In: Mechanical Engineering
A long, cylindrical, electrical heating element of diameter D=
10 mm, thermal conductivity k= 240 W/m·K, density ρ= 2700
kg/m3, and specific heat cp= 900 J/kg·K is installed in
a duct for which air moves in cross flow over the heater at a
temperature and velocity of 27°C and 15 m/s, respectively.
(a) Neglecting radiation, estimate the steady-state surface
temperature when, per unit length of the heater, electrical energy
is being dissipated at a rate of 1500 W/m.
(b) If the heater is activated from an initial temperature of 27°C,
estimate the time required for the surface temperature to come
within 10°C of its steady-state value.
Evaluate the properties of air at 450 K.
What is the value of the Reynolds number?
Re = 4613.05 (correct)
What is the value of the average Nusselt number?
not sure
What is the steady state temperature, in K?
got it correct
=666.96 K
What is the value of the Biot number?
Bi =0.0027
got correct
How long does it take for the element to come within 10°C of the steady state temperature, in s?
t= 168.21 correct
Knowing the steady state temperature, what is the actual value of the film temperature that should be used to find the air properties, in K? (Do not redo the problem.)
Tf=
(not sure )