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 10^{8} W/m^{3}. 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_{∞}+T_{s})/2 where T_{s} 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/m^{2}.K and 1250 W/m^{2}.K respectively. You may assumethat a fouling factor for the water side equal to 0.00015 m^{2}.K/W.

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

Q4)

- State the difference betweenfin efficiency and fin effectiveness
- 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?
- 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/m
^{2}. 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 T_{b }= 120 ᵒC,

- Calculate the fin heat transferrate per unit width,
- Calculate the fin effectiveness
- Calculate the fin efficiency,and
- 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 D_{f } = 0.4m and D_{2 }= 0.9m are maintainedat uniform temperatures T_{f }= 800K and T_{2 }= 500 K and haveemissivibes ζ =0.4 and ζ = 0.6, respectively

- Sketch a figure of this problem. Clearlylabeling it.
- Calculate the net rate ofradiation heat transfer between the two spheres.
- 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.
- 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 |