A somewhat sadistic yet decidedly normal child, James decides to pull out his magnifying glass and torture an ant. The ignition temperature of an ant is roughly \(300^{\circ} \mathrm{C}\). James' low power magnifying glass can deliver a heat flux of \(50 \mathrm{~W} / \mathrm{cm}^{2}\). The surrounding breeze provides for a heat-transfer coefficient of \(50 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K}\) and the ambient air temperature is \(20^{\circ} \mathrm{C}\). If we can describe an ant as a cylinder, \(5 \mathrm{~mm}\) long and \(1 \mathrm{~mm}\) in diameter with the properties of hair ( \(\left.\alpha=0.14 \mathrm{~mm}^{2} / \mathrm{s}, k=0.15 \mathrm{~W} / \mathrm{mK}\right)\), how long must the poor ant remain in the crosshairs for James to be successful?