Calculating thermal conductivity-heat transfer coefficient

Question

Question 1: A reactor wall 320 mm thick is made up of inner layer of fire brick (k = 0.84 W/mK) covered with a layer of insulation (k = 0.16 W/mK). The reactor operates at a temperature of 1325oC and the ambient temperature of 25^o C. Determine (a) thickness of fire brick and insulation which gives minimum heat loss. Calculate the heat loss presuming that the insulating material has a maximum temperature of 1200^o C at the interface.

Question 2: A furnace wall is made up of three layers of thickness 250 mm, 100 mm and 150 mm with thermal conductivities of 1.65 W/m^oC, k₂ and 0.2 W/m^oC respectively. The inside is exposed to gases at 1250^oC, with a convection coefficient of 25 W/m^{2 o}C and inside surface temperature is at 1100^oC, the outside surface is exposed to air at 25^o C with
convection coefficient of 12 W/m^2oC. Determine

i) The unknown thermal conductivity (k₂).
ii) The overall heat transfer coefficient. 
iii) All surface temperatures. 
 
Question 3: A steam main 250 mm in diameter and 225 m long is covered with 50 mm of high temperature insulation (k = 0.095 W/mK) and 40 mm of low temperature insulation (k = 0.065 W/mK). The inner and outer surface temperatures are 400^oC and 50^oC respectively. Calculate:

i) The total heat loss per hour
ii) The total heat loss per m3 of outer surface
iii) The heat loss per m2 of the pipe surface
iv) The temperature difference between two layers of insulation.

Question 4: A hollow sphere of pure iron contains a liquid chemical mixture which releases 30 kW of energy. The I.D and O.D of the sphere are 15 cm and 30 cm respectively. If the outside temperature of the sphere is 40^o C, determine the temperature at a location 2.5 cm away from the outer surface. Assume k = 70 W/m K.

Question 5: An electric current is passed through a composite wall made up of two layers. First layer is steel of 10 cm thickness and second layer is brass of 8 cm thickness. The outer surface temperature of steel and brass are maintained at 120^o C and 65^oC respectively.

Assuming that the contact between two slab is perfect and the heat generation is 1,65.000 W/m3. Determine (i) Heat flux through the outer surface of brass slab (ii) Interface temperature.

Question 6: A concrete wall of 1 m thick is poured with concrete. The hydration of concrete generates 150 W/m³ of heat. If both the surfaces of the wall are maintained at 35^o C, find the maximum temperature in the wall?

Question 7: A copper wire of 40 mm diameter carries 250 A and has a resistance of 0.25x10^-4 ? cm/length. Surface temperature of copper wire is 250^o C and the ambient air temperature is 10^oC. If the thermal conductivity of the copper wire is 175 W/mK, calculate:

i) Heat transfer coefficient between wire surface and ambient air.

ii) Maximum temperature in the wire.

Question 8: A sphere of 100 mm diameter having thermal conductivity of 0.18 W/mK. The outer surface temperature is 8^o C and 250 W/m² of energy is released due to heat source. Calculate the:

i) Heat generated.

ii) Temperature at the centre of the surface.

Question 9: Determine the heat transfer through the plane of length 6m, height 4m and thickness 0.30 m. The temperature of inner and outer surfaces are 100^o C and 40^o C. Thermal conductivity of wall is 0.55 W/mK. 
 
Question 10: A hollow cylinder 5 cm inner diameter and 10 cm outer diameter has inner surface temperature of 200^o C and outer surface temperature of 100oC. Determine heat flow through the cylinder per metre length. Also determine the temperature of the point half way between the inner and outer surfaces. Take k = 1 W/mK.