Consider operation of a single pass cross-flow heat exchanger with water (c_p = 4193 J/kg·K) (mixed) and methanol (c_p = 2577 J/kg·K) (unmixed). Water entering and exiting the heat exchanger at 90°C and 60°C, respectively, is used to heat the methanol initially at 10°C. The overall heat transfer coefficient and the total heat transfer rate are estimated to be 650 W/m²·K and 250 kW, respectively. In order to achieve an effectiveness of at least 0.5,

(a) What would be the mass flow rate of water and heat exchanger surface area?

(b) If the mass flow rate of water is changed within 630% of that determined in part (a) with the same surface area (As), plot the variation of heat transfer rate, methanol exit temperature, overall heat transfer coefficient and the effectiveness of heat exchanger with respect to change in the water flow rate.