thermodynamics applied to the control volumes shown in Fig. 7.4(b) gives for the hot fluid 

In order to minimize heat losses to the ambient, this is typically the arrangement used in actual heat exchangers. 

U being the total heat transfer coefficient and dAx = Pdx the differential heat transfer area. Recalling Chapter 2, when the effect of pipe curvature is negligible, say r0jri 2, the total heat transfer coefficient based on the mean of the inner and outer surface areas of the pipe wall is given by 

For the hot and cold fluids, consider again a radially lumped control volume, extending this time over the entire length of the heat exchanger (Fig, 7.6). The first law of thermodynamics applied to these control volumes gives for the hot fluid 

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