An experiment involves heating a very small spherethat is

Chapter 9, Problem 9.115

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An experiment involves heating a very small spherethat is suspended by a fine string in air with a laserbeam in order to induce the highest sphere tempera-ture possible. After inspecting Equation 9.64, aresearch assistant suggests inducing a uniform down-ward airflow to exactlyoffset free convection fromthe sphere, thereby minimizing heat losses and maxi-mizing the steady-state sphere temperature. In thelimiting case of a very smallsphere, what is the mini-mum value of the convection heat transfer coefficientexpressed in terms of the sphere diameter and thermalconductivity of the air?

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