Question

In: Mechanical Engineering

A long, cylindrical, electrical heating element of diameter D= 10 mm, thermal conductivity k= 240 W/m·K,...

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 )

Expert Solution

samet mamat answered 7 months ago

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