Chapter 8: Internal Forced Convection

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• Taking the limit as dr, dx 0 givesdPr dx( )• Substituting τ = µ(du/dr) givesd rτ+ = 0(8-36)drµ d ⎛ du dP⎜r⎞ ⎟ =rdr⎝dr⎠dx(8-37)• Rearranging and integrating it twice to give1 ⎛dP⎞ 2u( r) = ⎜ ⎟ C ln r C4µdxr + +⎝ ⎠漏 1 2(8-38)• Boundary Conditions:–symmetryabout the centerline : ∂u/∂r = 0 at r = 0,– no-slip condition: u = 0 at r = R.
• Eq. 6-38 with the boundary conditions( )u rR 2 2⎛ dP ⎞⎛1r ⎞=− ⎜ ⎟⎜ −2 ⎟4µ⎝ dx ⎠⎝ R ⎠(8-39)• Substituting Eq. 8–39 into Eq. 8–2, and performing theintegration gives the average velocityRR 2 22 2 R ⎛dP⎞⎛ r ⎞Vavg= ∫u 2( r)rdr =− ∫ 1 rdr2 ⎜ ⎟⎜ −2 ⎟R R 4µdx R0 0 ⎝ ⎠⎝ ⎠2R ⎛dP⎞=− ⎜ ⎟8µ⎝ dx ⎠(8-40)
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 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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