Solve the below problem:
Q: Heat is transferred from water to air through a brass wall (k = 54 W/(m K)). The addition of rectangular brass fins, 0.08 cm thick and 2.5 cm long, spaced 1.25 cm apart, is contemplated. Assuming a water-side heat transfer coefficient of 170 W/(m2 K) and an air-side heat transfer coefficient of 17 W/(m2 K), compare the gain in heat transfer rate achieved by adding fins to:
(a) the water side,
(b) the air side, and
(c) both sides. (Neglect temperature drop through the wall.)
GIVEN
A brass wall with brass fins between air and water
Thermal conductivity of the brass (k) = 54 W/(m K)
Fin thickness (t) = 0.08 cm = 0.0008 m
Fin length (L) = 2.5 cm = 0.025 m
Fin spacing (d) = 1.25 cm = 0.125 m
Water-side heat transfer coefficient ( hcw ) = 170 W/(m2 K)
Air-side heat transfer coefficient ( hca ) = 17 W/(m2 K)
ASSUMPTIONS
The thermal resistance of the wall is negligible
Steady state conditions prevail
Constant thermal conductivity
One dimensional conduction
Heat transfer from the tip of the fins isnegligible
