A steel plane of finite dimension and thickness of 13 mm has the initial (uniform) temperature of 35 C. put the plane into the solution in all sudden and the wall temperature is increased to 146 C spontaneously. The thermo diffusivity of the plane, is alpha = 2.6*10^-4 m2/h. Calculate the time it takes for the central position of the plane to reach 145 C.
(Hint: To solve the nonlinear equation, iteration is needed. The higher order terms can be firstly ignored. Then do the iteration to see the contribution of the other terms. If they contribute too small, they can be ignored and the equation is converged.)