help with heat transfer
've been given some work to do in heat transfer and i would like for someone to help me understand if what I've got is right or not
i am translating the question to english through chatGPT:
A copper electrical wire with a diameter of 20 cm is covered by insulation of 2 cm thickness. The wire generates heat due to electric current at a rate of:
S_wire = 5 kW/m³
The thermal conductivity of the wire is:
k_wire = 200 W/(m·K)
The thermal conductivity of the insulation is:
k_ins = 1 W/(m·K)
The outer surface of the insulation behaves as a black body and is exposed to ambient surroundings at a temperature of:
T_∞ = 300 K
It is explicitly stated that there is no convection at the outer surface – heat is transferred only by thermal radiation.
The system is assumed to be very long (infinite cylinder approximation) and in steady-state conditions.
Since only the outer surface of the insulation is exposed, heat transfer occurs exclusively in the radial direction.
Tasks:
a. Using the relevant equations and boundary conditions, determine the heat flux and temperature at all points within the wire and the insulation.
b. What is the radial heat flux profile in the wire and the insulation?
c. What is the radial temperature profile in the wire and the insulation?
d. Sketch and explain the heat flux and temperature profiles.
i am adding my solutions and the equations used
few things were odd to me:
the temperature profile in the cable is almost non existent, maximum temperature is only 1/16 more than the temperature at the r=r0 which is odd
the insulation that is 2cm thick only drops the temperature in 4 degrees kelvin
i would love for your help, much appreciated if accepted
Posted Jul 17, 2025, 8:34 AM UTC