A steel I-beam with a cross-sectional area as shown has its lower and upper surfaces maintained at 700 and 370 K, respectively. a. Assuming a negligible temperature change through both flanges,...

A steel I-beam with a cross-sectional area as shown has its lower and upper surfaces maintained at 700 and 370 K, respectively.

a. Assuming a negligible temperature change through both flanges, develop an expression for the temperature variation in the web as a function of the distance from the upper flange.

b. Plot the temperature profile in the web if the convective heat-transfer coefficient between the steel surface and the surrounding air is 57 W/m²
K. The air temperature is 300 K.

c. What is the net heat transfer at the upper and lower ends of the web?