It has been proposed to use large banks of recharge-able,

Chapter 9, Problem 9.103

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It has been proposed to use large banks of recharge-able, lithium ion batteries to power electric vehicles.The cylindrical batteries, each of which is of radiusri?9 mm and length L?65 mm, undergo exothermicelectrochemical reactions while being discharged.Since excessively high temperatures damage the batter-ies, it is proposed to encase them in a phase changematerial that melts when the batteries discharge (andresolidifies when the batteries are charged; charging isassociated with an endothermic electrochemical reac-tion). Consider the paraffin of 8.47 and 9.57.(a) At an instant in time during the discharge of a bat-tery, liquid paraffin occupies an annular region ofouter radius ro?19 mm around the battery, whichis generating ?1 W of thermal energy. Deter-mine the surface temperature of the battery.(b) At the time of interest in part (a), what is the rateat which the liquid annulus radius is increasing?(c) Plot the battery surface temperature versus theouter radius of the liquid-filled annulus. Explainthe relative insensitivity of the battery surface tem-perature to the size of the annulus for 15 mmro30 mm.

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