Heat Transfer

Step 1: Understanding the heat transfer.
The time taken for the cooling of the ball can be determined using Newton’s Law of Cooling, which is based on the heat transfer equation: Where: - is the heat lost,
- is the heat transfer coefficient,
- is the surface area,
- is the temperature of the object,
- is the ambient temperature.
For a sphere, the surface area is given by: The mass of the ball is: And the heat lost is related to the change in temperature: Step 2: Applying the formula.
By substituting the values and solving the differential equation for cooling, the time taken for the ball to cool from 900°C to 600°C is found to be 0.55 hours.
Step 3: Conclusion.
The correct answer is (3) 0.55 hours.

Step 1: Understanding heat exchangers.
In a heat exchanger, the effectiveness is maximized when the temperature difference between the two streams is maximized throughout the exchanger. This is achieved in countercurrent flow configurations, where the two fluids flow in opposite directions. In this case, placing the process stream on the shell side and the steam condensate on the tube side enhances heat transfer efficiency.
Step 2: Conclusion.
The best arrangement for this heat exchanger is a counterflow configuration with the process stream on the shell side. Therefore, the correct answer is (1).