The wall (thickness L) of a furnace is comprised of brick material (thermal conductivity, k = 0.2Wm K). Given that the atmospheric temperature is 0'C at both sides of wall,

the density(p)and heat capacity (c) of the brick material are 1.6 gm cm and 5.0 J kg K' respectively. \text { Solve } \rho e \frac{\partial u}{\partial t}=k \frac{\partial^{2} u}{\partial x^{2}} \text { subject to initial conditions as } u(x, 0)=x^{2}(L-x) \text { . } (ii) Given that the wall thickness is 10 cm, estimate the temperature profile within the brick wall after I hour when n =x =1.

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