Calculate exit temperatures of water and air and the total heat transfer rate

Question

A cross flow heat exchanger consists of  bundle of 32 straight 0.6 m long tubes in a rectangular duct of cross-sectional area of 0.6 m². Hot water at 150⁰C and a mean velocity of 0.5 m/s enters each tube having inner and outer diameters of 10.2 mm and 12.5 mm respectively. Atmospheric air at 10⁰C enters the heat exchanger with a volumetric flow rate of 1 m³/s. The mean convective W/m²-K. Assume tube side flow is fully developed and negligible thermal resistance due to tube wall. Heat transfer is only between air and water. Calculate exit temperatures of water and air and the total heat transfer rate. The following properties are known:

For air : at 10⁰C, r = 1.2407 kg/m³, at 40⁰C, r= 1.1181 kg/m³, C_p = 1007 J/kg-K.

For water : r = 922 kg/m³, C_p = 4297 J/kg-K, K = 0.688 W/m-K, m = 188 ´ 10^–6 N-s/m², Pr=1.18. Take cross flow correction factor as 0.8. Heat transfer correlations:

1. Nu_d = 4.364, for fully developed laminar tube flow,
2. Nu_d = 0.023 Re Pr^0.3, for turbulent flow, in tube
3. $\varepsilon = \frac{1-e^{\left \{ -c_{R}\left [ 1-e^{-N} \right ] \right \}}}{C_{R}}$  minimum fluid mixed and the other unmixed in cross flow exchanger

$\varepsilon =1-e^{-\left \{ \left [ 1-e^{-\left ( C_{R}N \right )} \right ].\frac{1}{C_{R}} \right \}}$ minimum fluid unmixed and the other mixed in cross flow exchanger, where $\varepsilon$ : effectiveness, C_R : capacity ratio, N : Number of Transfer Units.

Symbols have the usual meaning.