Combined Convection And Conduction Heat Transfer

Conduction and convection have been discussed separately in order to emphasize the different mechanisms that control the heating and cooling of food products. However, seldom is a food processing operation carried out in which the heat transfer is not a combination of conduction and convection. Although radiation is also present in most of these operations, the effect is usually quite insignificant unless the process is specifically a radiation process.

Figure 3 extends the transfer of heat from a liquid to a solid surface, through the solid, and then to another liquid. This could be the situation occurring in a heat exchanger where a hot liquid is being used to warm another liquid, with the solid being the wall of the heat exchanger. The resistances to heat flow through the hot fluid (R^), solid pipe wall (Rw), and fluid being heated (Rc) can be summed to give a total resistance

Although only three media are used in the example, there is no limit to the number of resistances that can be summed for a given problem.

An overall heat transfer coefficient U combining conduction and convection heat transfer coefficients now can be defined from equation 15, where, although only three media are used in the example, there is no limit to the summing of as many resistances as are necessary in a given situation

UA l/hhAh + xJkwAw + l/hcAc (1?) Thus the overall heat transfer equation becomes q = -UAAt (18)

As noted, U and A are not independent since, if the areas of the heat transfer surfaces vary (eg, a pipe heat exchanger), A must be based on a mean area (Am). For example, in the process of transferring heat through a pipe that has an inside scale deposit with a determined his, the overall conductance can be calculated as

A1W = Ais = jiDL Aow = Aos = nDL A;n = (Aow — Aiw)/ln(Aow/Aiw)

multiplying the denominator by Am/Am gives

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