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An experiment involves heating a very small sphere that is suspended by a fine string in air with a laser beam in order to induce the highest sphere temperature possible. After inspecting Equation 9.64, a research assistant suggests inducing a uniform downward airflow to exactly offset free convection from the sphere, thereby minimizing heat losses and maximizing the steady-state sphere temperature. In the limiting case of a very small sphere, what is the minimum value of the convection heat transfer coefficient expressed in terms of the sphere diameter and thermal conductivity of the air?

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