7 An electric heater is made of thin conducting wires forming a mesh. The diameter of the wire is 0.5 mm and the total length of all the wires is 2 m. The temperature of the wire is 1,000 K. The heat from the wire is dissipated to the air at 300 K flowing through the wire mesh at a velocity of 5 m/s. Ignore radiation of the heater and assume it has a uniform temperature. T Const = (a) Calculate the convection heat transfer coefficient(h) between the air and the heater. (b) If the total electrical resistance of the heater is 10 2, what is the electrical current? (c) Calculate the Biot number of the heater. V=IR (d) The electrical current is suddenly cut off. How long does it take for the heater temperature to drop to 500 K? Properties of the air: pa = 0.7 kg/m³, Cp,a= 1030 J/kg K, va = 38.8×106 m²/s, ka=0.041 W/m•K, aa =56.7×106 m²/s, and Pra = 0.684. Properties of the heater: ph = 8900 kg/m³, Cp,h= 380 J/kg K, and kn = 400 W/m.K.

The front window of an automobile has a thickness of 4 mm and is defrosted by the passage of a stream of hot air through the inner surface. The thermal conductivity of glass is around 0.78 W/(m oC). Assume the ambient air temperature is -10°C and the external convection coefficient is 65W/(m2 K). If the hot air blowing to defog the glass internally is at 40 ºC and the internal convection coefficient corresponds to 30 W/(m2 K), the internal surface temperatures will be _____________. However, if the car accelerates and maintains high speed, the external convection coefficient should _____________  [increase or decrease?] and if the condition is maintained long enough the temperature of the inner surface of the glass should _____________  [increase or decrease?].

IMPORTANT!!! ONLY ANSWER PART D Parts A, B, and C are solved and the answers are in the picture.

A thick-walled cylindrical tubing of hard rubber (k=0.151 W/m*K) having an inside radius of 5 mm and an outside radius of 20 mm is being used as a temporary cooling coil in a bath. Ice water is flowing rapidly inside, and the inside wall temperature is 275 K. The outside surface temperature is 300 K. A total of 20 W must be removed from the bath by the cooling coil. How many meter of tubing are needed?