The rate in kilowatts (kW) at which heat is conducted in a solid is proportional to the area and the temperature gradient with the constant of proportionality being the thermal conductivity k(kW/m · ? C). For a long, laterally insulated rod this takes the form q = -k A(dT/dx). At the left end heat is transferred at the rate of 10 kW. Determine the temperature distribution in the rod if the right end at x = 2 m is held constant at 50?C. The crosssectional area is 1200 mm2 and k = 100 kW/m · ? C.