FACULTY OF MECHANICAL ENGINEERING

TEST 2

(COURSE : HEAT TRANSFERCOURSE CODE : BMM3513LECTURER:IDRIS MAT SAHATPROF. DR. YUSOFF ALIHJ. AMIRRUDDIN ABDUL KADIRDATE: 14 DECEMBER 2012DURATION: 2 HOURSTIME:3:00 p.m.– 5:00 p.m.SESSION/SEMESTER: SESSION 2012/2013 SEMESTER I)

INSTRUCTIONS TO CANDIDATE:

1. This question paper consists of THREE (3) questions. Answer all questions.

2. All calculations and assumptions must be stated clearly.

3. Candidates are not allowed to bring any material other than those calculator and stationary

4. Fill in the particulars and staple this question together with your answer

(NAME:Q3 (Marks)Q1 (Marks)Q2 (Marks)/10/10/10MATRIC: LECTURER:SECTION:)

Q1. A production engineer need to design an air dryer to dry keropok lekor for SME's located near Kuala Pahang as a solution during Tengkujuh season. Cold air at atmospheric pressure and 20°C enters 5-m-long uninsulated rectangular duct of cross section 0.1 m × 0.2 m at a velocity of 2 m/s. The duct surface is observed to be nearly isothermal at 80°C. For the properties of air, use temperature at 30C. Determine

(a) the exit temperature of the air,

(b) the rate of heat gain to the air flow from the duct, and

(c) whether iteration is required or not together with your explanation.

Q2. A hot cube of 3 m × 3 m × 3 m has a temperature of 65C at all surface. A laboratory scientist then hold the cube with a very thick and high heat resistance insulator to prevent his hand from burns. Only the top and the bottom surface of the cube are exposed to surrounding air at 25C. Assuming no heat radiation and negligible heat conduction on the unexposed surface, determine the total rate of heat loss from the cube to the surrounding due to natural convection from the exposed surfaces.

Q3(a). A tetrahedron enclosure made of four triangle surface. Triangle surface 1 has a base length of a and height of c. Triangle surface 2, 3 and 4 are identical with base width of a and height of b. Determine the ratio of b/c if the view factor from surface 2 to surface 1, .(Figure Q3 (a))

(2431bacTetrahedron enclosureOpened tetrahedron enclosure )

Figure Q3 (a)

Q3(b). A spherical tank of radius, R1 = 3 m that is filled with liquid nitrogen at 100 K is kept in an evacuated cylindrical enclosure whose radius, R2 = 4 m and the height of the cylinder are three times the cylindrical enclosure radius which is shown in figure Q3(b). The emissivities of the spherical tank and the enclosure are 1 = 0.1 and 2 = 0.8, respectively. The temperature of the enclosure is measured to be 285 K.

(D2 = 2R2L = 3R2 D1 )

Figure Q3(b)

i. Draw the radiation resistance network for two surface (non black) enclosure which includes the potential emissivity, Eb and radiosity, J

ii. Show that net rate of radiation heat transfer from the liquid nitrogen sphere is given by

Whereas 1 indicates sphere surface, 2 indicate internal cylindrical enclosure surface, A is surface area, R is radius, T is surface temperature, is emissivity and is Stefan-Boltzmann constant.

Appendix

Internal Forced Convection

,

,

, ,

Fully develop laminar flow

Developing Laminar flow

Fully turbulent/Developing turbulent flow

,

Constant temperature

Constant heat flux

,,

Natural Convection

Nu=

Geometry

Characteristic length, Lc

Range of Ra

Nu

Vertical plate

L

Entire Range

Incline Plate

L

Use vertical plate equation and replace g with gcos

Horizontal Plate

Hot upper plate/cold lower plate

Hot lower plate/cold upper plate

As/p

104-107

107-1011

105-1011

(As= Surface Area)

(p = perimeter)

Vertical cylinder

L

A vertical cylinder can be treated as a vertical plate when

Horizontal cylinder

D

Sphere

D

View factorRadiation

p

A

D

c

h

4

=

n

m

r

D

V

D

V

m

m

=

=

Re

D

L

t

Pr

Re

05

.

0

laminar

,

=

pL

A

s

=

D

L

t

10

turbulent

,

=

k

hD

h

=

Nu

"

=

&

&

r

m

[

]

3

/

2

Pr

Re

)

/

(

04

.

0

1

Pr

Re

)

/

(

0.065

3.66

Nu

L

D

L

D

+

+

=

)

3

.

0

cooling,

,

4

.

0

heating,

(

Pr

Re

023

.

0

Nu

8

.

0

=

=

=

n

n

n

2

/

)

(

e

i

b

T

T

T

+

=

,

ln

lm

÷

÷

ø

ö

ç

ç

è

æ

-

-

-

=

D

i

s

e

s

e

i

T

T

T

T

T

T

T

lm

T

hA

Q

s

D

=

&

)

/

exp(

)

(

p

s

i

s

s

e

C

m

hA

T

T

T

T

&

-

-

-

=

)

(

i

e

p

s

s

T

T

C

m

A

q

Q

-

=

=

&

&

&

)

/

(

p

s

s

i

e

C

m

A

q

T

T

&

&

+

=

h

q

T

T

s

m

s

/

&

+

=

x

C

m

p

q

T

T

p

s

i

m

&

&

+

=

),

(

¥

-

=

T

T

hA

Q

s

s

conv

&

,

k

hL

c

Pr,

)

(

Pr

2

3

n

b

c

s

L

L

L

T

T

g

Gr

Ra

¥

-

=

=

,

2

¥

+

=

T

T

T

s

f

)

(

1

K

T

f

=

b

[

]

2

27

/

8

16

/

9

1/6

Pr)

/

492

.

0

(

1

Ra

387

.

0

825

.

0

Nu

ï

þ

ï

ý

ü

ï

î

ï

í

ì

+

+

=

L

1/4

0.54Ra

Nu

L

=

1/3

0.15Ra

Nu

L

=

1/4

0.27Ra

Nu

L

=

4

/

1

35

L

Gr

L

D

³

12

10

Ra

£

D

2

.

0

1

2

=

®

F

[

]

2

27

/

8

16

/

9

1/6

Pr)

/

559

.

0

(

1

Ra

387

.

0

6

.

0

Nu

ï

þ

ï

ý

ü

ï

î

ï

í

ì

+

+

=

D

)

7

.

0

(Pr

10

Ra

11

³

£

D

[

]

9

/

4

16

/

9

1/4

Pr)

/

469

.

0

(

1

Ra

589

.

0

2

Nu

+

+

=

D

symmetry

and

if

:

rule

Symmetry

:

rule

ion

Superposit

:

rule

y

Reciprocit

enclosure,

in the

surface

of

number

1

.....

:

rule

Summary

)

,

(

2

1

l

k

j

l

i

k

i

j

i

c

a

b

a

c

b

a

i

j

j

j

i

i

i

j

j

j

A

A

A

F

F

F

F

F

F

F

A

F

A

i

j

i

F

F

F

=

=

=

=

+

=

=

£

=

=

+

+

+

®

®

®

®

®

®

®

®

®

®

®

cylinder)

(for

2

(sphere)

2

2

4

D

DL

A

D

A

T

E

s

s

i

bi

p

p

p

s

+

=

=

=

2

2

1

2

2

1

4

2

4

1

1

12

5

.

0

1

1

)

(

÷

÷

ø

ö

ç

ç

è

æ

÷

÷

ø

ö

ç

ç

è

æ

-

+

-

=

R

R

T

T

A

Q

e

e

e

s

s