Heat conduction with temperature-dependent thermal conductivity (Fig. 108.12). The curved surfaces and the end surfaces (both...

  

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Heat conduction with temperature-dependent thermal conductivity (Fig. 108.12). The curved surfaces and the end surfaces (both shaded in the figure) of the solid in the shape of a half-cylindrical shell are insulated. The surface :0 = 0, of area (r, -r)L,is maintained at temperature To, and the surface at0 = 7, also of area (r, - r)Lis kept at temperature T. The thermal conductivity of the solid varies linearly with temperature from ko at T = Te to k, at T = T. a) Find the steady-state temperature distribution. (b) Find the total heat flow through the surface at e = 0 z =0 z =L Suríace at T, Surface at Tp Heat conduction with temperature-dependent thermal conductivity (Fig. 108.12). The curved surfaces and the end surfaces (both shaded in the figure) of the solid in the shape of a half-cylindrical shell are insulated. The surface :0 = 0, of area (r, -r)L,is maintained at temperature To, and the surface at0 = 7, also of area (r, - r)Lis kept at temperature T. The thermal conductivity of the solid varies linearly with temperature from ko at T = Te to k, at T = T. a) Find the steady-state temperature distribution. (b) Find the total heat flow through the surface at e = 0 z =0 z =L Suríace at T, Surface at Tp