This Eq tk can hen be used in the flat geometry equation by substituting Eq tk for tk.

It should be apparent that the heat flow Q is also equal for any combination of At and R values, as shown by the last equivalency above, which utilized two parts of the system instead of just one.

Finally, it is of critical importance to calculate the Rj values using the insulation mean temperature, not the operating temperature. The mean temperature is the sum of the temperatures on either side of the insulation divided by 2. Again for the last set of equivalencies:

Pipe vs. Flat Calculations—Equivalent Thickness

Because the radial heat flows in a path from a smaller-diameter pipe, through the insulation, and then off a larger-diameter surface, a phenomenon termed "equivalent thickness" (Eq tk) occurs. Because of the geometry and the dispersion of the heat to a greater area, the pipe really "sees" more insulation than is actually there. When the adjustment is made to enter a greater insulation thickness into the calculation, the standard flat geometry formulas can be used by substituting Eq tk for tk into the equations.

The formula for equivalent thickness is

Eqtk = r2 lnr1

where and r2 are the inner and outer radii of the insulation system. For example, an 8-in. IPS with 3-in. insulation would lead to an equivalent thickness as follows (8-in. IPS has 8.625 in. actual outside diameter):

The example above used an even insulation thickness of 3 in. Some products are manufactured to such even thicknesses, and Table 15.2 lists the Eq tk for such products. However, many products are manufactured to "simplified" thicknesses, which allow a proper fit when nesting double-layer materials. ASTM-C-5859 lists these standard dimensions, and Table 15.3 shows Eq tk values for the simplified thicknesses. Figure 15.3 also shows the conversion for any thickness desired and will be used later in the reverse fashion.

Surface Resistance

There is always diversity of opinion when it comes to selecting the proper values for the surface resistance Rs. The surface resistance is affected by surface emit-tance, surface air velocity, and the surrounding environment. Heat-transfer texts have developed procedures for calculating Rs values, but they are all based on speculated values of emittance and air velocity. In actuality, the emittance of a surface often changes with time, temperature, and surface contamination, such as dust. As a result, it is unnecessary to labor over calculating specific Rs values, when the conditions are estimates at best.

Table 15.4 lists a series of Rs values based on three different surface conditions and the temperature difference between the surface and ambient air. Also included are single-point Rs values for three different surface air velocities. See the note at the bottom of Table 15.4 relating to the effect of Rs on heat-transfer calculations.

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