As in Fig. P24.22, an insulated metal rod has a fixed temperature (T 0 ) boundary condition

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As in Fig. P24.22, an insulated metal rod has a fixed temperature (T0) boundary condition at its left end. On it right end, it is joined to a thin-walled tube filled with water through which heat is conducted. The tube is insulated at its right end and convicts heat with the surrounding fixed temperature air (T). The convective heat flux at a location x along the tube (W/m2) is represented by Jconv = h(T∞ − T2(x))  where h = the convection heat transfer coefficient [W/(m· K)]. Employ the finite-difference method with Δx = 0.1 m to compute the temperature distribution for the case where both the rod and tube are cylindrical with the same radius r (m). Use the following parameters for your analysis: Lrod = 0.6 m, Ltube = 0.8 m, T0 = 400 K, T = 300 K, r = 3 cm, ρ= 7870 kg/m3, Cp1 = 447 J/(kg · K), k1 = 80.2 W/(m · K), ρ= 1000 kg/m3, Cp2 = 4.18 kJ/(kg . K), k2 = 0.615 W/(m · K), and h = 3000 W/(m2 . K). The subscripts designate the rod (1) and the tube (2).


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