Question

It is desired to cool down (0.37) kg/s of an aqueous solution with a heat capacity similar to water from 60 to 50^oC. The cooling fluid will be (0.33) kg/s of water at 25^oC. A double-pipe heat exchanger will be used. The external diameter of the interior tube is 0.025 m. The overall heat transfer coefficient is estimated as 1,600 W/(m^2.K). Calculate the necessary tube length if:

1. A countercurrent arrangement is used.
2. A co-current arrangement is used.

Answer 1

Assuming the cooling water is used in interior tube.

We are given double pipe heat exchanger using water inside the pipe and aqueous solution between the annular space, used to cool aqueous solution at to and the inlet temperature of water is,

The mass flow rate of cold liquid, water is given as,

The mass flow rate of hot liquid, aqueous solution is given as,

Applying energy balance across the heat exchanger we get,

The heat capacity of the water and aqueous solution and can be taken as,

So the outlet temperature of the water will be 36.21⁰C

and heat transferred is given as,

a. Now for counter current, (right of the image),

Logarithmic mean temperature difference for counter current heat exchanger is defined as,

Now the heat transferred in the heat exchanger between the hot fluid and cold fluid is given as,

Overall heat transfer coefficient is given as,

Area of the heat transfer is given as,

external diameter of the interior tube is given as,

So,

So the length of the pipe needed for counter current arrangement is 5.053 m

b. Now for co current, (left of the image),

Logarithmic mean temperature difference for co-current heat exchanger is defined as,

Now the heat transferred in the heat exchanger between the hot fluid and cold fluid is given as,

So the length of the pipe needed for co-current arrangement is 5.413 m