Thermodynamics HW Solutions 534

Thermodynamics HW Solutions 534 - Chapter 6 Fundamentals of...

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Chapter 6 Fundamentals of Convection 6-46 The oil in a journal bearing is considered. The bearing is cooled externally by a liquid. The surface temperature of the shaft, the rate of heat transfer to the coolant, and the mechanical power wasted are to be determined. Assumptions 1 Steady operating conditions exist. 2 Oil is an incompressible substance with constant properties. 3 Body forces such as gravity are negligible. Properties The properties of oil are given to be k = 0.14 W/m-K and μ = 0.03 N-s/m 2 . The thermal conductivity of bearing is given to be k = 70 W/m-K. Analysis ( a ) Oil flow in a journal bearing can be approximated as parallel flow between two large plates with one plate moving and the other stationary. We take the x-axis to be the flow direction, and y to be the normal direction. This is parallel flow between two plates, and thus v = 0. Then the continuity equation reduces to Continuity : 0 = + y v x u ⎯→ 0 = x u ⎯→ u = u ( y ) Therefore, the
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