Importance of activation energy and heat source on nanoliquid flow with gyrotactic microorganisms

Document Type : Article

Authors

1 - Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan - Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University P. O. Box 80203, Jeddah 21589, Saudi Arabia

2 Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan

3 Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University P. O. Box 80203, Jeddah 21589, Saudi Arabia

4 Department of Mathematics, CUT, Chak Shahzad, Park Road, Islamabad, Pakistan

Abstract

This article addresses salient features of gyrotactic microorganism and activation energy in flow of nanofluid by rotating disk. An exponential space dependent heat source (ESHS) process is implemented to examine the thermal transport characteristics. Additionally nanoparticles mass flux condition is considered. The solutions are numerically computed. Impacts of various physical variables appearing in the solutions of non-linear systems are carefully analyzed. The current work identifies that temperature distribution of nanoliquid enhances for higher values of thermophoresis and Brownian motion variables. Moreover activation energy and temperature difference parameters diminish the nanoparticles concentration. Comparative study is provided in order to validate our outcomes.

Keywords


References
1. Choi, S.U.S. and Eastman, J.A. Enhancing thermal
conductivity of
uids with nanoparticles", The Proceedings
of the 1995 ASME International Mechanical
Engineering Congress and Exposition, San Francisco,
USA, ASME, FED 231/MD, 66, pp. 99{105 (1995).
2. Buongiorno, J. Convective transport in nano
uids",
J. Heat Transfer, 128(3), pp. 240{250 (2006).
3. Sheikholeslami, M., Hayat, T., and Alsaedi, A. Numerical
simulation of nano
uid forced convection heat
transfer improvement in existence of magnetic eld
using lattice Boltzmann method", Int. J. Heat Mass
Transfer, 108, pp. 1870{1883 (2017).
4. Tiwari, R.K. and Manab K.D. Heat transfer augmentation
in a two-sided lid-driven di erentially heated
square cavity utilizing nano
uids", Int. J. Heat Mass
Transfer, 50(9{10), pp. 2002{2018 (2007).
5. Shehzad, S.A., Hayat, T., Alsaedi, A., et al. A useful
model for solar radiation", Ener. Eco. and Environ.,
1(1), pp. 30{38 (2016).
6. Sheikholeslami, M., Hayat, T., and Alsaedi, A. On
simulation of nano
uid radiation and natural convection
in an enclosure with elliptical cylinders", Int. J.
Heat Mass Transfer, 115, pp. 981{991 (2017).
7. Alsaedi, A., Awais, M., and Hayat, T. E ects of
heat generation/absorption on stagnation point
ow of
nano
uid over a surface with convective boundary conditions",
Commun Nonlinear Sci. and Numer. Simul.,
17(11), pp. 4210{4223 (2012).
8. Hayat, T., Ullah, I., Muhammad, T., et al. Magnetohydrodynamic
(MHD) three-dimensional
ow of
second grade nano
uid by a convectively heated exponentially
stretching surface", J. Mol. Liq., 220, pp.
1004{1012 (2016).
9. Hayat, T., Ullah, I., Waqas, M., et al. Flow
of chemically reactive magneto Cross nanoliquid
with temperature-dependent conductivity", Applied
Nanoscience, 8(6), pp. 1453{1460 (2018).
10. Hsiao, K.L. Stagnation electrical MHD nano
uid
mixed convection with slip boundary on a stretching
sheet", Appl. Therm. Eng., 98, pp. 850{861 (2016).
11. Lin, Y., Zheng, L., Zhang, X., et al. MHD pseudoplastic
nano
uid unsteady
ow and heat transfer in
a nite thin lm over stretching surface with internal
heat generation", Int. J. Heat Mass Transfer, 84, pp.
903{911 (2015).
12. Mustafa, M., Hayat, T., Pop, I., et al. Stagnationpoint

ow of a nano
uid towards a stretching sheet",
Int. J. Heat Mass Transfer, 54(25{26), pp. 5588{5594
(2011).
13. Sheikholeslami, M., Hayat, T., and Alsaedi, A. On
simulation of nano
uid radiation and natural convection
in an enclosure with elliptical cylinders", Int. J.
Heat Mass Transfer, 115, pp. 981{991 (2017).
14. Hayat, T., Ullah, I., Alsaedi, A., et al. Threedimensional
mixed convection
ow of Sisko nanoliquid",
Int. J. Mech.l Sci., 133, pp. 273{282 (2017).
3388 T. Hayat et al./Scientia Iranica, Transactions F: Nanotechnology 27 (2020) 3381{3389
15. Hussain, Z., Hayat, T., Alsaedi, A., et al. Threedimensional
convective
ow of CNTs nano
uids
with heat generation/absorption e ect: A numerical
study", Comp. Methods Appl. Mech. Eng., 329, pp.
40{54 (2018).
16. Hayat, T., Ullah, I., Alsaedi, A., et al. MHD
ow of
Powell-Eyring nano
uid over a non-linear stretching
sheet with variable thickness", Results Phys., 7, pp.
189{196 (2017).
17. Ellahi, R., Zeeshan, A., Shehzad, N., et al. Structural
impact of Kerosene-Al2O3 nanoliquid on MHD
Poiseuille
ow with variable thermal conductivity:
application of cooling process", J. Mol. Liq., 264, pp.
607{615 (2018).
18. Hassan, M., Marin, M., Ellahi, R., et al. Exploration
of convective heat transfer and
ow characteristics
synthesis by Cu-Ag/water hybrid-nano
uids", Heat
Trans. Res., 49(18), pp. 1837{1848 (2018).
19. Rashidi, S., Akar, S., Bovand, M., et al. Volume of

uid model to simulate the nano
uid
ow and entropy
generation in a single slope solar still", Renew. Energy,
115, pp. 400{410 (2018).
20. Hassan, M., Marin, M., Alsharif, A., et al. Convective
heat transfer
ow of nano
uid in a porous medium over
wavy surface", Phys. Lett. A, 382(38), pp. 2749{2753
(2018).
21. Akbarzadeh, M., Rashidi, S., Karimi, N., et al. Convection
of heat and thermodynamic irreversibilities in
two-phase, turbulent nano
uid
ows in solar heaters
by corrugated absorber plates", Adv. Powder Technol.,
29(9), pp. 2243{2254 (2018).
22. Alamri, S.Z., Ellahi, R., Shehzad, N., et al. Convective
radiative plane Poiseuille
ow of nano
uid through
porous medium with slip: an application of Stefan
blowing", J. Mol. Liq., 273, pp. 292{304 (2019).
23. Shehzad, N., Zeeshan, A., Ellahi, R., et al. Modelling
study on internal energy loss due to entropy generation
for non-Darcy poiseuille
ow of silver-water nano
uid:
an application of puri cation", Entropy, 20(11), p. 851
(2018).
24. Ellahi, R., Zeeshan, A., Hussain, F., et al. Peristaltic
blood
ow of couple stress
uid suspended
with nanoparticles under the in
uence of chemical
reaction and activation energy", Symmetry, 11(2), p.
276 (2019).
25. Ashlin, T.S. and Mahanthesh, B. Exact solution of
non-coaxial rotating and non-linear convective
ow
of Cu-Al2O3-H2O hybrid nano
uids over an in nite
vertical plate subjected to heat source and radiative
heat", J. Nano
uids, 8(4), pp. 781{794 (2019).
26. Shruthy, M., and Mahanthesh, B. Rayleigh-Benard
convection in Casson and hybrid nano
uids: An analytical
investigation", J. Nano
uids, 8(1), pp. 222{229
(2019).
27. Amala, S. and Mahanthesh, B. Hybrid nano
uid
ow
over a vertical rotating plate in the presence of hall
current, nonlinear convection and heat absorption", J.
Nano
uids, 7(6), pp. 1138{1148 (2018).
28. Animasaun, I.L., Koriko, O.K., Adegbie, K.S., et al.
Comparative analysis between 36 nm and 47 nm
alumina-water nano
uid
ows in the presence of Hall
e ect", J. Therm. Anal. Calorim., 135(2), pp. 873{886
(2019).
29. Golshokooh, S., Ramazani, S.A., and Hekmatzadeh,
M. Investigating the e ect of hybrid silica
nanoparticles-copolymer on increasing oil recovery in
a three dimensional porous media", Sci. Iran., 24(6),
pp. 3466{3475 (2017).
30. AfzaliTabar, M., Alaeib, M., Khojasteh, R.R., et
al. Preference of nanoporous graphene to Single-
Walled Carbon Nanotube (SWCNT) for preparing silica
nanohybrid Pickering emulsion for potential Chemical
Enhanced Oil Recovery (C-EOR)", Sci. Iran., 24,
pp. 3491{9 (2017).
31. Karbasi, S., Zarei, M., and Foroughi, M.R. E ects of
Multi-Wall carbon Nano-Tubes (MWNTs) on structural
and mechanical properties of electrospun poly
(3-hydroxybutyrate) sca old for tissue engineering applications",
Sci. Iran., 23(6), p. 3145 (2016).
32. Hakeem, A.A., Ganesh, N.V., and Ganga, B. Heat
transfer of non-Darcy MHD
ow of nano
uid over a
stretching/shrinking surface in a thermally strati ed
medium with second order slip model", Sci. Iran.,
22(6), p. 2766 (2015).
33. Hari , T. and Montazer, M. TiO2 hematite or magnetite/
Ag nanoparticles synthesized on polyester fabric
at various temperatures producing di erent superparamagnetic,
self-cleaning and antibacterial textiles", Sci.
Iran., 21(6), p. 2490 (2014).
34. Hayat, T., Muhammad, K., Ullah, I., et al. Rotating
squeezed
ow with carbon nanotubes and melting
heat", Phys. Scr., 94, p. 035702 (2019).
35. Alsedi, F.E., Ullah, I., Hayat, T., et al. Entropy
generation in non-linear mixed convective
ow
of nano
uid in porous space in
uenced by Arrhenius
activation energy and thermal radiation", J.
Therm. Anal. Calorim., 140, pp. 799{809 (2020)
https://doi.org/10.1007/s10973-019-08648-0.
36. Zhou, C. and Ma, H. Ultrasonic degradation of
polysaccharide from a red algae (Porphyra yezoensis)",
J. Agric. Food Chem., 54(6), pp. 2223{2228 (2006).
37. Bestman, A.R. Natural convection boundary layer
with suction and mass transfer in a porous medium",
Int. J. Energ. Res., 14(4), pp. 389{396 (1990).
38. Awad, F.G., Motsa, S., and Khumalo, M. Heat and
mass transfer in unsteady rotating
uid
ow with
binary chemical reaction and activation energy", PloS
one, 9(9), p. e107622 (2014).
39. Makinde, O.D., Olanrewaju, P.O., and Charles, W.M.
Unsteady convection with chemical reaction and radiative
heat transfer past a
at porous plate moving
through a binary mixture", Afrika Mat., 22(1), pp.
65{78 (2011).
40. Maleque, K. E ects of exothermic/endothermic
chemical reactions with Arrhenius activation energy
T. Hayat et al./Scientia Iranica, Transactions F: Nanotechnology 27 (2020) 3381{3389 3389
on MHD free convection and mass transfer
ow in
presence of thermal radiation", J. Thermodyn., 2013
(2013).
41. Mustafa, M., Khan, J.A., Hayat, T., et al. Buoyancy
e ects on the MHD nano
uid
ow past a vertical
surface with chemical reaction and activation energy",
Int. J. Heat Mass Transfer, 108, pp. 1340{1346 (2017).
42. Abbas, Z., Sheikh, M., and Motsa, S.S. Numerical
solution of binary chemical reaction on stagnation
point
ow of Casson
uid over a stretching/shrinking
sheet with thermal radiation", Energy, 95, pp. 12{20
(2016).
43. Zeeshan, A., Shehzad, N., and Ellahi, R. Analysis
of activation energy in Couette-Poiseuille
ow of
nano
uid in the presence of chemical reaction and
convective boundary conditions", Results Phys., 8, pp.
502{512 (2018).
44. Hayat, T., Ullah, I., Farooq, M., et al. Analysis of
non-linear radiative stagnation point
ow of Carreau

uid with homogeneous-heterogeneous reactions", Microsyst.
Technol., 25(4), pp. 1243{1250 (2019).
45. Hayat, T., Ullah, I., Alsaedi, A., et al. Numerical
simulation for homogeneous-heterogeneous reactions in

ow of Sisko
uid", J. Braz. Soc. Mech. Sci. Eng.,
40(2), p. 73 (2018).
46. Archana, M. and Mahanthesh, B. Exploration of activation
energy and binary chemical reaction e ects on
nano Casson
uid
ow with thermal and exponential
space-based heat source", Multidiscip., 15(1), pp. 227{
245 (2019).
47. Chen, H., Chen, J., Geng, Y., et al. Threedimensional
boundary layer
ow over a rotating disk
with power-law stretching in a nano
uid containing
gyrotactic microorganisms", Heat Tran. Asian Res.,
47(3), pp. 569{582 (2017).
48. Zia, Q.Z., Ullah, I., Waqas, M., et al. Cross di usion
and exponential space dependent heat source impacts
in radiated three-dimensional (3D)
ow of Casson
uid
by heated surface", Results Phys., 8, pp. 1275{1282
(2018).
49. Hayat, T., Ullah, I., Waqas, M., et al. Attributes of
activation energy and exponential based heat source
in
ow of Carreau
uid with cross-di usion e ects", J.
Non-Equil. Thermody., 44(2), pp. 203{213 (2019).
50. Khan, A.A., Usman, H., Vafai, K., et al. Study of
peristaltic
ow of magnetohydrodynamic Walter's B

uid with slip and heat transfer", Sci. Iran., 23(6) pp.
2650{2662 (2016).
51. El-Aziz, M.A. and Salem, A.M. MHD-mixed convection
and mass transfer from a vertical stretching sheet
with di usion of chemically reactive species and spaceor
temperature-dependent heat source", Can. J. Phys.,
85(4), pp. 359{373 (2007).
52. Animasaun, I.L. E ects of thermophoresis, variable
viscosity and thermal conductivity on free convective
heat and mass transfer of non-darcian MHD dissipative
Casson
uid
ow with suction and nth order of
chemical reaction", J. Nigerian Math., 34(1), pp. 11{
31 (2015).