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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^oC and – 3 ^oC and the inner and outer convective heat transfer coefficients are 8W/m²k and 18W/m²k respectively. The brick have thermal conductivity of 1.1 W/m k. Calculate:

 

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

 

1. 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 ^oC. The rate of radiation heat transfer from tungsten is 40W and the Stefan- Boltzmann constant, s = 5.68 ´ 10 ^{– 8} W/m²k⁴. 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/m²:

 

 

U₁ = 6W/m²k   U₂ = 7.5W/m²k   U₃ = 8.34W/m²k

 

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

 

1. a) The ventilation volume flow rate.

 

1. b) If the inside temperature of the building is to be kept at 19^oC while the outside temperature is at – 2^oC, 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^oC.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/m²k^o and that for air outside is 10 W/m²k^o and the outside air temperature is 20^oC.

Determine:

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

 

1. b) The outside surface temperature.

 

1. 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^oC at the rate of 0.25kg/s with specific heat capacity C_pg = 1.02kJ/kgk^o. The gas is cooled to 150^oC with flowing water at the rate of 0.4kg/s through the shell with temperature of 15^oC and specific heat capacity of 4.2kJ/kgk^o. The surface heat transfer coefficients for the gas and water are 250W/m²k^o and 1700W/m²k^o respectively.

Calculate:

 

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

 

1. The overall heat transfer coefficient “U_T”.

1. The logarithmic mean temperature “ΔT_mean” for both parallel and counter flow.

 

1. 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^oC

 

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/m²k.

1 Door (front wall) and 1 door (rear wall) each have dimensions 2.2m ´ 1m with thermal transmittance of U = 3W/m²k.

Each wall has thermal transmittance of U = 0.8W/m²k.

For Floor, U = 0.45W/m²k and for Roof, U = 0.5W/m²k.

Ventilation rate is 1.5 air changes per hour.

 

Calculate:

 

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

 

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

 

1. c) The % rate of energy saved if the windows are replaced by double glazed windows with U = 2W/m²