An electric cable consists of an inner core and an outer protection layer. The shape of the cable can be approximated as a cylinder. The diameter of the inner core is D1 = 1.6 cm and the total diameter of the cable is D2 = 2 cm. The thermal conductivities for the cable inner core and outer layer are k = 50 W/m·K and k = 0.1 W/m·K, respectively. The electric current in the inner core causes a volumetric thermal energy generation rate of q ̇ = 10^(6) W/(m^(3)) . The cable is placed in an air crossflow of u∞ = 2 m/s and T∞ = 300 K. The air in the film around the cylinder has a kinematiccrossflow of u∞ = 2 m/s and T∞ = 300 K. The air in the film around the cylinder has a kinematic viscosity of ν = 2 × 10^(−5 )(m^2)/s, thermal conductivity of kf = 0.025 W/m · K, and Prandtl number of Pr=0.7.
An electric cable consists of an inner core and an outer protection layer. The shape of the cable can be approximated as a cylinder. The diameter of the inner core is D1 = 1.6 cm and the total diameter of the cable is D2 = 2 cm. The thermal conductivities for the cable inner core and outer layer are k = 50 W/m·K and k = 0.1 W/m·K, respectively. The electric current in the inner core causes a volumetric thermal energy generation rate of q ̇ = 10^(6) W/(m^(3)) . The cable is placed in an air crossflow of u∞ = 2 m/s and T∞ = 300 K. The air in the film around the cylinder has a kinematiccrossflow of u∞ = 2 m/s and T∞ = 300 K. The air in the film around the cylinder has a kinematic viscosity of ν = 2 × 10^(−5 )(m^2)/s, thermal conductivity of kf = 0.025 W/m · K, and Prandtl number of Pr=0.7.
Assume one-dimensional and steady-state conduction heat transfer along the radial direction of the cable cross section. Perform heat transfer analysis for a section of the cable with length L = 10 cm.
(1) Determine the radial direction heat rate qr across the external surface of the cable.
(2) Determine the averaged convection heat transfer coefficient h of the air flow around
the cable and the surface temperature T2.
(3) Determine the temperature T1 at the interface between the inner core and the outer
layer of the cable.
(4) The 1D heat transfer in the inner core of the cable (i.e., the conduction along the radial direction) satisfies the following equation in the image attached.
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