Annular region of outer radius

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Reference no: EM13946296

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 radius ri = 9 mm and length L = 65 mm, undergo exothermic electrochemical reactions while being discharged. Since excessively high temperatures damage the batter- ies, it is proposed to encase them in a phase change material that melts when the batteries discharge (and resolidifies when the batteries are charged; charging is associated with an endothermic electrochemical reac- tion). Consider the paraffin of Problems 8.47 and 9.57.

(a) At an instant in time during the discharge of a bat- tery, liquid paraffin occupies an annular region of outer radius ro = 19 mm around the battery, which is generating Eg = 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 rate at which the liquid annulus radius is increasing?

(c) Plot the battery surface temperature versus the outer radius of the liquid-filled annulus. Explain the relative insensitivity of the battery surface tem- perature to the size of the annulus for 15 mm ro 30 mm.

Reference no: EM13946296

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