To calculate the percentage increase in the heat dissipation rate, we can use the following formula:
Percentage increase = (New heat dissipation rate - Old heat dissipation rate) / Old heat dissipation rate * 100%
The old heat dissipation rate can be calculated using the following formula:
Q = h * A * (T_w - T_a)
where:
Q is the heat dissipation rate in Btu/hr
h is the coefficient of heat transfer in Btu/hr-ft^2-°F
A is the surface area of the wall in ft^2
T_w is the temperature of the wall in °F
T_a is the temperature of the surrounding air in °F
The new heat dissipation rate can be calculated using the following formula:
Q_f = h * A_f * (T_w - T_a)
where:
Q_f is the heat dissipation rate with fins in Btu/hr
A_f is the surface area of the fins in ft^2
We can calculate the surface area of the fins as follows:
A_f = n * pi * d * L
where:
n is the number of fins per square inch
d is the diameter of the fins in inches
L is the length of the fins in inches
Substituting the given values into the above equations, we get the following results:
Old heat dissipation rate, Q = h * A * (T_w - T_a) = 28 Btu/hr-ft^2-°F * 1 ft^2 * (650°F - 75°F) = 17,150 Btu/hr
New heat dissipation rate, Q_f = h * A_f * (T_w - T_a) = 28 Btu/hr-ft^2-°F * 3 fins/in^2 * pi * 1/8 in * 1 in * (650°F - 75°F) = 46,894 Btu/hr
Percentage increase = (New heat dissipation rate - Old heat dissipation rate) / Old heat dissipation rate * 100% = (46,894 Btu/hr - 17,150 Btu/hr) / 17,150 Btu/hr * 100% = 174.2%
Therefore, the percentage increase in the heat dissipation rate is 174.2%.