Chapter 8: Internal Forced Convection

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• In the fully developed region, thesurface temperature T s will alsoincrease linearly in the flow direction• Applying the steady-flow energybalance to a tube slice of thickness dx,the slope of the mean fluid temperatureT m can be determineddTmqspmcpdT = mqspdx → dx= mc =( ) constant• Noting that both the heat flux and h (forfully developed flow) are constantsp(8-20) (8-19):dTdxmdTs= (8-21)dx
• In the fully developed region (T s -T m =constant)∂ ⎛ T −T ⎞ 1 ⎛∂T ∂T⎞ ∂TdT⎜ ⎟= 0→ − = 0→ =∂x Ts Tm Ts T⎜mx x⎟⎝ − ⎠ − ⎝ ∂ ∂ ⎠ ∂x dxs s s• Combining Eqs. 8–20, 8–21, and 8–22 gives(8-22)dT dT qp∂x dx dx mc ∂ T =s =m =s =pconstant(8-23)• For a circular tube ( p = 2πR = πD)∂ T dTs dTm 2q= = =s = constant∂x dx dx ρV c Ravgp(8-24)
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 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 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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