Cold water (c_p= 4180 J/kg·K) leading to a shower enters a thin-walled double-pipe counter-flow heat exchanger at 15°C at a rate of 0.25 kg/s and is heated to 45°C by hot water (c_p= 4190 J/kg·K) that enters at 100°C at a rate of 3 kg/s. If the overall heat transfer coefficient is 950 W/m²·K, determine the rate of heat transfer and the heat transfer surface area of the heat exchanger using the ε-NTU method.

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Cold water 15°C 0.25 kg/s Hot water 100°C 3 kg/s T45°C