8/10/2019 08 Lecture Heat Transfer

1/28

MEL301 : Heat and Mass Transfer

by

Dr. Himanshu Tyagi

IIT Ropar 13-Oct-2014 (Mon)

Chapter 8Internal Forced Convection

Instructions for this chapter:a) Students must try to read this chapter from the textbook &

b) try out the various solved examples

before coming to class

8/10/2019 08 Lecture Heat Transfer

2/28

Circular vs. Non-circular

2Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.

8/10/2019 08 Lecture Heat Transfer

3/28

Average Velocity & Temperature

3Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.

8/10/2019 08 Lecture Heat Transfer

4/28

Average Velocity & Temperature

4Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.

8/10/2019 08 Lecture Heat Transfer

5/28

Average Velocity & Temperature

5Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.

8/10/2019 08 Lecture Heat Transfer

6/28

Q. How do we know if the flow is Laminar orTurbulent?

6Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.

Usually,

Re < 2300 Laminar

Re > 10,000 Turbulent

Q. Can Laminar flow occur ateven Re = 100,000 ??

Q. How is Re for non-circular pipes/ducts

defined?

8/10/2019 08 Lecture Heat Transfer

7/28

Hydraulic Diameter

7Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.

8/10/2019 08 Lecture Heat Transfer

8/28

Entrance Region (Hydrodynamic)

8Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.

Hydrodynamically fully developed:

8/10/2019 08 Lecture Heat Transfer

9/28

Entrance Region (Thermal)

9Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.

Q. Is the fluid being cooled or heated by the

surface?

Thermally fully developed:

8/10/2019 08 Lecture Heat Transfer

10/28

fxand hx

10Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.

Hydrodynamically fully developed:

Thermally fully developed:

8/10/2019 08 Lecture Heat Transfer

11/28

Entry Length (Lhand Lt)

11Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.

For laminar flow:

For turbulent flow:

8/10/2019 08 Lecture Heat Transfer

12/28

Nu (turbulent flows)

12Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.

Note (for laminar):

NuT ~ 3.66

NuH ~ 4.36

8/10/2019 08 Lecture Heat Transfer

13/2813Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.

Constant Surface Heat Flux Constant Surface TemperatureVs.

8/10/2019 08 Lecture Heat Transfer

14/28

Constant Surface Heat Flux

14Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.

8/10/2019 08 Lecture Heat Transfer

15/28

Constant Surface Temperature

15Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.

8/10/2019 08 Lecture Heat Transfer

16/28

NTU (Number of Transfer Units)

16Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.

8/10/2019 08 Lecture Heat Transfer

17/28

17Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.

8/10/2019 08 Lecture Heat Transfer

18/28

Laminar Flow in Tubes

18Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.

Q. What is the fully developed profile in laminar flows in

tubes?Q. Why is it parabolic in shape?

Q. What is the pressure drop in laminar flow in tubes?

Q. How does the stress vary (with r and x)?

Q. How does Tvary (with r and x)?

8/10/2019 08 Lecture Heat Transfer

19/28

Derivation of Parabolic Velocity Profile

19Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.

By substituting

We get

B.C.s ?

Finally, we obtain

the parabolic

velocity profile

8/10/2019 08 Lecture Heat Transfer

20/28

Average Velocity

20Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.

Lets substitute the

following expression to

Vavgterm

We get:

Which also shows that

8/10/2019 08 Lecture Heat Transfer

21/28

Pressure Drop

21Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.

From previous page, we

already have

By rearranging we can

easily write:

If length is doubled, Palso doubles

If mass flow rate is doubled, Palso

doubles

If Ris halved, Pincreases by 4 times!!

8/10/2019 08 Lecture Heat Transfer

22/28

Pumping Power

22Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.

PVWpump

Pumping

power is

given by:

is the volumetric flow rateV

4

2D

VAVV avgcavg

PSince,

28 avgpump LVW

42

216

8D

VL

2

4

144V

D

L

If Dis halved, pumping power increases by

16 times!!

We get,

8/10/2019 08 Lecture Heat Transfer

23/28

Temperature Profile

23Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.

Q. How does Tvary (with r and x)?

By substituting

We get

Next by

substituting

&

We get

8/10/2019 08 Lecture Heat Transfer

24/28

Temperature Profile

24Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.

Case A: Constant Surface Heat Flux

Q. How to solve this to get T(r)?

We already have:

Hence, we get

B.C.s ??

Finally T(r)is solved!!

Also, we can

calculate the mean

temperature Tm

8/10/2019 08 Lecture Heat Transfer

25/28

Temperature Profile

25Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.

Case A: Constant Surface Heat Flux

Q. Does this expression look

familiar?

Repeating a similar exercise

for constant surface

temperature gives us:

8/10/2019 08 Lecture Heat Transfer

26/28

Laminar Flow in

Non-circular

Tubes

26Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.

8/10/2019 08 Lecture Heat Transfer

27/28

Laminar Flow in Entrance Region

27Source: Cengel & Ghajar, Heat and Mass Transfer,4th ed., 2011, McGraw-Hill.

Q. Can we apply Nu = 4.36 and Nu = 3.66 in the entrance

region?

Q. If not, what relations can be applied?

Q. Will Nu be same/higher/lower in the entrance region

(compared to the fully developed region)?

8/10/2019 08 Lecture Heat Transfer

28/28

Comparing Laminar & Turbulent Flows (in Entrance Region)

Laminar flowTurbulent flow