problem4-29 - PROBLEM 4.29 KNOWN Dimensions and thermal...

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PROBLEM 4.29 KNOWN: Dimensions and thermal conductivity of concrete duct. Convection conditions of ambient ir. Inlet temperature of water flow through the duct. a FIND: (a) Heat loss per duct length near inlet, (b) Minimum allowable flow rate corresponding to aximum allowable temperature rise of water. m SCHEMATIC: 7 ASSUMPTIONS: (1) Steady state, (2) Negligible water-side convection resistance, pipe wall conduction resistance, and pipe/concrete contact resistance (temperature at inner surface of concrete corresponds to that of water), (3) Constant properties, (4) Negligible flow work and kinetic and otential energy changes. p A NALYSIS: (a) From the thermal circuit, the heat loss per unit length near the entrance is ( ) ( ) ( ) i i conv cond 2D T T T T q ln 1.08w / D R R 1 2 k h 4w π ′ = = + + where is obtained by using the shape factor of Case 6 from Table 4.1 with Eq. (4.21).
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