Description of task: In a particular application, it is desirable to maximise the heat transfer from a certain surface as shown in part (a) of Figure 1. An engineer suggests that the heat transfer performance could be increased by introducing extended surface/fin to that surface, resulting in the fin-like structure as shown in part (b) of the Figure. The extent to which the tip condition affects the thermal performance of a fin depends on the fin geometry and thermal conductivity, as well as the convection coefficient. Consider an alloyed aluminium (k = 180 W/m.K) rectangular fin of length L = 10 mm, thickness t = 1 mm, and width w >> t. The base temperature of the fin is T = 100C and the fin is exposed to fluid temperature of temperature To = 25C. a Ab=wxt Ab W -L- Afin (a) Surface without fins (b) Surface with a fin Figure 1. A surface (a) without fin and (b) with fin 1. Show one example of derivation for potential equation to be used in solving the problem. 2. Assuming a uniform convection coefficient of h = 100 W/m.K over the entire fin surface, determine the fin heat transfer rate per unit width, q, and the tip temperature, T(L), for the following cases: a. CASE A convection heat transfer at the tip b. CASE Badiabatic tip condition 3. Calculate the efficiency, , and effectiveness, &, of the fin for cases A and B. 4. Compare the results obtained in question 2. and 3. to those based on an infinite fin approximation. 5. Explore the effect of variation in the convection coefficient on the heat rate for 10