ANS:B - logarithmic

When dealing with the heat flow through a very thick-walled cylinder, it's common to use the logarithmic mean radius. So, the correct choice is: logarithmic The logarithmic mean radius (r_lm) is used to represent the average radius of a thick-walled cylinder when analyzing heat transfer. It is particularly useful when dealing with cylindrical geometries where the temperature gradient varies significantly across the radial direction, such as in the case of thick-walled cylinders. The formula for the logarithmic mean radius (r_lm) is given by: ���=�2−�1ln⁡(�2/�1)rlm​=ln(r2​/r1​)r2​−r1​​ Where:

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

The logarithmic mean radius takes into account the logarithmic difference between the outer and inner radii of the cylinder. This is important because the temperature gradient across the thickness of the cylinder is not uniform, especially in the case of very thick walls. Using the logarithmic mean radius helps in obtaining a more accurate representation of the average radial position where heat transfer occurs. By incorporating the logarithm of the ratio of outer to inner radius, the logarithmic mean radius provides a better estimate of the effective radius for heat transfer calculations in thick-walled cylinders. This is particularly relevant in scenarios where the temperature distribution is non-linear across the radial direction of the cylinder.