ANS:A - thin walled having the value of A_o A_i/< 2.

The arithmetic mean area method can be used in heat transfer problems to calculate the heat flow by conduction through a cylinder that is thin-walled. Explanation:

• The arithmetic mean area method assumes that the temperature difference across the thickness of the wall is small, allowing the use of the average area for heat transfer calculations.
• For a thin-walled cylinder, the difference in radius between the outer and inner surfaces is small compared to the overall radius. This means that the temperature difference across the thickness of the wall is relatively small.
• Therefore, the arithmetic mean area (Ao + Ai) / 2 can be used to approximate the heat transfer area for thin-walled cylinders.
• If the cylinder is thick-walled (where the difference in radius between the outer and inner surfaces is significant), the temperature difference across the thickness of the wall becomes more pronounced. In this case, the arithmetic mean area method would not provide an accurate representation of the heat transfer area.
• The condition Ao/Ai > 2 doesn't directly determine whether the cylinder is thin or thick-walled. It only specifies the ratio of outer area to inner area, which could be applicable to both thin and thick-walled cylinders depending on their specific dimensions.