A heater for boiling a saturated liquid consists of

Chapter 10, Problem 10.25

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A heater for boiling a saturated liquid consists of twoconcentric stainless steel tubes packed with dense boron nitride powder. Electrical current is passed through theinner tube, creating uniform volumetric heating (W/m3). The exposed surface of the outer tube is in con-tact with the liquid and the boiling heat flux is given asIt is feared that under high-power operation the stain-less steel tubes would severely oxidize if temperaturesexceed Tss,xor that the boron nitride would deteriorateif its temperature exceeds Tbn,x. Presuming that the sat-uration temperature of the liquid (Tsat) and the boilingsurface temperature (Ts) are prescribed, derive expres-sions for the maximum temperatures in the stainlesssteel (ss) tubes and in the boron nitride (bn). Expressyour results in terms of geometric parameters (r1, r2,r3, r4), thermal conductivities (kss, kbn), and the boilingparameters (C, Tsat, Ts).