thesis presentation

2. Mixed Convective Flow
of Jeffrey Nanofluid
along an Inclined
Stretching Sheet
PRESENTED BY
535-FBAS/MSMA/F18

3. • Introduction
CHAPTER
1
• Magnetohydrodynamic (MHD) Jeffrey
Fluid through Stretching Vertical
Surface with a Porous Medium
CHAPTER
2
• Mixed Convective Flow of Jeffrey
Nanofluid along an Inclined Stretching
Sheet
CHAPTER
3

5. The phenomenon reveals the swap of heat
energy through one body to another
compensation to their temperature
discrepancy.
HEAT TRANSFER

6. Conduction
(via direct
contact)
Convection
(via fluid)
Radiation
(via
electromagnetic
radiations)

7.  Convective heat transfer is phenomenon of
transportation of thermal energy through the
movement of molecules. Convection phenomenon
mostly occurs in liquids. Convection heat
transmission is farther categorized in three types.
Advection
(fluid
motion)
Conduction Convection

8. • In the phenomenon of free convection
transmission of heat occurs through the
dissemination of fluid as a result of buoyancy due
to the variation in density.
Free
Convection
• The mechanism of forced convection heat is
transferred due to some extrinsic force i.e., pumps,
heat exchangers e.t.c. applied on the fluid.
Forced
Convection
• Mixed convection is the phenomenon that
combined the mechanism of free and forced
convection collectively.
Mixed
Convection

9.  Magnetohydrodynamics deliberate the movement of electrically
conducting fluids persuaded by the magnetic field. Electrically
conducting fields implicate electrolytes, plasma and liquid metal
e.t.c.
Nanofluid
• Nanofluid can be contemplated as a very effective mean of
enhanced heat transfer in fluids. Nanofluids have suspended
nanoparticles which have high thermal conductivity that's grant
better thermal performance than conventional. Choi et al. [6]
presented a idea of enhancing thermal conductivity of fluids with
nanoparticles.

10. Predominately the non Newtonian fluids are further divided into
three crucial categories specifically, (i) Rate form (ii) Differential
form and (iii) Integral form. Rate form fluids construe the nature
of retardation and relaxation times. Maxwell fluid is a
subcategories of rate form material which reveal the demeanor of
relaxation time only. Thus Jeffrey fluid is prospective to fill this
void. Jeffrey fluid chronicle the linear viscoelastic properties of
fluids which takes broad utilizing in the polymer industries.
with
pI,
-
S
=
t
#2.5
t))).
?2((dr)/(d
+
?1))(r
+
(µ/(1
=
S
2.5
2.4
PI
S 













dt
r
d
r
S
.
2
.
1
1



r
.

11. CHAPTER 2
MAGNETOHYDRODYNAMIC (MHD) JEFFREY
FLUID THROUGH STRETCHING
VERTICAL SURFACE WITH A POROUS
MEDIUM

12. keep in consideration as two dimensional steady
incompressible, state of Jeffrey fluid passing through
porous sheet. Flow is taken in the system of rectangular
coordinate such that the fluid flow is through the x axis
and y axis are orthogonal particular orientation of flow.

13. After applying the boundary layer approximations the
continuity,momentum and the energy equations modelled,
relevant to the flow problem are expressible as
0






y
v
x
u






²
B
-
k
-
)
T
-
(T
gB
+
y²
x
³
y³
³
x
y²
²
y
y
x
²
y²
²
)
+
(1
y
x
0
T
2
1
x
x
x
x
x
y
x
x
x
x
x
x
y
x
x
V
V
V
V
V
V
V
V
V
V
V
V
V
V
V























































2
2
y
T
y
T
V
x
T
V y
x 
2.1
2.2
2.3

14. Along with the boundary conditions:
Introducing suitable transformations as:
0
0 



 at y
T
, T
cx , V
(x)
U
V w
y
w
x






  when y
T
T
y
V
,
V
x
x ,
0
0








T
T
T
T
c
y
a
V
axf
y
x
V
w
y
x )
(
,
),
f(
-
),
(
'
)
,
( 






2.4
2.5

15. Thus continuity equation is identically satisfied, however
momentum and energy equations are transformed into
ordinary dfferential equations
along with the transformed conditions
where serve as the the local Grashof number,
the Deborah number, the porosity parameter,and
signifies the Prandtl number.
0
=
+
)
f
+
Pr(-f' 

 


0
=
]
ff
-
[(f"²
+
]
'
ff'
+
M)
+
(K
-f'
f'
-
)[
+
'+(1
'
f' 2
1
iv


 2.6
2.7
     
      at
0
,
0
"
,
0
0
at
1
0
,
1
0
,
0
0



















f
f
f
f
2.8
w
U
T
T
Tg
2
)
(
= 



2

 a










c
B
M

 2
0









k
cp

Pr
ka
K



16. RESULTS
AND
DISSCUSSION

17. Fig.1a
Fig.1b

18. Fig.2a
Fig.2b

19. Fig.3a
Fig.3b

20. Fig.4a

Fig.4b

21. Fig.5a
Fig.5b

22. Mixed Convective Flow of Jeffrey Nanofluid
along an Inclined Stretching Sheet
CHAPTER 3

23. Examine the steady, incompressible, 2-dim tide of Jeffrey
nanofluid along stretching sheet accompanied by
convective conditions at boundary. The sheet is placed such
that fluid which is placed on the sheet is flowing ahead the
direction of x-axis and y-axis. As flow is developed along a
stretching sheet with velocity Vx =ax

24. After applying the boundary layer approximations the continuity,
momentum, energy and the concentration equations modeled are
expressible as
  x
x
x
x
x
x
y
x
x
x
x
y
x
V
V
V
V
V
V
V
V
V
V
y
V
V
x
V
u
k
-
)
C
-
(C
B
)
T
-
(T
B
gcos
+
y
x
²
y
x
y²
²
y³
³
y²
x
³
y²
²
)
+
(1
C
T
2
1






 








































0






y
V
x
V y
x
MATHEMATICAL MODELLING
 
 
2
2
B
2
2
2
B
2
2
D
DT
DT
D
y
C
y
T
T
y
C
V
x
C
V
y
T
T
y
T
y
C
c
c
y
T
y
T
V
x
T
V
y
x
f
p
y
x
















































3.1
3.2
3.3
3.4

25. with the boundary conditions defined as
Introducing suitable transformations as:
  0
,
0 






 at z
C
C
T
T
-h
y
T
, k
ax , V
V w
f
y
x




 
 as y
C
C
T
, T
Vx ,
0













C
C
C
C
T
T
T
T
c
y
a
V
axf
y
x
V
w
f
y
x )
(
,
)
(
,
),
f(
-
),
(
'
)
,
( 








3.4
3.5

26.  
0
'
"
N
N
Pr
'
'
0
'
'
N
'
'
N
Pr
'
'
b
t
b
2
t





















f
Le
f
0
cos
Grc
+
cosa
Grt
]
ff
-
[(f"²
+
]
'
ff'
+
M)
+
(K
-f'
f'
-
)[
+
'+(1
'
f' 2
1

 





 iv
       
   
        at
0
,
0
,
0
"
,
0
0
at
1
0
,
0
1
0
,
1
0
'
,
0
0



























f
f
f
f
B
D
Le


 
s
u
x
Grc 2
w
T C
-
gC 


 
s
u
x
Grt 2
w
T T
-
gT 





Pr
3.6
3.7
3.8
  
 f
p
w
T
c
c
T
T
D






t
N
  
 f
p
w
B
c
c
C
C
D






B
N
where represents the Lewis number, is the local temperature
Grashof number, the local concentration,
thermospheres parameter, , Brownian motion parameter,
Prandtl number, 2

 a
 the Deborah number and indicates Biot number









c
k
h 

3.9

27. By utilizing the HAM series inflation method are secured
akin to the governing coupled non linear differential
equations with ordinary derivatives and linked boundary
conditions given by Eqs. (3.21)-(3.25). Whereas, the operator
and initial guesses for the velocity, thermal and concentration
field are cull as pursue
,
      








 






 e
e
e
f 0
0
0 ,
1
,
1
4
y


1
²
d
d²
,
1
²
d
d²
,
d
³
d
d³











 L
L
d
Lf
3.10
1
)
0
(
,
0
)
0
( 2
1 
 y
y
3.9

28. RESULTS
AND
DISSCUSSION

29. Fig.1a

Fig.1b
Fig.1c

30. Fig.2a
Fig.2b

31. Fig.3b
Fig.3a

32. Fig.4a
Fig.4b

33. Fig.5a
Fig.5
b

34. Fig.6a

Fig.6b

35. Fig.7
Fig.8

36. Fig.9a
Fig.9b

37. • Chapter 3 is an analysis of mixed convection
movement of Jeffrey nanofluid through stretching
sheet. The boundary condition were contemplated
as convective type. A keen observation reveals that
enlargement of the angle of inclination has enhanced
the temperature and concentration field although the
opposite behavior is recognized for velocity field.
As influence of Nt was to increase the temperature
and concentration field. The temperature field is
intensified by expanding biot number.
CONCLUSIONS

38. 1. Carragher, P., and L. J. Crane. "Heat transfer on a continuous stretching
sheet." ZAMM-Journal of Applied Mathematics and
Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik 62.10
(1982): 564-565..
2. Ranganathan, P., & Viskanta, R. (1984). Mixed convection boundary-
layer flow along a vertical surface in a porous medium. Numerical Heat
Transfer, 7(3), 305-317.
3. Nakayama, A., & Koyama, H. (1987). Effect of thermal stratification on
free convection within a porous medium. Journal of thermophysics and
heat transfer, 1(3), 282-285. 4 .
4. Kumari, M., Takhar, H. S., & Nath, G. (1990). MHD flow and heat
transfer over a stretching surface with prescribed wall temperature or
heat flux. Wärme-und Stoffübertragung, 25(6), 331-336. 5 .
5. Andersson, H. I. (1992). MHD flow of a viscoelastic fluid past a
stretching surface. Acta Mechanica, 95(1-4), 227-230
6. Al-Sharifi, H. A. M., Kasim, A. R. M., Salleh, M. Z., Sarif, N. M.,
Mohammad, N. F., Shafie, S., & Ali, A. (2006). Influence of slip velocity
on convective boundary layer flow of Jeffrey fluid under convective
boundary conditions
REFERENCES

39. 7. Ishak, A., Nazar, R., & Pop, I. (2006).unsteady mixed convection boundary
layer flow due to a stretching vertical surface. Arabian Journal for Science &
Engineering (Springer Science & Business Media BV), 31
8. Al-Sharifi, H. A. M., Kasim, A. R. M., Salleh, M. Z., Sarif, N. M., Mohammad,
N. F., Shafie, S., & Ali, A. (2006). Influence of slip velocity on convective
boundary layer flow of Jeffrey fluid under convective boundary conditions.
9. Ishak, A., Nazar, R., & Pop, I. (2006). Steady and unsteady boundary layers due
to a stretching vertical sheet in a porous medium using Darcy-Brinkman
equation model. applied mechanics and engineering, 11(3), 623.
10.Khan, M. (2007). Partial slip effects on the oscillatory flows of a fractional
Jeffrey fluid in a porous medium. Journal of Porous Media, 10(5).
11.Jat, R. N., & Chaudhary, S. (2009). MHD flow and heat transfer over a
stretching sheet. Applied Mathematical Sciences, 3(26), 1285-1294.
12.Ali, F. M., Nazar, R., Arifin, N. M., & Pop, I. (2011). MHD boundary layer
flow and heat transfer over a stretching sheet with induced magnetic field. Heat
and Mass transfer, 47(2), 155-162.
13.Nadeem, S., Zaheer, S., & Fang, T. (2011). Effects of thermal radiation on the
boundary layer flow of a Jeffrey fluid over an exponentially stretching surface.
Numerical Algorithms, 57(2), 187-205

40. 14. Imran, S. M., Asghar, S., & Mushtaq, M. (2012). Mixed convection flow
over an unsteady stretching surface in a porous medium with heat source.
Mathematical Problems in Engineering, 2012.
15. Hayat, T., Nawaz, M., Awais, M., & Obaidat, S. (2012). Axisymmetric
magnetohydrodynamic flow of Jeffrey fluid over a rotating disk.
International journal for numerical methods in fluids, 70(6), 764-774.
16. Qasim, M. (2013). Heat and mass transfer in a Jeffrey fluid over a
stretching sheet with heat source/sink. Alexandria Engineering Journal,
52(4), 571-575.
17. Hayat, T., Shehzad, S. A., Qasim, M., & Alsaedi, A. (2014). Mixed
convection flow by a porous sheet with variable thermal conductivity and
convective boundary condition. Brazilian Journal of Chemical
Engineering, 31(1), 109-117.
18. Samyuktha, N., & Ravindran, R. (2015). Thermal Radiation Effect on
Mixed Convection Flow Over a Vertical Stretching Sheet Embedded in a
Porous Medium with Suction (Injection). Procedia Engineering, 127,
767-774.
19. Mabood, F., Khan, W. A., & Ismail, A. M. (2015). MHD boundary layer
flow and heat transfer of nanofluids over a nonlinear stretching sheet: a
numerical study. Journal of Magnetism and Magnetic Materials, 374,
569-576

41. 20. Babu, D. H., & Narayana, P. S. (2016). Joule heating effects on MHD mixed
convection of a Jeffrey fluid over a stretching sheet with power law heat flux: A
numerical study. Journal of Magnetism and Magnetic Materials, 412, 185-193.
21. Shahzad, A., Ali, R., Hussain, M., & Kamran, M. (2017). Unsteady
axisymmetric flow and heat transfer over time-dependent radially stretching
sheet. Alexandria Engineering Journal, 56(1), 35-41
22. Bhargava, R., & Chandra, H. (2017). Numerical simulation of MHD boundary
layer flow and heat transfer over a nonlinear stretching sheet in the porous
medium with viscous dissipation using hybrid approach. arXiv preprint
arXiv:1711.03579.
23. Hayat, T., Aziz, A., Muhammad, T., & Alsaedi, A. (2017). A revised model for
Jeffrey nanofluid subject to convective condition and heat
generation/absorption. PloS one, 12(2).
24. Ahmad, K., & Ishak, A. (2017). Magnetohydrodynamic (MHD) Jeffrey fluid
over a stretching vertical surface in a porous medium. Propulsion and Power
Research, 6(4), 269-276.
25. : Alarifi, I. M., Abokhalil, A. G., Osman, M., Lund, L. A., Ayed, M. B.,
Belmabrouk, H., & Tlili, I. (2019). MHD flow and heat transfer over vertical
stretching sheet with heat sink or source effect 412, 185-193.. Symmetry, 11(3),
297.