The thermal design of tank coils involves the determination of the area of heat-transfer surface required to maintain the contents of the tank at a constant temperature or to raise or lower the temperature of the contents by a specified magnitude over a fixed time.
Nomenclature A = area; Ab = area of tank bottom; Ac = area of coil; Ae = equivalent area; As = area of sides; At = area of top; Ai = equivalent area receiving heat from external coils; A2 = equivalent area not covered with external coils; Dt = diameter of tank; F = design (safety) factor; h = film coefficient; ha = coefficient of ambient air; hc = coefficient of coil; hh = coefficient of heating medium; hi = coefficient of liquid phase of tank contents or tube-side coefficient referred to outside of coil; hz = coefficient of insulation; k = thermal conductivity; ke = thermal conductivity of ground below tank; M = mass of tank contents when full; t = temperature; ta = temperature of ambient air; td = temperature of dead-air space; tf = temperature of contents at end of heating; tg = temperature of ground below tank; th = temperature of heating medium; t0 = temperature of contents at beginning of heating; U = overall coefficient; Ub = coefficient at tank bottom; Uc = coefficient of coil; Ud = coefficient of dead air to the tank contents; Ut = coefficient through insulation; Us = coefficient at sides; Ut = coefficient at top; and U2 = coefficient at area A 2.
Typical coil coefficients are listed in Table ii-2. More exact values can be calculated by using the methods for natural convection or forced convection given elsewhere in this section.
Maintenance of Temperature Tanks are often maintained at temperature with internal coils if the following equations are assumed to be applicable:
These make no allowance for unexpected shutdowns. One method of allowing for shutdown is to add a safety factor to Eq. 11-36a.
In the case of a tank maintained at temperature with internal coils, the coils are usually designed to cover only a portion of the tank. The temperature td of the dead-air space between the coils and the tank is obtained from
The heat load is
The coil area is
where F is a safety factor.
Heating
Heating with Internal Coil from Initial Temperature for Specified Time
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