Chapter 8: Internal Forced Convection

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Laminar Flow in TubesAssumptions:• steady laminar flow,• incompressible fluid,• constant properties,• fully developed region,and• straight circular tube.• The velocity profile u(r)remains unchanged inthe flow direction.• no motion in the radialdirection.• no acceleration.
• Consider a ring-shapeddifferential volume element.• A force balance on the volumeelement in the flow directiongives( 2 πrdrP) − ( 2 πrdrP)x+( πrdxτ) ( πrdxτ)x dx+ 2 − 2 = 0rr+dr(8-34)• Dividing by 2π dr dx and rearrangingrP( ) ( )x dxP rτrτ+−−x r+ dr rdx+ =dr0(8-35)
Page 1: Chapter 8:Internal Forced Convectio
Page 4 and 5: Average Velocity• The value of th
Page 6 and 7: • For incompressible flow in a ci
Page 8 and 9: The Entrance Region• A fluid ente
Page 10 and 11: Thermal Entrance Region• Consider
Page 12 and 13: • Surface heat flux can be expres
Page 14 and 15: Entry Lengths ()- HydrodynamicLamin
Page 16 and 17: General Thermal Analysis• In the
Page 18 and 19: • In the fully developed region,
Page 20 and 21: Constant Surface Temperature• The
Page 22 and 23: • The temperature difference betw
Page 26 and 27: • Taking the limit as dr, dx 0 g
Page 28 and 29: • Combining the last two equation
Page 30 and 31: • A pressure drop due to viscous
Page 32 and 33: • Or∂T1 ∂Qu =−( )∂ x ρc
Page 34 and 35: • Separating the variables and in
Page 36 and 37: Constant Surface temperature (circu
Page 38 and 39: - HydrodynamicLaminar flowLh,lamina
Page 40 and 41: Turbulent flow in Tubes• Most cor
Page 42: Moody Diagram

Chapter 8: Internal Forced Convection

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