Final answer:
The student's inquiry on calculating fin efficiency and effectiveness involves thermal engineering principles of heat transfer. Specific formulas that consider fin dimensions, material properties, and thermal conditions would be used to derive these parameters. The precise calculations, however, would require further information and are not provided in this response.
Step-by-step explanation:
The student's question pertains to the efficiency and effectiveness of annular aluminum fins on a circular tube in heat transfer scenarios. To determine fin efficiency and effectiveness, we need to understand and apply concepts from the field of thermal engineering, such as the convection heat transfer coefficient, fin dimensions, and the temperature difference between the fin's base and the ambient air.
Firstly, fin efficiency (η) is a measure of how effectively the fin transfers heat compared to an ideal fin. An ideal fin would have a uniform temperature along its length and would dissipate the maximum possible heat.
In reality, the temperature along the fin decreases from the base to the tip, leading to less than ideal heat dissipation. Fin efficiency can be calculated using the formula that relates the actual heat transfer from the fin to the heat transfer if the fin were at the base temperature along its entire length.
Fin effectiveness (ε) is the ratio of the heat transfer from the fin to the heat transfer that would occur without the fin present, which can be represented by the increase in heat transfer due to the addition of fins to the surface. It is a way to measure how much the heat transfer has increased due to the addition of the fins.
In order to calculate these parameters, formulas that take into account the fin's geometry, material properties, and boundary conditions are utilized. For this specific scenario, detailed calculations including the fin's dimensions, thermal conductivity, and the given convection heat transfer coefficient would be required to provide a complete answer.