In: Mechanical Engineering
Water ( ρ= 1000 kg/m3; Cp= 4.2 kJ/kg.K; k= 0.58 W/m.K ) at 1,537 kg/hr and 26oC enters a 10-mm-diameter smooth tube whose wall temperature is maintained at 79oC. If the water's Nusselt number (Nu) = 375, and the tube length is 7.6, calculate the water outlet temperature,in oC.
The heat transfer is through the tubular surface and therefore the equivalent diameter is equal to the diameter of the tube.
The Nusselt number is given by the expression:
Substituting the given values;
Next, we will find the LMTD:
Now, we can apply the first law of thermodynamics, i.e., the law of conservation of energy:
This equation cannot be solved analytically, and therefore, needs to be solved numerically.
Using the graphical method, the value of temperature at exit is found as: