Fins, or extended surfaces, commonly are used in a variety of engineering applications t...

Fins, or extended surfaces, commonly are used in a variety of engineering applications to enhance cooling. Common examples include a motorcycle engine head, a lawn mower engine head, heat sinks used in electronic equipment, and finned tube heat exchangers in room heating and cooling applications. For long fins, the temperature distribution along the fin is given by the exponential relationship:

h = the heat transfer coefficient (W/m² · K)

p = perimeter of the fin (m)

A = cross-sectional area of the fin (m²)

k = thermal conductivity of the fin material

x = distance from the base of the fin (m)

What is the appropriate unit for k if the preceding equation is to be homogeneous in units? Show all steps of your work.