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A plane wall with surface temperature of 350°C is attached with straight rectangular fins (k = 235 W/m·K). The fins are exposed to an ambient air condition of 25°C and the convection heat transfer coefficient is 154 W/m^2·K. Each fin has a length of 82 mm, a base of 5 mm thick and a width of 100 mm. Determine the efficiency, heat transfer rate, and effectiveness of each fin

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Answer:The efficiency of fin is 64.20%Heat transfer rate 543.03249WEffectiveness of each fin is 21.6996 Explanation:GivenSurface temperature = Tb = 350°CThermal Conductivity = k = 235 W/m·KAmbient air temperature = T = 25°CConvective heat transfer coefficient of air = h = 154 W/m^2·K. Length of fin = L = 82 mmBase of fin = t = 5 mmWidth of fin = w = 100 mmThe mass of fin is calculated by;m = √(2h/kt)m = √(2 * 154/235*0.005)m = 16.19Then the critical length is calculated;Lc. = L + ½tLc = 0.082 + ½ * 0.005.Lc = 0.0845mTherefore, the efficiency of the fin can be calculated as follows:tanh (mLc)/mLc= tanh(16.19 * 0.0845)/((16.19 * 0.0845)tanh(1.368055)/1.368055= 0.878248/1.368055= 0.6420Eff = 64.20%Area of the fin is calculated as followsA = 2wLcA = 2 * 0.1 * 0.0845A = 0.0169m²Rate of heat transfer is calculated by;Eff * h * A(Tb - T)= 0.642 * 154 * 0.0169 * (350 - 25)E = 543.03249WThe base area of the fin is calculated by;A = wtA = 0.1 * 0.005A = 0.0005m²Lastly, the effectiveness of each fin is calculated as follows;Eff = E/(hA(TB - T))Eff = 543.03249/(154 * 0.0005(350 - 25))Eff = 21.6996Therefore, the efficiency of fin is 64.20% , heat transfer rate 543.03249W and effectiveness of each fin is 21.6996 .

Answerd by blhughes
11 months ago 11 1.0