The rate of heat flow (conduction) between two points on a cylinder heated at one end is given by
dQ/dt = λAdT/dx
where λ = a constant, A = the cylinder’s cross-sectional area, Q = heat flow, T = temperature, t = time, and x = distance from the heated end. Because the equation involves two derivatives, we will simplify this equation by letting
dT/dx = 100(L - x)(20 - t)/100 - xt
where L is the length of the rod. Combine the two equations and compute the heat flow for t = 0 to 25 s. The initial condition is Q(0) = 0 and the parameters are λ = 0.5 cal · cm/s, A = 12 cm2, L = 20 cm, and x = 2.5 cm. Plot your results.