Consider a concentric tube annulus for which the inner and outer diameters are 25 and \(50 \mathrm{~mm}\). Water enters the annular region at \(0.03 \mathrm{~kg} / \mathrm{s}\) and \(25^{\circ} \mathrm{C}\). If the inner tube wall is heated electrically at a rate (per unit length) of \(q^{\prime}=3000 \mathrm{~W} / \mathrm{m}\), while the outer tube wall is insulated, how long must the tubes be for the water to achieve an outlet temperature of \(85^{\circ} \mathrm{C}\) ? What is the inner tube surface temperature at the outlet, where fully developed conditions may be assumed?