Q1} A long electric heater wire made ofNichrome has a diameter of 6 mm and is used to heat air in furnace. Theelectric current passing through the wire results in uniform heat generated ata rate of 5 x 108 W/m3. The temperature of the outersurface of the wire remains at 400C. Take the thermal conductivity of theNichrome wire to be uniform with a value of k = 11.3 W/mK. For a one-dimensionheat conduction steady process.

a) Derive an expression for the temperaturevariation across the radios using the boundary conditions for heat conduction.

b) Determine the temperature at r = 2 mm

c) Check if the wire will have localmelting if the melting temperature is 1400C.

Q2) A 0.4W cylindrical electronic component with diameter 0.3 cm and length 2cm and mounted on a circuit board is cooled by air flowing across it at avelocity of 240 m/min. Assume the air inlet temperature is 35 C For airproperties evaluations assume a film temperature of 50C. For cross flow over acylinder.

The fluid properties are evaluated at thefilm temperature = (T+Ts)/2 where Ts is thepipe surface temperature and T∞ is the fluid far field temperature.

a)Calculatethe heat transfer coefficient

b)Determine the surface temperature of the component.

c)Check if the 50 C is a reasonable temperature to evaluate the air properties?  

Q3/ A counter flow double pipe heat exchangeruses superheated steam at a temperature of 250C to heat feed water at 35C to a temperatureof 65C. The superheated steam experiences a temperature drop of 70C as it existsthe heat exchange. The water to be heated flows through the heat exchanger tubethat has a relatively negligible thickness at a constant rate of 3.47 Kg/s. Theconvective heat transfer coefficient on the superheated steam and water side is850 W/m2.K and 1250 W/m2.K respectively. You may assumethat a fouling factor for the water side equal to 0.00015 m2.K/W.

  1. Calculate the overall heattransfer coefficient
  2.  Calculate the rate of heat transfer in theheat exchanger.
  3. Determine the heat exchangerarea required.
  4. What would be the required heatexchanger area in the case of the parallel flow arrangement.

Q4)

  1. State the difference betweenfin efficiency and fin effectiveness
  2. To enhance the heat transferfrom a flat surface, a fellow engineer attached a fin with an effectiveness of1.1 to it. Has this fin enhanced or degraded the heat transfer from the flatsurface?
  3. A rectangular fin ( k = 170 W/m. K) of length L= 10 mm, thickness t = 2mm, is exposed to a medium of uniformconvective coefficient of h = 150 W/m2 . K at a temperature T=30 ᵒC , if an adiabatic fin approximations is assumed, the width w>> t and the temperature at the bace ofthe fin is Tb = 120  ᵒC,
  1. Calculate the fin heat transferrate per unit width,
  2. Calculate the fin effectiveness
  3. Calculate the fin efficiency,and
  4. Calculate the fin tiptemperature

Q5

a) What properties are used to describe anelectromagnetic wave? Describe how these properties are related to each other.

b) Two concentric spheres of diameters Df  = 0.4m and D2 = 0.9m are maintainedat uniform temperatures Tf = 800K and T2 = 500 K and haveemissivibes ζ =0.4 and ζ = 0.6, respectively

  1.  Sketch a figure of this problem. Clearlylabeling it.
  2. Calculate the net rate ofradiation heat transfer between the two spheres.
  3. Calculate the radiation heattransfer rate from the outer sphere to the surrounding surfaces are at 40 C,and that the emissivity of the outer surface is 0.3.
  4. Is the value calculated in (c)above (between the sphere and the surrounding surfaces) greater than thecalculated in (b) above (between the two spheres)? Why?
Figure 1. FOR QUESTION 2  
Q1} A long electric heater wire made of Nichrome has a diameter of 6 mm and is used to heat air in furnace. The electric current passing through the wire results in uniform heat generated at a rate of 5 x 108 W/m3. The temperature of the outer surface of the wire remains at 400C. Take the thermal conductivity of the Nichrome wire to be uniform with a value of k = 11.3 W/mK. For a one-dimension heat conduction steady process. a) Derive an expression for the temperature variation across the radios using the boundary conditions for heat conduction.
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