Extended heat transfer surface like fins are used to increase the heat transfer rate. Fin efficiency is defined as the ratio of heat transferred across the fin surface to the theoretical heat transfer across an equal area held at the

ANS:D - constant temperature equal to that of the base

In the context of fin efficiency, the term "constant temperature equal to that of the base" refers to the hypothetical condition where the entire fin is maintained at the same temperature as the base to which it is attached. When a fin is attached to a base (or a surface), the base typically acts as a heat source or sink, and heat flows from the base into the fin. The purpose of the fin is to enhance heat transfer by increasing the surface area available for heat exchange with the surrounding fluid (usually air or a liquid). In the concept of fin efficiency, we compare the actual heat transfer across the fin surface to the theoretical heat transfer that would occur if the entire fin were maintained at a constant temperature equal to that of the base. This theoretical condition represents an ideal situation where there is no temperature gradient along the fin's length. By comparing the actual heat transfer to this theoretical limit, we can quantify how effectively the fin is transferring heat. The fin efficiency is thus a measure of the performance of the fin in enhancing heat transfer. In summary, "constant temperature equal to that of the base" is used as a reference condition for calculating fin efficiency, representing the ideal scenario where the entire fin operates at the same temperature as the base, without any temperature gradient along its length.