Question

This is for the subject of Heat Transfer. Any clues on how to solve this would be greatly appreciated thanks

2 [ABET]) An electric cable of radius ri andTaur thermal conductivity ke is enclosed by an insulating sleeve whose outer surface is of radius r2 and experiences convection heat transfer and radiation exchange with the adjoining air and large surroundings, respectively. When electric current passes through the cable, thermal energy is generated within the cable at a volumetric rate q. Electrical cable Insulation Ts1 ri Ambient air T-,h Write the steady-state forms of the heat diffusion equation for the insulation and the cable. Verify that these equations are satisfied by the following temperature distributions a. Insulation: T) T,+(T-T) To-ひ剟ーr) Cable: 4k In Sketch the temperature distribution, To), in the cable and the sleeve, labeling key features. Applying Fourier's law, show that the rate of conduction through the sleeve may be expressed as b. q, = In 2 Applying an energy balance to a control surface placed around the cable, obtain an alternative expression for q', expressing your result in terms of g and ri. Applying an energy balance to a control surface placed around the outer surface of the sleeve, obtain an expression from which T2 may be determined as a function of j, Pi, h, T, e, and Tu Consider conditions for which 250 A are passing through a cable having an electric resistance per unit length ofR,' 0.005 Ω/m, a radius ofr.-15 mm, and a thermal conductivity of k-200 w/rm-K. For k, = 0.15 W/m-K,ク= 15.5 mm, h = 25 W/㎡-K, ε 0.9, Te = 25℃, and Tsur-35°C, evaluate the surface temperatures 7si and T2, as well as the temperature To at the centerline of the cable. With all other conditions remaining the same, compute and plot To, T.l, and T2 as a function of r for 15.5 sr2s 20 mm. c. d. e.

Answer 1

Solutiont ④ "The tempera-kre distibution 2. TS2 Os D"乙

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