ANS:B - Logarithmic mean area is used for calculating the heat flow rate through a thick walled cylinder.

The concept of logarithmic mean area (LMA) is often used in calculating the heat flow rate through a thick-walled cylinder because it provides an effective way to account for the varying cross-sectional area along the radial direction. In the case of a thick-walled cylinder, such as a pipe or a vessel, heat conduction occurs through the thickness of the cylinder from the inner surface to the outer surface. However, due to the differing areas at different radial positions, a simple average of the inner and outer surface areas would not accurately represent the heat transfer area. The LMA method takes into consideration the varying surface areas along the radial direction and provides a more accurate representation of the effective heat transfer area. It is calculated using the logarithmic mean of the inner and outer surface areas. Mathematically, the logarithmic mean area (LMAALMA​) for a thick-walled cylinder is given by: LMA=21�2ln⁡(2/1)ALMA​=ln(r2​/r1​)2πr1​r2​​ Where:

• 1r1​ is the inner radius of the cylinder,
• 2r2​ is the outer radius of the cylinder.

Using the logarithmic mean area in heat transfer calculations for a thick-walled cylinder ensures that the varying cross-sectional areas are appropriately accounted for, leading to more accurate results in determining the heat flow rate through the cylinder. This method is particularly useful in engineering applications where precise calculations of heat transfer are required, such as in the design of heat exchangers, boilers, and piping systems.