A very long cylinder (diameter 1mm) is placed perpendicular to a steady airstream whose velocity is 10 m/sec. The cylinder is heated electrically at 100 watts/meter span. At what distance downstream is the rms temperature fluctuation in the wake of the cylinder reduced to 1?C? Assume that the distribution of the mean temperature difference in the wake is similar to the distribution of the mean velocity defect. For air at room temperature and pressure, ? = 1.25kg/m3, cp = 103joule/kg?C. Hint: the dimension of the heating is joules/sec/meter. The dimension of the heat flux through position x is (?cp)T times the velocity times the integrated profile in y, which will have a dimension of length. The dimensions of the heating and the dimensions of this heat flux are the same.