1512 Heat Transfer

There are many texts dedicated to the physics of heat transfer, some of which are listed in the references. In its simplest form, however, the basic law of energy flow can be stated as follows:

A steady flow of energy through any medium of transmission is directly proportional to the force causing the flow and inversely proportional to the resistance to that force.

In dealing with heat energy, the forcing function is the temperature difference and the resistance comes from whatever material is located between the two temperatures.

heat flow =

temperature difference resistance to heat flow

Fig. 15.1 Contribution of each mode of heat transfer. (From Ref. 15.)

This is the fundamental equation upon which all heat-transfer calculations are based.

Temperature Difference

By definition, heat transfer will continue to occur until all portions of the system are in thermal equilibrium (i.e., no temperature difference exists). In other words, no amount of insulation is able to provide enough resistance to totally stop the flow of heat as long as a temperature difference exists. For most insulation applications, the two temperatures involved are the operating temperature of the piping or equipment and the surrounding ambient air temperature.

Thermal Resistance

Heat flow is reduced by increasing the thermal resistance of the system. The two types of resistances commonly encountered are mass and surface resistances. Most insulations are homogeneous and as such have a thermal conductivity or k value. Here the insulation resistance, Ri = tk/k, where tk represents the thickness of the insulation. In cases of nonhomogeneous products such as multifoil metallic insulations, the thermal properties of the products at their actual finished thicknesses are expressed as conductances rather than conductivities based on a 1-in. thickness. In this case the resistance Rl = 1/C, where C represents the measured conductance. The other component of insulation resistance is the surface resistance, Rs = 1/f where f represents the surface film coefficient. These values are dependent on the emittance of the surface and the temperature difference between the surface and the surrounding environment.

Thermal resistances are additive and as such are the most convenient terms to deal with. Following are several expressions for the heat-transfer equation, showing the relationships between the commonly used R, C, and U values. For a single insulation with an outer film:

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