Final answer:
The efficiency, heat transfer rate, and effectiveness of the fin can be calculated using the fin's geometry, thermal conductivity, convection heat transfer coefficient, dimensions, and temperature difference.
Step-by-step explanation:
To determine the efficiency, heat transfer rate, and effectiveness of each fin with the given parameters, we can use the fin efficiency and effectiveness formulas. To calculate the efficiency (η) of the fin, it is important to consider the fin's geometry (straight rectangular), thermal conductivity (k), convection heat transfer coefficient (h), fin dimensions (ℓ, t, and w for length, thickness, and width, respectively), and temperature difference (ΔT) between the fin surface and the ambient air. These include formulas involving hyperbolic tangents for efficiency, and ratios of the fin's heat transfer rate to the heat transfer rate without a fin for effectiveness.
The efficiency of a fin is given by the formula:
η = (tanh(mℓ))/(mℓ), where m is the square root of (h•P)/(k•A_c), with P representing the perimeter of the fin cross-section, and A_c representing the fin's cross-sectional area. The heat transfer rate (q) is then found using q = η•h•A_s•ΔT, where A_s is the fin surface area.
The fin's effectiveness (ε) is a measure of the fin's heat transfer improvement over a no-fin situation, calculated as ε = q / (h•A_b•ΔT), where A_b is the area of the fin base. The effectiveness indicates how much more effective the fin is compared to the bare surface without fins.
Using the given data and incorporating the precise formulas, one can calculate the required values for a single fin attached to the wall. Remember to convert all measurements to consistent units before performing calculations (e.g., millimeters to meters).