Abstract

This article studies the natural convection in an annular porous microchannel in case of one wall being heated and another being cooled. For the first time, such a problem was solved using discrete symmetries of the Navier–Stokes equations. Using discrete symmetries, self-similar forms of differential equations were obtained. Solutions of self-similar equations made it possible to obtain velocity and temperature profiles incorporating slip and temperature jump at the channel walls as boundary conditions. The effects of Grashof, Knudsen, Darcy, and Prandtl numbers on the velocity and temperature profiles in the microchannel and Nusselt numbers are demonstrated. At high Grashof numbers, an ascending flow forms near the hot cylinder, while a descending flow develops near the cold cylinder. As the Knudsen number increases, rise of velocity and temperature jump at the walls as well as heat transfer coefficients decrease is observed. An increase in the Darcy number results in higher velocities for both flows. The temperature jump at the heated cylinder increases, remaining unchanged at the cooled cylinder, and the heat transfer coefficient at the heated cylinder drops.

References

1.
Ganguli
,
A. A.
, and
Pandit
,
A. B.
,
2021
, “
Hydrodynamics of Liquid-Liquid Flows in Micro Channels and Its Influence on Transport Properties: A Review
,”
Energies
,
14
(
19
), p.
6066
.10.3390/en14196066
2.
Yagodnitsyna
,
A.
,
Kovalev
,
A.
, and
Bilsky
,
A. V.
,
2016
, “
Flow Patterns of Immiscible Liquid-Liquid Flow in a Rectangular Microchannel With T-Junction
,”
Chem. Eng. J.
,
303
, pp.
547
554
.10.1016/j.cej.2016.06.023
3.
Nourdanesh
,
N.
,
Hossainpour
,
S.
, and
Adamiak
,
K.
,
2020
, “
Numerical Simulation and Optimization of Natural Convection Heat Transfer Enhancement in Solar Collectors Using Electrohydrodynamic Conduction Pump
,”
Appl. Therm. Eng.
,
180
, p.
115825
.10.1016/j.applthermaleng.2020.115825
4.
Dutta
,
S.
,
Biswas
,
A. K.
, and
Pati
,
S.
,
2019
, “
Numerical Analysis of Natural Convection Heat Transfer and Entropy Generation in a Porous Quadrantal Cavity
,”
Int. J. Numer. Methods Heat Fluid Flow
,
29
(
12
), pp.
4826
4849
.10.1108/HFF-11-2018-0678
5.
Saha
,
L. K.
,
Bala
,
S. K.
, and
Roy
,
N. C.
,
2021
, “
Natural Convection Flow in a Fluid-Saturated non-Darcy Porous Medium Within a Complex Wavy Wall Reactor
,”
J. Therm. Anal. Calorim.
,
146
(
1
), pp.
325
340
.10.1007/s10973-020-09945-9
6.
Abdollahi
,
S. A.
,
Jalili
,
P.
,
Jalili
,
B.
,
Nourozpour
,
H.
,
Safari
,
Y.
,
Pasha
,
P.
, and
Ganji
,
D. D.
,
2023
, “
Yaghub Safari, Pooya Pasha and Davood Domiri Ganji. “Computer Simulation of Cu: ALOOH/Water in a Microchannel Heat Sink Using a Porous Media Technique and Solved by Numerical Analysis AGM and FEM
,”
Theor. Appl. Mech. Lett.
,
13
(
3
), p.
100432
.10.1016/j.taml.2023.100432
7.
Sindhu
,
S.
,
Gireesha
,
B. J.
, and
Ganji
,
D. D.
,
2020
, “
Simulation of Cu:γ−ALOOH/Water in a Microchannel Heat Sink by Dint of Porous Media Approach
,”
Case Stud. Therm. Eng.
,
21
, p.
100723
.10.1016/j.csite.2020.100723
8.
Nabi
,
H.
,
Gholinia
,
M.
, and
Ganji
,
D. D.
,
2023
, “
Employing the (SWCNTs-MWCNTs)/H2O Nanofluid and Topology Structures on the Microchannel Heatsink for Energy Storage: A Thermal Case Study
,”
Case Stud. Therm. Eng.
,
42
, p.
102697
.10.1016/j.csite.2023.102697
9.
Rajalingam
,
A.
, and
Chakraborty
,
S.
,
2023
, “
Microchannel Heat Sink With Microstructured Wall — A Critical Study on Fluid Flow and Heat Transfer Characteristics
,”
Therm. Sci. Eng. Prog.
,
38
, p.
101613
.10.1016/j.tsep.2022.101613
10.
Bhatti
,
M. M.
,
Sarris
,
I.
,
Michaelides
,
E. E.
, and
Ellahi
,
R.
,
2024
, “
Sisko Fluid Flow Through a non-Darcian Micro-Channel: An Analysis of Quadratic Convection and Electro-Magneto-Hydrodynamics
,”
Therm. Sci. Eng. Prog.
,
50
, p.
102531
.10.1016/j.tsep.2024.102531
11.
Tahiri
,
A.
,
Ragueb
,
H.
,
Moussaoui
,
M.
,
Mansouri
,
K.
,
Guerraiche
,
D.
, and
Guerraiche
,
K.
,
2024
, “
Heat Transfer and Entropy Generation in Viscous-Joule Heating MHD Microchannels Flow Under Asymmetric Heating
,”
Int. J. Numer. Methods Heat Fluid Flow
,
34
(
10
), pp.
3953
3978
.10.1108/HFF-05-2024-0380
12.
Aina
,
B.
, and
Malgwi
,
P. B.
,
2019
, “
MHD Convection Fluid and Heat Transfer in an Inclined Micro-Porous-Channel
,”
Nonlinear Eng.
,
8
(
1
), pp.
755
763
.10.1515/nleng-2018-0081
13.
Ojemeri
,
G.
,
Hamza
,
M. M.
,
Tambuwal
,
B. H.
,
Bello
,
I.
, and
Shuaibu
,
A.
,
2023
, “
Influence of Soret and Radial Magnetic Field on Natural Convection of a Chemically Reactive Fluid in an Upright Porous Annulus
,”
UMYU Sci.
,
2
(
3
), pp.
108
120
.10.56919/usci.2323.017
14.
Oni
,
M.
, and
Rilwan
,
U. S.
,
2023
, “
Role of Suction/Injection on Electromagnetohydrodynamics Natural Convection Flow in a Porous Microchannel With Electroosmotic Effect
,”
Int. J. Appl. Mech. Eng.
,
28
(
4
), pp.
94
113
.10.59441/ijame/173021
15.
Ojemeri
,
O.
,
Omokhuale
,
E.
,
Hamza
,
M.
,
Onwubuya
,
I. O.
, and
Shuaibu
,
A.
,
2023
, “
A Computational Analysis on Steady MHD Casson Fluid Flow Across A Vertical Porous Channel Affected By Thermal Radiation Effect
,”
Int. J. Sci. Global Sustainability
,
9
(
1
), p.
13
.10.57233/ijsgs.v9i1.393
16.
Goli
,
A.
,
Zahmatkesh
,
I.
,
Saleh
,
S. R.
, and
Abolhasan Alavi
,
S. M.
,
2024
, “
MHD Mixed Convection of Developing Slip Flow in a Vertical Porous Microchannel Under Local Thermal Non–Equilibrium Conditions
,”
Nanoscale Microscale Thermophys. Eng.
,
28
(
1
), pp.
28
45
.10.1080/15567265.2023.2257748
17.
Hamza
,
M. M.
,
Shuaibu
,
A.
, and
Kamba
,
A. S.
,
2022
, “
Unsteady MHD Free Convection Flow of an Exothermic Fluid in a Convectively Heated Vertical Channel Filled With Porous Medium
,”
Sci. Rep.
,
12
(
1
), p.
11989
.10.1038/s41598-022-16064-y
18.
Kuznetsov
,
A. V.
, and
Avramenko
,
A. A.
,
2009
, “
A Minimal Hydrodynamic Model for a Traffic Jam in an Axon
,”
Int. Commun. Heat Mass Transfer
,
36
(
1
), pp.
1
5
.10.1016/j.icheatmasstransfer.2008.09.004
19.
Kuznetsov
,
A. V.
, and
Avramenko
,
A. A.
,
2003
, “
Stability Analysis of Bioconvection of Gyrotactic Motile Microorganisms in a Fluid Saturated Porous Medium
,”
Transp. Porous Media
,
53
(
1
), pp.
95
104
.10.1023/A:1023582001592
20.
Avramenko
,
A. A.
,
Tyrinov
,
A. I.
,
Shevchuk
,
I. V.
,
Dmitrenko
,
N. P.
,
Kravchuk
,
A.
, and
Shevchuk
,
V. I.
,
2017
, “
Mixed Convection in a Vertical Circular Microchannel
,”
Int. J. Therm. Sci.
,
121
, pp.
1
12
.10.1016/j.ijthermalsci.2017.07.001
21.
Avramenko
,
A. A.
,
Kovetska
,
Y. Y.
,
Shevchuk
,
I. V.
,
Tyrinov
,
A. I.
, and
Shevchuk
,
V. I.
,
2018
, “
Mixed Convection in Vertical Flat and Circular Porous Microchannels
,”
Transp. Porous Media
,
124
(
3
), pp.
919
941
.10.1007/s11242-018-1104-4
22.
Avramenko
,
A. A.
,
Tyrinov
,
A. I.
,
Shevchuk
,
I. V.
,
Dmitrenko
,
N. P.
,
Kravchuk
,
A.
, and
Shevchuk
,
V. I.
,
2017
, “
Mixed Convection in a Vertical Flat Microchannel
,”
Int. J. Heat Mass Transfer
,
106
, pp.
1164
1173
.10.1016/j.ijheatmasstransfer.2016.10.096
23.
Ojemeri
,
G.
, and
Hamza
,
M. M.
,
2022
, “
Heat Transfer Analysis of Arrhenius-Controlled Free Convective Hydromagnetic Flow With Heat Generation/Absorption Effect in a Micro-Channel
,”
Alexandria Eng. J.
,
61
(
12
), pp.
12797
12811
.10.1016/j.aej.2022.06.058
24.
Ojemeri
,
G.
,
Onwubuya
,
I.
,
Shuaibu
,
A.
,
Omokhuale
,
E.
, and
Altine
,
M.
,
2023
, “
Arrhenius-Controlled Heat Transfer Fluid Provoked by Porosity Effect Through a Vertical Micro-Channel: An Analytical Approach
,”
Zenodo
,
18
, pp.
18
40
.10.5281/zenodo.7932942
25.
Avramenko
,
A. A.
,
Shevchuk
,
I. V.
,
Kovetskaya
,
M. M.
,
Kovetska
,
Y. Y.
, and
Kobzar
,
A. S.
,
2024
, “
Application of Discrete Symmetry to Natural Convection in Vertical Porous Microchannels
,”
J. Non-Equilib. Thermodyn.
,
49
(
3
), pp.
391
404
.10.1515/jnet-2024-0006
26.
McDonald
,
K.
, and
Sun
,
D.
,
2000
, “
Vacuum Cooling Technology for the Food Processing Industry: A Review
,”
J. Food Eng.
,
45
(
2
), pp.
55
65
.10.1016/S0260-8774(00)00041-8
27.
Lu
,
C.
,
Liu
,
C.
,
Shao
,
M.
,
Wu
,
Z.
,
Jiang
,
C.
,
Cao
,
J.
, and
Chen
,
T.
,
2023
, “
Design and Performance Analysis of the Highly Sensitive Deep Vacuum Cooling sCMOS Imaging System for Highly Sensitive Detection of Space Targets
,”
Photonics
,
10
(
7
), p.
819
.10.3390/photonics10070819
28.
Veneroni
,
S.
,
Dugo
,
M.
,
Daidone
,
M. G.
,
Iorio
,
E.
,
Valeri
,
B.
,
Pinciroli
,
P.
,
De Bortoli
,
M.
, et al.,
2016
, “
Applicability of Under Vacuum Fresh Tissue Sealing and Cooling to Omics Analysis of Tumor Tissues
,”
Biopreserv. Biobanking
,
14
(
6
), pp.
480
490
.10.1089/bio.2015.0093
29.
Moghaddam
,
R. N.
, and
Jamiolahmady
,
M.
,
2016
, “
Slip Flow in Porous Media
,”
Fuel
,
173
, pp.
298
310
.10.1016/j.fuel.2016.01.057
30.
Nield
,
D. A.
, and
Bejan
,
A.
,
1992
,
Convection in Porous Media
, Springer, New York.
31.
Olver
,
P. J.
,
1986
,
Applications of Lie Groups to Differential Equations
, Springer, New York.
32.
Avramenko
,
A. A.
, and
Shevchuk
,
I. V.
,
2019
, “
Lie Group Analysis and General Forms of Self-Similar Parabolic Equations for Fluid Flow, Heat and Mass Transfer of Nanofluids
,”
J. Therm. Anal. Calorim.
,
135
(
1
), pp.
223
235
.10.1007/s10973-018-7053-x
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