A small aluminum sphere of diameter D, initially at a uniform temperature To, is immersed in a liquid whose temperature, T??, varies sinusoidally according toT?? ?? Tm = A sin (ωt)where: Tm = time-averaged temperature of the liquidA = amplitude of the temperature fluctuationΩ = frequency of the fluctuationsIf the heat transfer coefficient between the fluid in the sphere, ha, is constant and the system may be treated as a ??lumped capacity,?? derive an expression for the sphere temperature as a function of time.GIVENA small aluminum sphere is immersed in a liquid whose temperature varies sinusoidallyDiameter of sphere = DLiquid temperature variation: T?? ?? Tm = A sin (ωt)The heat transfer coefficient = ha (constant)The system may be treated as a ??lumped capacity??ASSUMPTIONSConstant thermalconductivity

Transcribed Image Text:

D- - T-- Tm-A sin (a) /,