1 **What are the heat transfer mechanisms involved during heat transfer from the hot fluid to the cold fluid?**

# Numerical Problems

**1.Find the Overall heat transfer coefficient for a shell and tube counter flow heat exchanger where the heat exchanged is 11.27 GJ/hour with the heat transfer area of 96 m2. Assume the LMTD as 76 oC.**

**2.. In a double pipe heat exchanger hot fluid is entering at 220°C and leaving at 115°C. Cold fluid enters at 10°C and leaves at 75°C. Mass flow rate of hot fluid 100 kg/hr, Cp of hot fluid 1.1 kcal/kg°C. Cp of cold fluid 0.95 kcal/kg°C. Calculate LMTD?**

- If the flow is parallel
- If the flow is counter current
- Find the mass flow rate of cold fluid if the heat loss during the exchange is 5%.

**3. When a heat exchanger was designed its overall heat transfer co-efficient was 600 kcal/hr mt²°C. The heat transfer area provided = 10mt². Over a period of time, its overall heat transfer co-efficient has fallen to 450 kcal/hr mt²°C due to fouling. Assume Counter flow.Data:**

- Specific heat of hot fluid = 1 kcal/kg °C
- Hot fluid entering temperature = 80°C
- Hot fluid leaving temperature = 60°C
- Cold fluid entering temperature = 25 °C
- Cold fluid leaving temperature = 40°C

**Calculate: How much additional area is to be added to maintain the same rate of heat transfer?**

**4. In a parallel flow double-pipe heat exchanger water flows through the inner pipe and is heated from 20°C to 70°C. Oil flowing through the annulus is cooled from 200°C to 100°C. It is desired to cool the oil to a lower exit temperature by increasing the length of the heat exchanger. Determine the minimum temperature to which the oil may be cooled?**

**5. The flow rates of hot and cold water streams running through a parallel flow heat exchanger are 0.2 kg/. and 0.5 kg/s respectively. The inlet temperatures on the hot and cold sides are 75°C and 20°C respectively. The exit temperature of hot water is 45°C. If the individual heat transfer coefficients on both sides are 650 w/m2°C, calculate the area of the heat exchanger.**

**6. In a counter flow double pipe heat exchanger, water is heated from 25°C to 65°C by an oil with a specific heat of 1.45 kJ/kg K and mass flow rate of 0.9 kg/s. The oil is cooled from 230°C to 160°C. If the overall heat transfer coefficient is 420 W/m2°C, calculate the following:**

- The rate of heat transfer
- The mass flow rate of water, and
- The surface area of the heat exchanger

**7. An oil cooler for a lubrication system has to cool 1000 kg/h of oil (cp = 2.09kJ/kg°C) from 8°C to 4O°C by using a cooling water flow of 1000 kg/h at 30°C. Give your choice for a parallel flow or counter-flow heat exchanger, with reasons. Calculate the surface area of the heat exchanger, if the overall heat transfer coefficient is 24 W/m2°C. Take Cp of water = 4.18 kJ/kg°C.**

**8. A counter-flow double pipe heat exchanger using superheated steam is used to heat water at the rate of 10500 kg/h. The steam enters the heat exchanger at 180°C and leaves at 13O°C. The inlet and exit temperatures of water are 30°C and 80°C respectively. I f overall heat transfer coefficient from steam to water is 814 W/m2°C, calculate the heat transfer area. What would be the increase in area if the fluid flows were parallel?**

**9. The amount of F¬12 used in compression refrigeration system is 4 tonnes/hour. The brine flowing at 850 kg/min, with inlet temperature of 12°C is cooled in the evaporator. Assuming F¬12entering and leaving the evaporator as saturated liquid and saturated vapour respectively, determine the area of evaporator required. Take the following properties: For F¬12 : Saturation temperature : - 23°C; cp = 1.1 7 kJ/kg°C; hfg = 167.4 kJ/kg Cp(brine) = 6.3 kJ/kg°C; U = 8368 kJ/m2h°C.**

**10. An after cooler of shell and tube type with single pass is used for cooling compressed air from 85 oC to 35 oC. The compressed air generated is 1350 m3/h at mean air temperature. Calculate:**

- The amount of cooling water to be circulated at a temperature of 30 oC. Assume the cooling water outlet temperature as 35 oC.
- The LMTD and no of tubes if the dia of the tube is 25.4 mm and 2500 mm length. Assume overall heat transfer coefficient for air to water is 150 W/m2.K.
- The hp of the pump required if the pressure required is 3.5 kg/cm2.g.