A 2-mm-diameter electrical wire is insulated by a 2-mm-thick rubberized sheath (k = 0.13 W/m K), and the wire/sheath interface i
s characterized by a thermal contact resistance of R"t,c= 3x10-4 m2 K/W. The convection heat transfer coefficient at the outer surface of the sheath is 10 W/m2 K, and the temperature of the ambient air is 20o C. If the temperature of the insulation may not exceed 50o C, what is the maximum allowable electrical power that may be dissipated per unit length of the conductor? What is the critical radius of the insulation?
1 answer:
Answer:
maximum allowable electrical power=4.51W/m
critical radius of the insulation=13mm
Explanation:
Hello!
To solve this heat transfer problem we must initially draw the wire and interpret the whole problem (see attached image)
Subsequently, consider the heat transfer equation from the internal part of the tube to the external air, taking into account the resistance by convection, and conduction as shown in the attached image
to find the critical insulation radius we must divide the conductivity of the material by the external convective coefficient
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Answer:
Ts =Ta E)- 300(
569.5 K
5
Q12-W12 = -4014.26
Mol
AU2s = Q23= 5601.55
Mol
AUs¡ = Ws¡ = -5601.55
Explanation:
A clear details for the question is also attached.
(b) The P,V and T for state 1,2 and 3
P =1 bar Ti = 300 K and Vi from ideal gas Vi=
10
24.9x10 m
=
P-5 bar
Due to step 12 is isothermal: T1 = T2= 300 K and
VVi24.9 x 10x-4.9 x 10-3 *
The values at 3 calclated by Uing step 3l Adiabatic process
B-P ()
Since step 23 is Isochoric: Va =Vs= 4.99 m* and 7=
14
Ps-1x(4.99 x 103
P-1x(29x 10)
9.49 barr
And Ts =Ta E)- 300(
569.5 K
5
(c) For step 12: Isothermal, Since AT = 0 then AH12 = AU12 = 0 and
Work done for Isotermal process define as
8.314 x 300 In =4014.26
Wi2= RTi ln
mol
And fromn first law of thermodynamic
AU12= W12 +Q12
Q12-W12 = -4014.26
Mol
F'or step 23 Isochoric: AV = 0 Since volume change is zero W23= 0 and
Alls = Cp(L3-12)=5 x 8.311 (569.5 - 300) = 7812.18-
AU23= C (13-72) =5 x 8.314 (569.3 - 300) = 5601.53
Inol
Now from first law of thermodynamic the Q23
AU2s = Q23= 5601.55
Mol
For step 3-1 Adiabatic: Since in this process no heat transfer occur Q31= 0
and
AH
C,(T -Ts)=x 8.314 (300- 569.5)= -7842.18
mol
AU=C, (T¡-T)= x 8.314 (300
-5601.55
569.5)
mol
Now from first law of thermodynamie the Ws1
J
mol
AUs¡ = Ws¡ = -5601.55
