Question

Water flows through a cast steel pipe (k = 50 W m.K, ε = 0.8) with an outer diameter of 104mm and 2 mm wall thickness. Calculate the heat loss (convection and radiation) per meter length of uninsulated pipe when the water temperature is 90 oC, the outside air temperature is -10 oC, the water side heat transfer coefficient is 300 W m2.K and theoutside heat transfer coefficient is 20 W/m^2K.

Answer 1

Answer:

The heat loss per unit length is   $\frac{Q}{L} = 2981 W/m$

Explanation:

From the question we are told that

     The outer diameter of the pipe is $d = 104mm = \frac{104}{1000} = 0.104 m$

     The thickness is  $D = 2mm = \frac{2}{1000} = 0.002m$  

      The temperature  of water is  $T = 90^oC = 90 + 273 = 363K$  

      The outside air temperature is $T_a = -10^oC = -10 +273 = 263K$

        The water side heat transfer coefficient is $z_1 = 300 W/ m^2 \cdot K$

       The  heat transfer coefficient is  $z_2 = 20 W/m^2 \cdot K$

The heat lost per unit length is mathematically represented as

           $\frac{Q}{L} = \frac{2 \pi (T - Ta)}{ \frac{ln [\frac{d}{D} ]}{z_1} + \frac{ln [\frac{d}{D} ]}{z_2}}$

Substituting values

         $\frac{Q}{L} = \frac{2 * 3.142 (363 - 263)}{ \frac{ln [\frac{0.104}{0.002} ]}{300} + \frac{ln [\frac{0.104}{0.002} ]}{20}}$

           $\frac{Q}{L} = \frac{628}{0.2107}$

           $\frac{Q}{L} = 2981 W/m$