A uniform solid sphere of radius 1 at an initial constant temperature Uo throughout is

Chapter 14, Problem 10

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A uniform solid sphere of radius 1 at an initial constant temperature Uo throughout is dropped into a large container of fluid that is kept at a constant temperature u1 (u1 > Uo) for all time. See RGURE 14.3A. Since there is heat transfer across determined. the boundary r = 1, the temperature u(r, t) in the sphere is from the boundary-value problem -+--=- a2u 2 au au OO ar2 r ar at' ' au I = -h(u(l,t) - u1), O < h < 1 or r-1 u(r, 0) = Uo. 0 < r < 1. Solve for u(r, t). [Hint: Proceed as in 9.)

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