Question

An electric resistance heater is embedded in a long cylinder of diameter 30 mm. when water with a temperature of 25°c and velocity 1 m/s flows crosswise over the cylinder, the power per unit length required to maintain the surface at a uniform temperature of 80°c is 38 kw/m. when air, also at 25°c, but with a velocity of 10 m/s is flowing, the power per unit length required to maintain the same surface temperature is 400 w/m. assume unit length. calculate and compare the convection coefficients for the flows of water and air. according to your calculations, which is a better convective heat transfer media, air or water?

Answer 1

KNOWN: Long, 30mm-diameter cylinder with embedded electrical heater; power required to maintain a specified surface temperature for water and air flows.
 FIND: Convection coefficients for the water and air flow convection processes, hw and ha, respectively.
 ASSUMPTIONS: Flow is cross-wise over cylinder which is very long in the direction normal to flow.
 The convection heat rate from the cylinder per unit length of the cylinder has the form
 q' = h*(pi*D)*(Ts-Tinf)
 and solving for the heat transfer convection coefficient, find
 Water
 hw = q'/((pi*D)*(Ts-Tinf))
 hw = (38*10^3 W/m) / ((pi*(0.030m))*(80-25)C)= 7330.77314  W/m^2K
 Air
 ha = (400W/m) / ((pi*(0.030m))*(80-25)C)= 77.166033  W/m^2K
 COMMENTS: Note that the air velocity is 10 times that of the water flow, yet
hw ≈ 95 × ha.
 These values for the convection coefficient are typical for forced convection heat transfer with liquids and gases
 Watter is a better convective heat transfer media than air