The development of safe nuclear fuel pellets is critical to future reactor designs. one project the engineers have is to look into what happens when the reactor cooling system fails and the heat transfer mechanism changes from forced convective cooling of the pellets to free con vective cooling (coefficient-h) the reactor cooling fluid is essentially infinite in extent and remains at a uniform temperature of t the pellet generates heat at a rate that varies with the pellet temperature: q* = q(t-t)w/m3 k =50 w/m k p 1500 kg/m3 c 450 j/kg k t, 20°c h55 w/m2 k t, = 125°c - q0= 55,000 w/m3 k peller= 4 mm assuming the lumped capacitance approach is appropriate, derive the transient differ- ential heat balance and solve the resulting differential equation (pellet temperature at t 0 is t)