Consider a semi-infinite medium with thermal diffusivity alpha at an initial temperature of
T_(i). For t>0, a constant temperature, T_(0), is applied to the surface (x=0).
a) Determine a 3rd order polynomial approximation for the temperature profile T((x)/(delta )).
b) Determine an expression for the penetration depth, delta (t), using the integral method of
weighted residuals and compare to the exact solution given in class (Ex 7.1 part b )).
c) Determine an expression for the heat transfer coefficient defined according to
q_(x)(x=0)=h(T_(0)-T_(i)) and compare to the exact solution.
2. Consider a semi-infinite medium with thermal diffusivity a at an initial temperature of Ti. For t>0, a constant temperature, To, is applied to the surface (x=0). a) Determine a 3rd order polynomial approximation for the temperature profile T(x/S). b) Determine an expression for the penetration depth, (t), using the integral method of weighted residuals and compare to the exact solution given in class (Ex 7.1 part b)) c) Determine an expression for the heat transfer coefficient defined according to qx(x=0) = h(To - Ti) and compare to the exact solution.