Watt Density Calculations

Watt density = wattage divided by surface area in square inches (or if in metric - wattage divided by surface area in square centimeters).

Example 1:

Heater output of 100 watts
Heater surface area dissipating the 100 watts = 10 square inches

SOLUTION:

Watt density = 100 watts divided by 10 square inches
=10 watts per square inch (10 w/sq. in.)

EXAMPLE 2:

Vulcan Thunderboltª Heater with an output of 500 watts heater is 10 inches long with a heated length of 9 inches heater is .375" diameter Incoloy¨ 800

SOLUTION:

a. Determine heated surface area (remember surface area must be in square inches)
Heated surface area = sheath diameter x pi (3.1416) x heated length

=.375 in. x 3.1416 x 9 in.
=10.6 sq. in.

b. Apply watt density formula
Watt density = wattage divided by surface area in square inches

=500 watts divided by 10.6 sq. in.
=47.1 watts per sq. in. (47.1 w/sq. in.)

EXAMPLE 3:

Vulcan tubular heater with an output of 1000 watts heater sheath length is 100 inches with cold ends of 6 inches heater is .445" diameter 321 stainless steel

SOLUTION:

a. Determine heated length
heated length = total sheath length minus cold end lengths
=100 in. - (2 x 6 in.)
=88 in.

b. Determine heated surface area (remember surface area must be in square inches) heated surface area = sheath diameter x pi (3.1416) x heated length

=.445 in. x 3.1416 x 88 in.
=123.03 sq. in.

c. Apply watt density formula
Watt density = wattage divided by surface area in square inches
=1000 watts/123.03 sq. in.
=8.13 watts per sq. in. (8.13 w/sq. in.)

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