4. A small metal bridge crosses a creek. We will model the bridge as a rectangular fin with thickness t =0.5 m, width w = 2 m, and length L = 3 m and thermal conductivity k = 40 W/m-K. Since the earth is such a large thermal mass, we can assume both ends of the bridge (where the bridge joins the earth at x = 0 and x = L) are pinned at the earth's temperature Te = 18 °C.

a. If the surrounding air is at a temperature T∞

b.On a cold, windy day the air has a heat transfer coefficient h = 20 W/m²-K. Determine the temperature of the air To such that ice begins to form on the bridge.

c. Sketch the temperature profile T(x) in the bridge.d.Draw the temperature profile T(x) on a day without wind where h = 10 W/m²-K on the plot from part (c).