# Heat Transfer and Temperature

A 50 mm diameter, thin wall metal pipe covered by 25 mm thick layer of insulation (ki = 0.085 W/m.K) and carrying a superheated steam at atmospheric pressure is suspended from the ceiling of a large room. The steam temperature entering the pipe is 120 oC, and the air temperature is 20 oC. The overall heat transfer coefficient on the outer surface of the covered pipe is 10 W/m2.K. if the velocity of the steam is 10 m/s, at what point along the pipe will the steam begin condensing and what distance will be required for the steam to reach a mean temperature of 100 oC?

Question 2:

Consider a horizontal, thin walled circular tube of diameter D = 0.025 m submerge in a container of n-octadecane (paraffin), which is used to store thermal energy. As hot water flows through the tube, heat is transferred to the paraffin, converting it from the solid to liquid state at the phase change temperature of T∞ = 27.4 oC. The latent heat of fusion and density of paraffin are hsf = 244 kJ/kg and ρ = 770 kg/m3, respectively and thermophysical properties of the water may be taken as cp = 4.185 kJ/kg.K, k = 0.635 W/m.K, and μ = 467 x 10-6 kg/s.m. Assuming the tube surface to have a uniform temperature corresponding to that of the phase change, determine the water outlet temperature and total heat transfer rate for a water flow-rate of 0.1 kg/s and inlet temperature of 60 oC. If the height, width and length of the container are 0.25 m, 0.25 m and 3 m, respectively, how long would it take to completely liquefy the paraffin, from an initial state for which all of the paraffin is solid and at 27.4 oC?

Question 3:

Consider the process by which ice is formed for an indoor rink. A parallel array of cooling tube is submerge in a shallow layer of water, and a refrigerant (Freon-12) is passed through the tubes. The layer height is H = 60 mm and the tube pitch, diameter and length are S = 50 mm, D = 12 mm, and L = 5 m, respectively. The temperature and flow rate of refrigerant entering each tube are -33 oC and 0.02 kg/s, respectively. The refrigerant remains at liquid state through out the tube, and average thermo physical property value may be taken to be cp = 900 J/kg.K, k = 0.07 W/m.K, m = 3.5 x 10-4 kg/s.m, and Npr = 4.6. The density of water ρ = 1000 kg/m3, and the latent heat of fusion is hsf = 3.34 x 105 J/kg.

a. consider the process whereby the water is taken from the saturated liquid to solid states to be at the freezing point throughout the process, at what temperature does the refrigerant leave the tube? What is the rate of heat transfer to the refrigerant for a single tube length? b. For the condition of part (a), how long would it take to completely freeze the water.

Question 4:

Water enters counter flow, double pipe heat exchanger at a rate of 150 lbm/min and is heated from 60 oF to 140 oF by an oil with specific heat of 0.45 Btu/lbm.oF. The oil enters at 240 oF and leaves at 80 oF. The overall heat transfer coefficient is 50 Btu/hr. oF. a. What heat transfer area is required ?

b. What area is required if all condition remain the same except that a shell and tube heat exchanger is used with the water making one shell pass and the oil making two tube passes? c. What exit water temperature would result if, for the exchanger part (a), the water flow rate were decreased to 120 lbm/hr?

Question 5:

A cold air chamber is proposed for quenching steel ball bearings of diameter D = 0.2 m and initial temperature Ti = 400 oC. Air in the chamber is maintained at – 15 oC by refrigeration system, and the steel ball pass through the chamber on a conveyor belt. Optimum bearing production requires that the temperature at the center of ball bearing reach 80 oC. Recommended the drive velocity of conveyor belt and estimated the power is required to maintain the chamber condition.

Question 6:

A sphere 30 mm in diameter initially at 800 K is quenched in a large bath having a constant...

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