We are interested in determining the temperature distribution inside a concrete slab at a stoplight. The slab is exposed to cars' catalytic converters whose surface temperatures are \(300^{\circ} \mathrm{C}\). Figure P9.11 shows all the other important details.

a. Derive the partial differential equation governing the temperature profile inside the slab. Could we use a 1-d approximation?

b. Solve the differential equation for the temperature field. How hot does the surface at \(y=0\) get?

Transcribed Image Text:

FIGURE P9.11 y=0/ T300C, h=7 W/mK Concrete y=0.22 T=15C x=-5 x=0 x=5