Answer to Question #178306 in Mechanical Engineering for luke

Question #178306

Consider a 5m high 8m long and 0.22m thick wall whose representative cross section is given in the figure. The thermal conductivities of various materials used in W/m-C are kA = kF = 2, kB = 8, kC = 20, kD = 15, and kE = 35. The left and right surfaces of the wall are maintained at uniform temperature s of 300C and 100C respectively. Assuming heat transfer through the wall to be one-dimensional, Determine the rate of heat transfer through the wall in W


1
Expert's answer
2021-04-12T01:55:03-0400

Consider the diagram below

"R _1=R_A=\\frac{L}{kA}=\\frac{0.01}{2 \\times 0.12 \\times 1}=0.04 ^0C\/W"

"R _2=R_4=R_C=\\frac{L}{kA}=\\frac{0.05}{20 \\times 0.04 \\times 1}=0.06 ^0C\/W"

"R _3=R_B=\\frac{L}{kA}=\\frac{0.05}{8 \\times 0.04 \\times 1}=0.16 ^0C\/W"

"R _5=R_D=\\frac{L}{kA}=\\frac{0.01}{15 \\times 0.06 \\times 1}=0.11 ^0C\/W"

"R _6=R_E=\\frac{L}{kA}=\\frac{0.01}{35 \\times 0.06 \\times 1}=0.05 ^0C\/W"

"R _7=R_F=\\frac{L}{kA}=\\frac{0.06}{2 \\times 0.12 \\times 1}=0.25 ^0C\/W"

"R _8=\\frac{0.00012}{ 0.12}=0.001 ^0C\/W"

"\\frac{1}{R_{mid,1}}=\\frac{1}{R_2}+\\frac{1}{R_3}+\\frac{1}{R_4}=\\frac{1}{0.06}+\\frac{1}{0.16}+\\frac{1}{0.06}"

"R_{mid,1}=0.025^0C\/W"

"\\frac{1}{R_{mid,2}}=\\frac{1}{R_5}+\\frac{1}{R_6}=\\frac{1}{0.11}+\\frac{1}{0.05}"

"R_{mid,2}=0.034^0C\/W"

"R_{Total}=0.04+0.025+0.034+0.25+0.001=0.35^0C\/W"

"Q=\\frac{300-100}{0.35}=571.43 W"

"Q_{Total}=571.43\\frac{5 \\times8}{0.12 \\times1}=190476.67 W"


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