The shell-and-tube exchanger shown in Fig. 1.125(a) can be modeled as shown in Fig. 1.125(b) for a simplified vibration analysis. Find the cross-sectional area of the tubes so that the total stiffness of the heat exchanger exceeds a value of 200 x 106 N/m in the axial direc-tion and 20 X 106 N-m/rad in the tangential direction. Assume that the tubes have the same length and cross section and are spaced uniformly.