(Solved): this is the whole problem A long cylindrical rod of diameter 200mm with thermal conductivity of 0 ...

A long cylindrical rod of diameter $$200\mathrm{mm}$$ with thermal conductivity of $$0.5\mathrm{W}/\mathrm{m}?\mathrm{K}$$ experiences uniform volumetric heat generation of $$3.7\times 10^4\mathrm{W}/{\mathrm{m}}^3$$. The rod is encapsulated by a circular sleeve having an outer diameter of $$400\mathrm{mm}$$ and a thermal conductivity of 4 $$\mathrm{W}/\mathrm{m}?\mathrm{K}$$. The outer surface of the sleeve is exposed to cross flow of air at $$27^{?}\mathrm{C}$$ with a convection coefficient of $$25\mathrm{W}/{\mathrm{m}}^2?\mathrm{K}$$ (a) Find the temperature at the interface betweeh the rod and sleeve and on the outer surface. (b) What is the temperature at the center of the rod? (a) $$\begin{array}{l}{T}_{\text{intarine }}={}^{?}\mathrm{C}\\ T_{\text{oulet }}=?+{}^{?}\mathrm{C}\end{array}$$ (b) $$T(0)=$$ $${}^{?}\mathrm{C}$$ A long cylindrical rod of diameter $$200\mathrm{mm}$$ with thermal conductivity of $$0.5\mathrm{W}/\mathrm{m}?\mathrm{K}$$ experiences uniform volumetric heat generation of $$3.7\times 10^4\mathrm{W}/{\mathrm{m}}^3$$. The rod is encapsulated by a circular sleeve having an outer diameter of $$400\mathrm{mm}$$ and a thermal conductivity of 4 $$\mathrm{W}/\mathrm{m}?\mathrm{K}$$. The outer surface of the sleeve is exposed to cross flow of air at $$27{\mathrm{C}}^{\mathrm{C}}$$ with a convection coefficient of $$25\mathrm{W}/{\mathrm{m}}^2?\mathrm{K}$$. (a) Find the temperature at the interface between the rod and sleeve and on the outer surface. (b) What is the temperature at the oenter of the rod? $$\begin{array}{ll}{T}_{\text{intafice }}=& \\ T_{\text{ouice }}=& \\ \text{ (b) }T(0)=& {}^{?}\mathrm{C}\\ T\mathrm{C}& \end{array}$$ (a)