Solve the below problem:
Q: A plane wal1 of thickness 0.6 m (L = 0.3 m) is made of steel (k = 30 W/m · K. p = 7900 kg/m3, c = 640 J/kg · K). It is initially at a uniform temperature and is then exposed to air on both surfaces. Consider two different convection conditions: natural convection, characterized by h = 10 W/m2 · K, and forced convection, with h = 100 W/m2 · K. You are to calculate the surface temperature at three different times-t = 2.5 min, 25 min, and 250 min-for a total of six different cases.
(a) For each of these six cases, calculate the non-dimensional surface temperature: = (Ts - T8) / (Ti- T8), using four different methods: exact solution first-term-of-the-series solution, lumped capacitance, and semi-infinite solid. Present your results in a table.
(b) Briefly explain the conditions for which
(i) the first-term solution is a good approximation to the exact solution,
(ii) the lumped capacitance solution is a good approximation,
(iii) the semi-infinite solid solution is a good approximation