Determine the percentage increase in heat transfer associated with attaching aluminum fins of rectangular pro- file to a plane wall. The fins are 50 mm long, 0.5 mm thick, and are equally spaced at a distance of 4 mm (250 fins/m). The convection coefficient associated with the bare wall is 40 W/m2 K, while that resulting from attachment of the fins is 30 W/m2 K

Definitionb 1.1. Given two integers a and d with d non-zero, we say that d divides a (written d | a) if there is an integer c with a = cd. If no such integer exists, so d does not divide a, we write d - a. If d divides a, we say that d is a divisor of a. Proposition 1.2.1: Assume that a, b, and c are integers. If a | b and b | c, then a | c. Proposition 1.3. Assume that a, b, d, x, and y are integers. If d | a and d | b then d | ax + by. Corollary 1.4. Assume that a, b, and d are integers. If d | a and d | b, then d | a + b and d | a − b. Prime: A prime number is an integer p ≥ 2 whose only divisors are 1 and p. A composite number is an integer n ≥ 2 that is not prime. Ex: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. The Division Algorithm: Let a and b be integers with b > 0. Then there exist