Answer to Question #217157 in Mechanical Engineering for Shivu

Question #217157

A 2 cm diameter glass rod(k=0.8W/mk) is 6 cm long.I t has base temperature at 120°C and is exposed to the air at 20°C. The temperature at the tip of the rod is measured as 35°C. What is the convection heat transfer coefficient.H ow much heat is lost by the rod?


1
Expert's answer
2021-07-16T03:55:37-0400

Part 1

Perimeter of the rod "P= \\pi d= \\pi*0.02 = 0.0628 m"

Cross sectional area "=\\frac{\\pi d^2}{4}=\\frac{\\pi 0.02^2}{4}=3.14 *10^{-4}m^2"

"m= \\sqrt{\\frac{hp}{kA}} = \\sqrt{\\frac{h*0.0628}{0.8*3.14*10^{-4}}} \\\\\n\\implies m= 15.8\\sqrt{h}\\\\"

"125 h=-15.8 \\sqrt{h}C_1e^{-15.8\\sqrt{h}*0.06}+15.8 \\sqrt{h}C_2e^{15.8\\sqrt{h}*0.06}\\\\\n15= C_1e^{-0.06\\sqrt{h}}+C_2e^{-0.948\\sqrt{h}}\\\\\n\\implies C_1 = 82.3\\\\\nC_2=0.8994\\\\\n\\therefore h=7.615 W\/m^2C"


Part 2

"q= \\sqrt{hpkA}*tanhmL\\\\\nq=\\sqrt{h*0.0628*0.8*8.14*10^{-4}}*83.144 tanh(15.8*\\sqrt{h}tan0.06\\\\\nq=0.010960*82.314\\\\\nq=0.9021 W"


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