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 lo

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.

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Farah 6 months 2021-07-22T02:00:06+00:00 1 Answers 185 views 0

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    2021-07-22T02:01:23+00:00

    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

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