A 'long' steel shaft of 10 cm diameter is austenised at 870°C and then quenched in a liquid at 30°C. The average surface heat transfer coefficient is 2000 W/m² °C. The relevant thermophysical properties of the shaft material are k = 20 W/m °C; p= 7800 kg/m³; c, = 0.46 kJ/kg °C. Calculate: (i) the time required for the centre-line temperature to drop down to 200°C (martensite forms at this temperature), (ii) the temperature at half-radius at that moment, and (iii) the amount of heat that has been transferred to the liquid by that time per metre length of the shaft.

Steel pipe 3 cm thick, 1.0 m long and 10 cm deep, covered with 6 cm thick insulation. The wall temperature in the steel pipe is 100 ° C. The ambient temperature around the insulated pipe is 24 ° C. The convection heat transfer coefficient outside the insulation surface is 50 W / (m² K). The thermal conductivity of steel is 54 W / (m K), and the thermal conductivity of the insulation is 0.04 W / (m K). Count; a. Heat loss per meter of pipe = Answer watt. b. Temperature between steel pipe and insulation. = Answer ° C.

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Air at 25 ° C blows over the hot steel plate whose surface temperature is maintained at 200 ° C. The plates have dimensions of 50 cm x 50 cm and a thickness of 2.5 cm. The convection heat transfer coefficient on the upper surface is 25 W / (m² ° C). The thermal conductivity of steel is 45 W / (m ° C). Calculate the hourly heat loss from the plate surface. a. heat loss per hour = AnswerkJ. b. If the reverse side surface temperature is maintained, specify hourly heat loss = AnswerkJ.

for chemical engineers

A plane wall has a thermal conductivity of 20 W/(m-K) and generates heat at 0.5 MW/m3. The wall is 0.2 meters thick and is perfectly insulated on one side. The other side is exposed to fluid at 100 °C. The convective heat transfer coefficient between the wall and the fluid is 400 W/(m2 K). Determine the maximum temperature in the wall.

The exhaust duct from a heater has an inside diameter of 114.3 mm with ceramic walls 6.4 mm thick. The average k=1.52 W/m· K. Outside this wall, an insulation or rock wool 102 mm thick is installed. The thermal conductivity of the rock wool is k= 0.046+ 1.56 x 104 T°C (W/m · K). The inside surface * = temperature of the ceramic is T1 = 588.7 K, and the outside surface temperature of the insulation is 311 K. Calculate the heat loss for 1.5 m of duct and the interface temperature T2 between the ceramic and the insulation. [Hint: The correct value of km for the insulation is that evaluated at the mean temperature of (T2 + T3)/2. Hence, for the first trial assume a mean temperature of, say, 448 K. Then calculate the heat loss and T2 Using this new T2, calculate a new mean temperature and proceed as before.]

2-2 A certain material 2.5 cm thick, with a cross-sectional area of 0.1 m², has one side maintained at 35°C and the other at 95°C. The temperature at the center plane of the material is 62°C, and the heat flow through the material is 1 kW. Obtain an expression for the thermal conductivity of the material as a function of temperature.

A cylindrical container is being designed to contain an exothermic chemical reaction. The container has an external diameter of 80 mm and is 0.2 m tall. The temperature of the cylinder must not exceed 500 °C. To improve cooling of the container, fins of thickness t=5 mm and length L= 40 mm are spaced at least 10 mm apart. Each fin has an efficiency of n= 40%. The ambient temperature is maintained at 22 °c and the heat transfer coefficient between the ambient air and the cylinder is 50 W/m2K. If the chemical reaction produces a maximum of 3.2 kW per kilogram of substance, the maximum mass of substance which can safely be processed in the container to 2 decimal places is kg. The effectiveness of each fin to 1 decimal place is You may neglect heat transfer from the tips of the fins and from the circular surfaces of the cylinder.

.240mm steam main pipe, 210m long is covered with 50mm of high temperature insulation (k-0.092 W/m °C) and 40mm of low temperature insulation (k-0.062 W/m °C). The inner and the outer surface temperature as measured are 390 °C and 40 °C respectively. Calculate: 1- The total heat loss per hour. 2- The temperature between two layers of insulation.