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Answer:
a) 1,607,973.9 K/W
b)
i) 0.3082 = 30.82%
ii) 0.1821 = 18.21%
iii) 0.1293 = 12.93%
iv) 0.1002 = 10.02%
Explanation:
Value of thermal conductivity ( calculated value ) KCN = 3113 W/m-k
Thermal conductivity ( theoretical value ) K = 4500 W/m-k
Island separation = 5 μm
<u>a) Determine the thermal contact resistance </u>
Resistance due to contact between carbon nano tube and top surfaces can be determined using the relation below
( I / A*K ) + 2Rc = ( l / A*KCN ) ------- ( 1 )
where ; I = 5 * 10^-6 m
A = π * ( 14 * 10^-9 )^2 m^2 = 153.93 * 10^-18 , K = 4500 , KCN = 3113
<em>input values into equation 1 above</em>
hence Rc = 1,607,973.9 K/W
<u>b) Determine fraction of total resistance between heated and sensing </u>
fraction of total resistance ; f1 =
where : Rc = 1607973.9, K = 4500, A = 153.93 * 10^-18 ,
i) for I = 5 * 10^-6 m
fraction = 0.3082 = 30.82%
ii) for I = 10 * 10^-6 m
fraction = 0.1821 = 18.21%
iii) for I = 15 * 10^-6 m
fraction = 0.1293 = 12.93%
iv) for I = 20*10^-6
fraction = 0.1002 = 10.02%