Cold water (cp = 4180 J/kg·K) leading to a shower enters a thin-walled double-pipe counterflow heat exchanger at 15°C at a rate of 0.25 kg/s and is heated to 45°C by hot water (cp = 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. Answers: 31.35 kW, 0.482 m2

The rate of heat transfer is  

The heat transfer surface area is  

Explanation:

From the question we are told that  

          The  specific heat of water is

           The temperature of cold water is

            The rate of cold the flow is

           The temperature of the heated water

            The specific heat of hot water is  

              The temperature of the hot water is

               The rate of hot the flow is

               The heat transfer coefficient is

From the method we have that

Where is the heat capacity rate of hot  water

      Substituting the value

Also

Where is the heat capacity rate of cold  water

The maximum heat capacity and the minimum  heat capacity is

       The maximum heat transfer is

Substituting values  

The actual heat transfer is mathematically evaluated as

Substituting values

The effectiveness of the heat exchanger is mathematically evaluated as

  Substituting values  

The NTU of the heat exchanger is mathematically represented as

Where C is the ratio of the minimum to the maximum heat capacity which is mathematically represented as

Substituting values

Substituting values in to the equation for NTU

Generally the heat transfer surface area can be mathematically represented as

Substituting values

do you have any options?

answer:

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explanation: