Problem

Water flows in a 2-cm-diameter tube at an average flow velocity of 8 m/s If the water enters at 20°C and leaves at 30°C and the tube length is 10 m, estimate the average wall temperature necessary to effect the required heat transfer.

Step-by-step solution

1. Step 1 of 6

   Determine the mean temperature of water by using the following equation:

   

   Here, the entrance temperature is  and exit temperature is 

   Substitute  for  and  for 

   

   Comment

2. Step 2 of 6

   Determine the cross-sectional area of the tube using the following equation:

   

   Here, the diameter of the tube is 

   Substitute 0.02 m for 

   

   Comment

3. Step 3 of 6

   Determine the mass flow rate of the water by using the following equation:

    …… (1)

   Here the density of the water is  and its velocity is 

   Obtain properties of water at  mean temperature of water at atmospheric pressure

   Dynamic viscosity 

   Prandtl Number 

   Thermal conductivity 

   Density of water 

   Specific Heat capacity 

   Comment

4. Step 4 of 6

   Substitute  for ,  for ,  for  in equation (1)

   

   Calculate the Reynolds’s number from the equation as given below:

   

   Substitute 0.02 m for ,  for ,  for  and  for 

   

   Comment

5. Step 5 of 6

   Write the expression for average convective heat transfer coefficient using the following equation:

   

   Substitute 177857.14 for , 6.13 for Pr,  for k, 0.02 m for 

   

   Comment

6. Step 6 of 6

   Write the expression for the heat transfer using the following equation:

   

   Here, change in the temperature of the water is , length of the tube is L, the average tube wall temperature is , water bulk temperature is 

   Substitute 0.02 m for ,  for ,  for ,  for  , for , 10 m for L and  for 

   

   Thus, the average wall temperature is .

   Comment