The problem of transient radial heat flow in a circular rod in nondimensional form is described by

∂2u/∂r2 + 1/r ∂u/∂r = ∂u/∂t

Boundary conditionsu(1, l) = 1∂u/∂t(0, l) = 0

Initial conditionsu(x, 0) = 00 ≤ x ≤ 1

Solve the nondimensional transient radial heat conduction equation in a circular rod for the temperature distribution at various times as the rod temperature approaches steady state. Use second-order accurate finite-difference analogues for the derivatives with a Crank-Nicolson formulation. Write a computer program for the solution. Select values of Δr and Δt for good accuracy. Plot the temperature u versus radius r for various times t.