Two cylinders of different materials are brought into contact as shown in Fig. 2

Question

Two cylinders of different materials are brought into contact as shown in Fig. 2.15. Cylinder 1 is 2 m long with cross sectional area of 0.03 m2 and thermal conductivity 0.7W m-1K-1. Cylinder 2 is 3m long with cross sectional area of 0.04 m2 and thermal conductivity 1.2 W m-1 K-1 The temperatures at each end of the apparatus are 280 (T1) and 310 K (T3), as shown in Fig. 2.15. Find the temperature T2 at the point where the two cylinders are joined. FIGURE 2.15 Heat transfer in adjoining cylinders (Problems 2.13 and 2.14).

Explanation / Answer

Thermal Resistance offered by cylinder 1 , R1= L/KA = 2 / (.7 x .03) = 95.238

Let the thermal conductivity of cylinder 2 be K2

Thermal Resistance offered by cylinder 2 , R2= 3 / (K2 x .04) = 75 / K2


Q = Qtotal = Q(between 3-2) = Q(between 2-1) = Q(between 3-1)

Q = T / R = (T2 - T1) / R1 = (300 -280) / 95.238 = .21 W



(T3 - T2) = Q x R2
=> 310 - 300 = .21 x R2

=> R2 = 47.619

=>  75 / K2 = 47.619

=>K2 = 1.575 W/mK

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