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# 1)Consider a large plane wall of thickness L = 0.4 m, thermal conductivity k = 1.8 W/mK, and surface area A = 30 m2 .

1)Consider a large plane wall of thickness L = 0.4 m, thermal conductivity k = 1.8 W/m·K, and surface area A = 30 m2 . The left side of the wall is maintained at a constant temperature of T1 = 90°C while the right side wall is maintained at a constant temperature at T2 =25°C. Assuming constant thermal conductivity and no heat generation in the wall.

(a) Express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the wall

(b) Obtain a relation for the variation of temperature in the wall by solving the differential equation (c) Evaluate the rate of heat transfer through the wall

2)The wall of a refrigerator is constructed of fiberglass insulation (k = 0.035 W/m·K) sandwiched between two layers of 1-mm-thick sheet metal (k = 15.1 W/m·K). The

refrigerated space is maintained at 3°C, and the average heat transfer coefficients at the inner and outer surfaces of the wall are 4 W/m2·K and 9 W/m2·K, respectively. The kitchen temperature averages 25°C. It is observed that condensation occurs on the outer surfaces of the refrigerator when the temperature of the outer surface drops to 20°C. Determine the minimum thickness of fiberglass insulation that needs to be used in the wall in order to avoid condensation on the outer surfaces.