Flow inside the ducts (Heat transfer).pdf

Developing and fully developed flows, Hydrodynamic and Thermal entrance length

1. Flow inside Ducts (Internal Flow)
Prepared by:
Ankur Sachdeva
Assistant Professor, ME

2. Introduction to Internal Flows
•Liquidorgasflowthroughpipesorductsiscommonly
usedinheatingandcoolingapplications.
•Thefluidinsuchapplicationsisforcedtoflowbyafan
orpumpthroughatubethatissufficientlylongto
accomplishthedesiredheattransfer.
•Inexternalflow,thefluidhasafreesurface,andthus
theboundarylayeroverthesurfaceisfreetogrow
indefinitely.
•Ininternalflow,however,thefluidiscompletely
confinedbytheinnersurfacesofthetube,andthus
thereisalimitonhowmuchtheboundarylayercan
grow.

3. Pipes, Ducts and Tubes
•Mostfluids,especiallyliquids,aretransportedin
circularpipes.
•Pipe,duct,tube,andconduitareusuallyused
interchangeablyforflowsections.
•Flowsectionsofcircularcrosssectionare
referredtoaspipes(especiallywhenthefluidisa
liquid)
•Flowsectionsofnoncircularcrosssectionas
ducts(especiallywhenthefluidisagas).
•Smalldiameterpipesareusuallyreferredtoas
tubes.

4. Pipes, Ducts and Tubes
Pipes
Conduits
Tubes
Ducts

5. Hydrodynamic Entrance Length
The region from the tube inlet to the point at which the boundary layer merges at the
centerline is called the hydrodynamic entrance region, and the length of this region is
called the hydrodynamic entry length L
h
Hydrodynamic Entry Length, L
h = 0.05 Re.D…… for laminar flow
Hydrodynamic Entry Length, L
h = 1.359 Re
1/4
… for turbulent flow

6. Hydrodynamically Developing and
Developed Flow
•Flow in the entrance region is called hydrodynamically
developing flow since this is the region where the
velocity profile develops.
•The region beyond the entrance region in which the
velocity profile is fully developed and remains
unchanged is called the hydrodynamically fully
developed region

7. Thermal Entrance Length
•Flow in the thermal entrance region is called thermally developing
flow since this is the region where the temperature profile
develops.
•The region beyond the thermal entrance region in which the
dimensionless temperature profile expressed as (Ts -T)/ (Ts -Tm)
remains unchanged is called the thermally fully developed region.

8. Thermal Entrance Length
Thermal Entrance Length, L
t = 0.05 Re.Pr. D…… for laminar flow
Thermal Entrance Length, L
t = 10.D……………… for turbulent flow
The region of flow over which the thermal boundary layer develops and reaches the
tube center is called the thermal entrance region, and the length of this region is
called the thermal entry length L
t.

9. Internal Flow
•Mean velocity is used to calculate the Reynolds
number of the flow.
•Mean velocity remains constant for
incompressible flow when the cross-sectional
area of the tube is constant.
•Mass flow rate, ሶ??????= ??????????????????????????????
??????
•Reynolds Number, Re =
4ሶ??????
????????????
????????????
–Re < 2300 ….(laminar flow)
–Re > 4000 ….(turbulent flow)
•Hydraulic diameter, ??????
ℎ =
4????????????
??????

10. Flow in Pipes (Re
D< 2300)
•Velocity Profile,
•Skin Friction Coefficient, C
f =
16
??????&#3627408466;??????
•Friction factor,
•Pressure Drop,

11. Heat Transfer Relations
•Fully Developed Laminar Flow
–Constant Surface Temperature, Nu =
ℎ??????
??????
??????
= 3.66
–Constant Surface Heat Flux, Nu =
ℎ??????
??????
??????
= 4.36
•Fully Developed Turbulent Flow
–Nu = 0.023 Re
0.8
Pr
n
–n = 0.4 for heating, n = 0.3 for cooling

12. Numerical Problem
Water entering at 10°C is heated to 40°C in the tube of 0.02 m ID at a
mass flow rate of 0.01 kg/s. The outside of the tube is covered with an
insulated heating element that produces a uniform heat flux of 15000
W/m2 over the surface. Neglecting any entrance effect, determine ;
(a) Reynolds number ;
(b) The heat transfer coefficient ;
(c) The length of pipe needed for a 30°C increase in average
temperature ;
(d) The inner tube surface temperature at the outlet ;
(e) The friction factor ;
(f ) The pressure drop in the pipe ;
(g) The pumping power required, if the pump is 50% efficient.

13. Solution
•Given : Flow through pipe ;
–D
i = 0.02 m, m = 0.01 kg/s, T
o = 40°C, T
i = 10°C,
–q = 15000 W/m
2
, η
pump= 0.5
•To find :
–Reynolds Number, Re
–Heat transfer coefficient, h
i
–Length of the pipe, L
–Temperature of the inner surface at outlet, T
so
–Friction factor, f
–Pressure drop, ∆p
–Pumping Power, W
pump

14. Solution
•Properties : The properties of water at its
mean temperature, ??????
??????=
??????
??????+??????
??????
2
=
10+40
2
= 25°C
–The properties of water at 25°C
–ρ = 997 kg/m
3
, kf = 0.608 W/m.K,
–Cp = 4180 J/kg K, μ = 910 ×10
–6
Ns/m
2
.
•(a) The Reynolds number:
•????????????=
4ሶ??????
????????????
????????????
=
4×0.01
??????×0.02 ×910×10
–6
= 700
–Therefore the flow is laminar

15. Solution
•For constant heat flux, Nu
D = 4.36
–h
i = 132.5 W/m
2
K
•Length of the pipe, L
????????????
??????=
ℎ
????????????
??????
??????
&#3627408467;
ℎ
??????=
????????????
????????????
&#3627408467;
??????
??????
=
4.36×0.608
0.02

16. Solution

17. Solution