Chapter 8: Internal Forced Convection

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• Combining the last two equations, the velocityprofile is rewritten as2⎛ r ⎞u( r)= 2Vavg⎜1 − ; u2 ⎟max= 2V⎝ R ⎠avg(8-41)
Pressure Drop• One implication from Eq. 8-37 is that the pressure dropgradient (dP/dx) must be constant (the left side is a functiononly of r, and the right side is a function only of x).• Integrating from x=x 1 where the pressure is P 1 to x=x 1 =Lwhere the pressure is P 2 gives ( 度 )dPdx2 1constant P −= =PL(8-43)• Substituting Eq. 8–43 into the V avg expression in Eq. 8–408µ LVavg32µLVavg∆ P= P1− P2 = = (8-44)2 2R D
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 24 and 25: Laminar Flow in TubesAssumptions:
Page 26 and 27: • Taking the limit as dr, dx 0 g
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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