**Paper, Order, or Assignment Requirements**

__PART (A)__

__ __

A single brick wall has a dimension of 4.5m´2.5m and thickness of 100mm. The inner and the outer air temperatures are 21^{o}C and – 3 ^{o}C and the inner and outer convective heat transfer coefficients are 8W/m^{2}k and 18W/m^{2}k respectively. The brick have thermal conductivity of 1.1 W/m k. Calculate:

- a) The total thermal resistance and the rate of heat transfer through the wall.

- b) If the rate of heat transfer is going to be reduced by 20%, calculate the new thickness of the wall.

A piece of tungsten wire has length 15mm and diameter of 0.5mm. The emissivity of the tungsten is 0.4 and the surrounding temperature is – 4 ^{o}C. The rate of radiation heat transfer from tungsten is 40W and the Stefan- Boltzmann constant, s = 5.68 ´ 10 ^{– 8} W/m^{2}k^{4}. Calculate the temperature of tungsten wire in degree C.

For the following wall, calculate the overall U value and the rate of Fabric heat loss/m^{2}:

**U _{1} = 6W/m^{2}k U_{2} = 7.5W/m^{2}k U_{3} = 8.34W/m^{2}k**

A building of dimensions 12m ´ 6.5m ´ 3.5m is to be ventilated at the rate of 6 air changes per hour. Calculate:

- a) The ventilation volume flow rate.

- b) If the inside temperature of the building is to be kept at 19
^{o}C while the outside temperature is at – 2^{o}C, determine the rate of energy loss by ventilation and ventilation power.

__PART (B)__

A steam pipe line has an internal diameter of 100mm and wall thickness of 5mm and carries steam at temperature of 250^{o}C.The pipe is lagged with a cylindrical jacket of thickness 30mm. The thermal conductivity of the pipe material is 60W/mk^{o} and that of the insulation 0.04W/mk^{o}. The convective heat transfer coefficient for fluid inside is 10000W/m^{2}k^{o} and that for air outside is 10 W/m^{2}k^{o} and the outside air temperature is 20^{o}C.

Determine:

- a) The total thermal resistance and the rate of heat transfer per meter length of the pipe.

- b) The outside surface temperature.

- c) The thickness of insulator if the rate of heat transfer is to be reduced by 20%.

A recuperator consists of a shell and parallel pipes of inside and outside diameters of 25mm and 30mm with thermal conductivity of 50W/mk^{o}. Hot gas enters the pipes with temperature of 500^{o}C at the rate of 0.25kg/s with specific heat capacity C_{pg} = 1.02kJ/kgk^{o}. The gas is cooled to 150^{o}C with flowing water at the rate of 0.4kg/s through the shell with temperature of 15^{o}C and specific heat capacity of 4.2kJ/kgk^{o}. The surface heat transfer coefficients for the gas and water are 250W/m^{2}k^{o} and 1700W/m^{2}k^{o} respectively.

Calculate:

- The rate of heat transfer from the gas to the water and hence the exit temperature of the water.

- The overall heat transfer coefficient “U
_{T}”.

- The logarithmic mean temperature “ΔT
_{mean}” for both parallel and counter flow.

- The required surface area for both parallel and counter flow and hence the required water pipes length.

A flat roof building has the following dimensions:

T_{o} = 0^{o}C

5m8m 5 m

8 m

14m

2 Windows (front wall) and 2 windows (rear wall) each have dimensions of 3m ´ 1.8m with thermal transmittance of U = 6W/m^{2}k.

1 Door (front wall) and 1 door (rear wall) each have dimensions 2.2m ´ 1m with thermal transmittance of U = 3W/m^{2}k.

Each wall has thermal transmittance of U = 0.8W/m^{2}k.

For Floor, U = 0.45W/m^{2}k and for Roof, U = 0.5W/m^{2}k.

Ventilation rate is 1.5 air changes per hour.

Calculate:

- a) The average U values for front and rear walls.

- b) The rate of fabric and ventilation losses and hence the total losses from the building.

- c) The % rate of energy saved if the windows are replaced by double glazed windows with U = 2W/m
^{2}

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