The convection coefficient for flow over a solid sphere may be determined by
submerging the sphere, which is initially at \(25^{\circ} \mathrm{C}\), into the
flow, which is at \(75^{\circ} \mathrm{C}\), and measuring its surface
temperature at some time during the transient heating process.
(a) If the sphere has a diameter of \(0.1 \mathrm{~m}\), a thermal conductivity
of \(15 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\), and a thermul diffusivity
of \(10^{-5} \mathrm{~m}^{2} / \mathrm{s}\), at what time will a surface
tempertiture of \(60^{\circ} \mathrm{C}\) be recorded if the convection
coefficient is \(300 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) ?
(b) Assess the effect of thermal diffusivity on the thermal response of the
material by computing center and surface temperature histories for
\(\alpha=10^{-6}\). \(10^{-5}\), and \(10^{-4} \mathrm{~m}^{2} / \mathrm{s}\). Plot
your results for the perid \(0 \leq t \leq 300 \mathrm{~s}\). In a similar
manner, assess tte effect of themal conductivity by considering vak ues of
\(k=1.5,15\), and \(150 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\).