The novelty of the current paper is to study the bioconvection effects in Walter's B nanofluid flow due to stretchable surface, which leads to important properties, i.e., thermal radiation, activation energy, motile microorganisms and convective boundary constraints. The considered analysis is explained via partial differential equations (PDEs), which are first embedded into the dimensionless system of nonlinear ODEs through suitable transformations. The governing equations are solved in MATLAB using the bvp4c solver. The impact of interesting parameters on the velocity field, thermal field, concentration of species and concentration of microorganisms is exhibited in graphical and tabular forms. The velocity field increases for higher estimations of the modified Hartmann and mixed convection parameters. The thermal field decays for a higher magnitude of the Prandtl number, while it is enhanced for a larger deviation of the thermal conductivity parameter. The volumetric concentration of nanoparticles enhances the larger activation energy and thermophoresis parameters. The microorganism concentration diminishes for higher Peclet number. The current model is more useful in various fields such as tissue engineering, recombinant proteins, synthetic biology, and biofuel cell and drug delivery devices.
Citation: M. S. Alqarni. Thermo-bioconvection flow of Walter's B nanofluid over a Riga plate involving swimming motile microorganisms[J]. AIMS Mathematics, 2022, 7(9): 16231-16248. doi: 10.3934/math.2022886
The novelty of the current paper is to study the bioconvection effects in Walter's B nanofluid flow due to stretchable surface, which leads to important properties, i.e., thermal radiation, activation energy, motile microorganisms and convective boundary constraints. The considered analysis is explained via partial differential equations (PDEs), which are first embedded into the dimensionless system of nonlinear ODEs through suitable transformations. The governing equations are solved in MATLAB using the bvp4c solver. The impact of interesting parameters on the velocity field, thermal field, concentration of species and concentration of microorganisms is exhibited in graphical and tabular forms. The velocity field increases for higher estimations of the modified Hartmann and mixed convection parameters. The thermal field decays for a higher magnitude of the Prandtl number, while it is enhanced for a larger deviation of the thermal conductivity parameter. The volumetric concentration of nanoparticles enhances the larger activation energy and thermophoresis parameters. The microorganism concentration diminishes for higher Peclet number. The current model is more useful in various fields such as tissue engineering, recombinant proteins, synthetic biology, and biofuel cell and drug delivery devices.
| [1] |
K. Walters, Non-newtonian effects in some elastic-viscous liquids whose behaviour at small rates of shear is characterized by a general linear equation of state, Quart. J. Mech. Appl. Math., 15 (1962), 63-76. https://doi.org/10.1093/qjmam/15.1.63 doi: 10.1093/qjmam/15.1.63
|
| [2] |
M. M. Nandeppanavar, M. S. Abel, J. Tawade, Heat transfer in a Walter's liquid B fluid over an impermeable stretching sheet with non-uniform heat source/sink and elastic deformation, Commun. Nonlinear Sci. Numer. Simul., 15 (2010), 1791-1802. https://doi.org/10.1016/j.cnsns.2009.07.009 doi: 10.1016/j.cnsns.2009.07.009
|
| [3] | S. Nadeem, R. Mehmood, S. S. Motsa, Numerical investigation on MHD oblique flow of a Walter's B type nano fluid over a convective surface, Int. J. Therm. Sci., 92 (2015), 162-172. https://doi.org/10.1016/j.ijthermalsci.2015.01.034 |
| [4] |
T. Hayat, S. Qayyum, M. Imtiaz, A. Alsaedi, Radiative Falkner-Skan flow of Walter-B fluid with prescribed surface heat flux, J. Theor. Appl. Mech., 55 (2017), 117-127. https://doi.org/10.15632/jtam-pl.55.1.117 doi: 10.15632/jtam-pl.55.1.117
|
| [5] |
A. Majeed, T. Javed, S. Shami, Numerical analysis of Walters-B fluid flow and heat transfer over a stretching cylinder, Can. J. Phys., 94 (2016), 522-530. https://doi.org/10.1139/cjp-2015-0511 doi: 10.1139/cjp-2015-0511
|
| [6] |
T. Hayat, S. Asad, M. Mustafa, H. H. Alsulami, Heat transfer analysis in the flow of Walters' B fluid with a convective boundary condition, Chinese Phys. B, 23 (2014), 084701. https://doi.org/10.1088/1674-1056/23/8/084701 doi: 10.1088/1674-1056/23/8/084701
|
| [7] | M. Ijaz, M. Yousaf, A. M. El Shafey, Arrhenius activation energy and Joule heating for Walter-B fluid with Cattaneo-Christov double-diffusion model, J. Therm. Anal. Calorim., 143 (2021), 3687-3698. https://doi.org/10.1007/s10973-020-09270-1 |
| [8] |
K. Loganathan, N. Nithyadevi, P. Boopathi, K. Mohana, Inquiry of inclined magnetic field effects on Walter-B nanofluid flow with heat generation/absorption, IOP Conf. Ser.: Mater. Sci. Eng., 872 (2020), 012097. https://doi.org/10.1088/1757-899X/872/1/012097 doi: 10.1088/1757-899X/872/1/012097
|
| [9] | M. Mueller, O. A. Igbokwe, B. Walter, C. L. Pederson, S. Riechelmann, D. K. Richter, et al., Testing the preservation potential of early diagenetic dolomites as geochemical archives, Sedimentology, 67 (2020), 849-881. https://doi.org/10.1111/sed.12664 |
| [10] | B. Meier, A. Schmidt, N. Glaser, A. Meining, B. Walter, A. Wannhoff, et al., Endoscopic full-thickness resection of gastric subepithelial tumors with the gFTRD-system: A prospective pilot study (RESET trial), Surg. Endosc., 34 (2020), 853-860. https://doi.org/10.1007/s00464-019-06839-2 |
| [11] | S. U. S. Choi, J. A. Eastman, Enhancing thermal conductivity of fluids with nanoparticles, ASME Pub Fed., 231 (1995), 99-106. |
| [12] |
J. Buongiorno, Convective transport in nanofuids, J. Heat Transfer, 128 (2006), 240-250. https://doi.org/10.1115/1.2150834 doi: 10.1115/1.2150834
|
| [13] |
K. L. Hsiao, Stagnation electrical MHD nanofuid mixed convection with slip boundary on a stretching sheet, Appl. Therm. Eng., 98 (2016), 850-861. https://doi.org/10.1016/j.applthermaleng.2015.12.138 doi: 10.1016/j.applthermaleng.2015.12.138
|
| [14] |
M. M. Rashidi, N. Freidoonimehr, A. Hosseini, O. A. Beg, T. K. Hung, Homotopy simulation of nanofuid dynamics from a non-linearly stretching isothermal permeable sheet with transpiration, Meccanica, 49 (2014), 469-482. https://doi.org/10.1007/s11012-013-9805-9 doi: 10.1007/s11012-013-9805-9
|
| [15] |
M. Sheikholeslami, M. M. Bhatti, Forced convection of nanofluid in presence of constant magnetic field considering shape effects of nanoparticles, Int. J. Heat Mass Tran., 111 (2017), 1039-1049. https://doi.org/10.1016/j.ijheatmasstransfer.2017.04.070 doi: 10.1016/j.ijheatmasstransfer.2017.04.070
|
| [16] |
M. Turkyilmazoglu, Condensation of laminar film over curved vertical walls using single and two-phase nanofluid models, Eur. J. Mech.-B/Fluids, 65 (2017), 184-191. https://doi.org/10.1016/j.euromechflu.2017.04.007 doi: 10.1016/j.euromechflu.2017.04.007
|
| [17] | R. Ellahi, Recent developments of nanofluids, MDPI-Multidisciplinary Digital Publishing Institute, 2018. https://doi.org/10.3390/books978-3-03842-834-3 |
| [18] | A. Pantokratoras, Discussion: "Computational analysis for mixed convective flows of viscous fluids with nanoparticles"(Farooq, U., Lu, DC, Ahmed, S., and Ramzan, M., 2019, ASME J. Therm. Sci. Eng. Appl., 11(2), p. 021013), J. Thermal. Sci. Eng. Appl., 11 (2019), 055503. https://doi.org/10.1115/1.4043092 |
| [19] |
M. Rashid, A. Alsaedi, T. Hayat, B. Ahmed, Magnetohydrodynamic flow of Maxwell nanofluid with binary chemical reaction and Arrhenius activation energy, Appl. Nanosci., 10 (2020), 2951-2963. https://doi.org/10.1007/s13204-019-01143-w doi: 10.1007/s13204-019-01143-w
|
| [20] |
T. Tayebi, A. J. Chamkha, Magnetohydrodynamic natural convection heat transfer of hybrid nanofluid in a square enclosure in the presence of a wavy circular conductive cylinder, J. Therm. Sci. Eng. Appl., 12 (2020), 031009. https://doi.org/10.1115/1.4044857 doi: 10.1115/1.4044857
|
| [21] |
T. Hayat, R. Riaz, A. Aziz, A. Alsaedi, Influence of Arrhenius activation energy in MHD flow of third grade nanofluid over a nonlinear stretching surface with convective heat and mass conditions, Physica A, 549 (2020), 124006. https://doi.org/10.1016/j.physa.2019.124006 doi: 10.1016/j.physa.2019.124006
|
| [22] |
T. Muhammad, H. Waqas, S. A. Khan, R. Ellahi, S. M. Sait, Significance of nonlinear thermal radiation in 3D Eyring-Powell nanofluid flow with Arrhenius activation energy, J. Therm. Anal. Calorim., 143 (2021), 929-944. https://doi.org/10.1007/s10973-020-09459-4 doi: 10.1007/s10973-020-09459-4
|
| [23] |
S. Z. Alamri, R. Ellahi, N. Shehzad, A. Zeeshan, Convective radiative plane Poiseuille flow of nanofluid through porous medium with slip: An application of Stefan blowing, J. Mol. Liq., 273 (2019), 292-304. https://doi.org/10.1016/j.molliq.2018.10.038 doi: 10.1016/j.molliq.2018.10.038
|
| [24] |
I. Khan, A. Hussain, M. Y. Malik, S. Mukhtar, On magnetohydrodynamics Prandtl fluid flow in the presence of stratification and heat generation, Physica A, 540 (2020), 123008. https://doi.org/10.1016/j.physa.2019.123008 doi: 10.1016/j.physa.2019.123008
|
| [25] |
S. E. Awan, M. A. Z. Raja, A. Mehmood, S. A. Niazi, S. Siddiqa, Numerical treatments to analyze the nonlinear radiative heat transfer in MHD nanofluid flow with solar energy, Arab. J. Sci. Eng., 45 (2020), 4975-4994. https://doi.org/10.1007/s13369-020-04593-5 doi: 10.1007/s13369-020-04593-5
|
| [26] | A. Gailitis, O. Lielausis, On a possibility to reduce the hydrodynamic resistance of a plate in an electrolyte, Appl. Magnetohydrodynamics Rep. Inst. Riga, 13 (1961), 143-146. |
| [27] |
R. Ahmad, M. Mustafa, M. Turkyilmazoglu, Buoyancy effects on nanofluid flow past a convectively heated vertical Riga-plate: A numerical study, Int. J. Heat Mass Tran., 111 (2017), 827-835. https://doi.org/10.1016/j.ijheatmasstransfer.2017.04.046 doi: 10.1016/j.ijheatmasstransfer.2017.04.046
|
| [28] |
Z. Iqbal, Z. Mehmood, E. Azhar, E. N. Maraj, Numerical investigation of nanofluid transport of gyrotactic microorganisms submerged in water towards Riga plate, J. Mol. Liq., 234 (2017), 296-308. https://doi.org/10.1016/j.molliq.2017.03.074 doi: 10.1016/j.molliq.2017.03.074
|
| [29] |
R. Ellahi, M. Hassan, A. Zeeshan, Aggregation effects on water base Al2O3-nanofluid over permeable wedge in mixed convection, Asia‐Pac. J. Chem. Eng., 11 (2016), 179-186. https://doi.org/10.1002/apj.1954 doi: 10.1002/apj.1954
|
| [30] |
R. M. Kasmani, S. Sivasankaran, M. Bhuvaneswari, Z. Siri, Effect of chemical reaction on convective heat transfer of boundary layer flow in nanofluid over a wedge with heat generation/absorption and suction, J. Appl. Fluid Mech., 9 (2015), 379-388. https://doi.org/10.18869/acadpub.jafm.68.224.24151 doi: 10.18869/acadpub.jafm.68.224.24151
|
| [31] |
M. Khan, M. Azam, A. S. Alshomrani, Effects of melting and heat generation/absorption on unsteady Falkner-Skan flow of Carreau nanofluid over a wedge, Int. J. Heat Mass Tran., 110 (2017), 437-446. https://doi.org/10.1016/j.ijheatmasstransfer.2017.03.037 doi: 10.1016/j.ijheatmasstransfer.2017.03.037
|
| [32] |
A. K. Pandey, M. Kumar, Chemical reaction and thermal radiation effects on a boundary layer flow of nanofluid over a wedge with viscous and Ohmic dissipation, St. Petersburg Polytechnical Univ. J.: Phys. Math., 3 (2017), 322-332. https://doi.org/10.1016/j.spjpm.2017.10.008 doi: 10.1016/j.spjpm.2017.10.008
|
| [33] |
M. Khan, M. Azam, A. S. Alshomrani, Unsteady slip flow of Carreau nanofluid over a wedge with nonlinear radiation and new mass flux condition, Res. Phys., 7 (2017), 2261-2270. https://doi.org/10.1016/j.rinp.2017.06.038 doi: 10.1016/j.rinp.2017.06.038
|
| [34] |
A. Chamkha, S. Abbasbandy, A. M. Rashad, Non-Darcy natural convection flow for non-Newtonian nanofluid over cone saturated in porous medium with uniform heat and volume fraction fluxes, Int. J. Numer. Method. Heat Fluid Flow, 25 (2015), 422-437. https://doi.org/10.1108/HFF-02-2014-0027 doi: 10.1108/HFF-02-2014-0027
|
| [35] |
M. Macha, N. Kishan, Boundary layer flow of viscoelastic nanofluid over a wedge in the presence of buoyancy force effects, Comput. Therm. Sci.: An Int. J., 9 (2017), 257-267. https://doi.org/10.1615/ComputThermalScien.2017016742 doi: 10.1615/ComputThermalScien.2017016742
|
| [36] |
A. V. Kuznetsov, Thermo bioconvection in a suspension of oxytactic bacteria, Int. Commun. Heat Mass Tran., 32 (2005), 991-999. https://doi.org/10.1016/j.icheatmasstransfer.2004.11.005 doi: 10.1016/j.icheatmasstransfer.2004.11.005
|
| [37] |
Y. R. Li, H. Waqas, M. Imran, U. Farooq, F. Mallawi, I. Tlili, A numerical exploration of modified second-grade nanofluid with motile microorganisms, thermal radiation, and Wu's slip, Symmetry, 12 (2020), 393. https://doi.org/10.3390/sym12030393 doi: 10.3390/sym12030393
|
| [38] |
T. Muhammad, S. Z. Alamri, H. Waqas, D. Habib, R. Ellahi, Bioconvection flow of magnetized Carreau nanofluid under the influence of slip over a wedge with motile microorganisms, J. Therm. Anal. Calorim., 143 (2021), 945-957. https://doi.org/10.1007/s10973-020-09580-4 doi: 10.1007/s10973-020-09580-4
|
| [39] |
S. U. Khan, H. Waqas, M. M. Bhatti, M. Imran, Bioconvection in the rheology of magnetized couple stress nanofluid featuring activation energy and Wu's slip, J. Non-Equil. Thermody., 45 (2020), 81-95. https://doi.org/10.1515/jnet-2019-0049 doi: 10.1515/jnet-2019-0049
|
| [40] |
T. P. Zhang, S. U. Khan, M. Imran, I. Tlili, H. Waqas, N. Ali, Activation energy and thermal radiation aspects in bioconvection flow of rate type nanoparticles configured by a stretching/shrinking disk, J. Energy Resour. Technol., 142 (2020), 112102. https://doi.org/10.1115/1.4047249 doi: 10.1115/1.4047249
|
| [41] |
H. Waqas, M. Imran, T. Muhammad, S. M. Sait, R. Ellahi, Numerical investigation on bioconvection flow of Oldroyd-B nanofluid with nonlinear thermal radiation and motile microorganisms over rotating disk, J. Therm. Analy. Calorim., 145 (2021), 523-539. https://doi.org/10.1007/s10973-020-09728-2 doi: 10.1007/s10973-020-09728-2
|
| [42] |
N. S. Khan, Q. Shah, A. Bhaumik, P. Kumam, P. Thounthong, I. Amiri, Entropy generation in bioconvection nanofluid flow between two stretchable rotating disks, Sci. Rep., 10 (2020), 4448. https://doi.org/10.1038/s41598-020-61172-2 doi: 10.1038/s41598-020-61172-2
|
| [43] |
S. U. Mamatha, K. R. Babu, P. D. Prasad, C. S. K. Raju, S. V. K. Varma, Mass transfer analysis of two-phase flow in a suspension of microorganisms, Arch. Thermodyn., 41 (2020), 175-192. https://doi.org/10.24425/ather.2020.132954 doi: 10.24425/ather.2020.132954
|
| [44] |
M. Ferdows, M. G. Reddy, F. Alzahrani, S. Y. Sun, Heat and mass transfer in a viscous nanofluid containing a gyrotactic micro-organism over a stretching cylinder, Symmetry, 11 (2019), 1131. https://doi.org/10.3390/sym11091131 doi: 10.3390/sym11091131
|
| [45] |
N. A. Amirsom, M. J. Uddin, M. F. M. Basir, A. Ismail, O. A. Beg, A. Kadir, Three-dimensional bioconvection nanofluid flow from a bi-axial stretching sheet with anisotropic slip, Sains Malays., 48 (2019), 1137-1149. http://doi.org/10.17576/jsm-2019-4805-23 doi: 10.17576/jsm-2019-4805-23
|
| [46] |
S. Kasaragadda, I. M. Alarifi, M. Rahimi-Gorji, R. Asmatulu, Investigating the effects of surface superhydrophobicity on moisture ingression of nanofiber-reinforced bio-composite structures, Microsyst. Technol., 26 (2020), 447-459. https://doi.org/10.1007/s00542-019-04507-y doi: 10.1007/s00542-019-04507-y
|
| [47] |
M. S. Ansari, O. Otegbeye, M. Trivedi, S. P. Goqo, Magnetohydrodynamic bio-convective Casson nanofluid flow: A numerical simulation by paired quasilinearisation, J. Appl. Comput. Mech., 7 (2021), 2024-2039. https://doi.org/10.22055/JACM.2020.31205.1839 doi: 10.22055/JACM.2020.31205.1839
|
| [48] |
M. S. Alqarni, S. Yasmin, H. Waqas, S. A. Khan, Recent progress in melting heat phenomenon for bioconvection transport of nanofluid through a lubricated surface with swimming microorganisms, Sci. Rep., 12 (2022), 8447. https://doi.org/10.1038/s41598-022-12230-4 doi: 10.1038/s41598-022-12230-4
|
| [49] |
S. M. H. Zadeh, S. A. M. Mehryan, M. A. Sheremet, M. Izadi, M. Ghodrat, Numerical study of mixed bio-convection associated with a micropolar fluid, Therm. Sci. Eng. Prog., 18 (2020), 100539. https://doi.org/10.1016/j.tsep.2020.100539 doi: 10.1016/j.tsep.2020.100539
|
| [50] |
M. M. Bhatti, E. E. Michaelides, Study of Arrhenius activation energy on the thermo-bioconvection nanofluid flow over a Riga plate, J. Therm. Anal. Calorim., 143 (2021), 2029-2038. https://doi.org/10.1007/s10973-020-09492-3 doi: 10.1007/s10973-020-09492-3
|
| [51] |
H. Waqas, S. U. Khan, M. Imran, M. M. Bhatti, Thermally developed Falkner-Skan bioconvection flow of a magnetized nanofluid in the presence of a motile gyrotactic microorganism: Buongiorno's nanofluid model, Phys. Scr., 94 (2019), 115304. https://doi.org/10.1088/1402-4896/ab2ddc doi: 10.1088/1402-4896/ab2ddc
|
| [52] |
A. M. Alwatban, S. U. Khan, H. Waqas, I. Tlili, Interaction of Wu's slip features in bioconvection of Eyring Powell nanoparticles with activation energy, Processes, 7 (2019), 859. https://doi.org/10.3390/pr7110859 doi: 10.3390/pr7110859
|
| [53] |
Y. Wang, H. Waqas, M. Tahir, M. Imran, C. Y. Jung, Effective Prandtl aspects on bio-convective thermally developed magnetized tangent hyperbolic nanoliquid with Gyrotactic microorganisms and second order velocity slip, IEEE Access, 7 (2019), 130008-130023. https://doi.org/10.1109/ACCESS.2019.2940203 doi: 10.1109/ACCESS.2019.2940203
|
| [54] |
M. Z. Ullah, T. S. Jang, An efficient numerical scheme for analyzing bioconvection in von-Kármán flow of third-grade nanofluid with motile microorganisms, Alex. Eng. J., 59 (2020), 2739-2752. https://doi.org/10.1016/j.aej.2020.05.017 doi: 10.1016/j.aej.2020.05.017
|
| [55] |
A. S. Alshomrani, M. Z. Ullah, D. Baleanu, Importance of multiple slips on bioconvection flow of cross nanofluid past a wedge with gyrotactic motile microorganisms, Case Stud. Therm. Eng., 22 (2020), 100798. https://doi.org/10.1016/j.csite.2020.100798 doi: 10.1016/j.csite.2020.100798
|
| [56] |
A. Shafiq, Z. Hammouch, A. Turab, Impact of radiation in a stagnation point flow of Walters' B fluid towards a Riga plate, Therm. Sci. Eng. Prog., 6 (2018), 27-33. https://doi.org/10.1016/j.tsep.2017.11.005 doi: 10.1016/j.tsep.2017.11.005
|
| [57] |
M. M. Peiravi, J. Alinejad, D. Ganji, S. Maddah, Numerical study of fins arrangement and nanofluids effects on three-dimensional natural convection in the cubical enclosure, Chall. Nano Micro Scale Sci. Technol., 7 (2019), 97-112. https://doi.org/10.22111/tpnms.2019.4845 doi: 10.22111/tpnms.2019.4845
|
| [58] | M. M. Peiravi, J. Alinejad, Hybrid conduction, convection and radiation heat transfer simulation in a channel with rectangular cylinder, J. Therm. Anal. Calorim., 140 (2020), 2733-2747. https://doi.org/10.1007/s10973-019-09010-0 |
| [59] |
J. Alinejad, M. M. Peiravi, Numerical analysis of secondary droplets characteristics due to drop impacting on 3D cylinders considering dynamic contact angle, Meccanica, 55 (2020), 1975-2002. https://doi.org/10.1007/s11012-020-01240-z doi: 10.1007/s11012-020-01240-z
|
| [60] |
M. M. Peiravi, J. Alinejad, D. D. Ganji, S. Maddah, 3D optimization of baffle arrangement in a multi-phase nanofluid natural convection based on numerical simulation, Int. J. Numer. Method. Heat Fluid Flow, 30 (2020), 2583-2605. https://doi.org/10.1108/HFF-01-2019-0012 doi: 10.1108/HFF-01-2019-0012
|
| [61] |
M. M. Peiravi, J. Alinejad, Nano particles distribution characteristics in multi-phase heat transfer between 3D cubical enclosures mounted obstacles, Alex. Eng. J., 60 (2021), 5025-5038. https://doi.org/10.1016/j.aej.2021.04.013 doi: 10.1016/j.aej.2021.04.013
|
| [62] |
J. K. Madhukesh, A. Alhadhrami, R. N. Kumar, R. J. P. Gowda, B. C. Prasannakumara, R. S. V. Kumar, Physical insights into the heat and mass transfer in Casson hybrid nanofluid flow induced by a Riga plate with thermophoretic particle deposition, P. I. Mech. Eng. Part E: J. Proc. Mech. Eng., 2021, https://doi.org/10.1177/09544089211039305 doi: 10.1177/09544089211039305
|
| [63] |
J. K. Madhukesh, R. S. V. Kumar, R. J. P. Gowda, B. C. Prasannakumara, S. A. Shehzad, Thermophoretic particle deposition and heat generation analysis of Newtonian nanofluid flow through magnetized Riga plate, Heat Transf., 51 (2022), 3082-3098. https://doi.org/10.1002/htj.22438 doi: 10.1002/htj.22438
|
| [64] |
R. J. P. Gowda, R. N. Kumar, A. M. Jyothi, B. C. Prasannakumara, I. E. Sarris, Impact of binary chemical reaction and activation energy on heat and mass transfer of Marangoni driven boundary layer flow of a non-Newtonian nanofluid, Processes, 9 (2021), 702. https://doi.org/10.3390/pr9040702 doi: 10.3390/pr9040702
|
| [65] |
A. M. Jyothi, R. N. Kumar, R. J. P. Gowda, Y. Veeranna, B. C. Prasannakumara, Impact of activation energy and gyrotactic microorganisms on flow of Casson hybrid nanofluid over a rotating moving disk, Heat Transf., 50 (2021), 5380-5399. https://doi.org/10.1002/htj.22129 doi: 10.1002/htj.22129
|
| [66] |
B. Shaker, M. Gholinia, M. Pourfallah, D. D. Ganji, CFD analysis of Al2O3-syltherm oil Nanofluid on parabolic trough solar collector with a new flange-shaped turbulator model, Theor. Appl. Mech. Lett., 12 (2022), 100323. https://doi.org/10.1016/j.taml.2022.100323 doi: 10.1016/j.taml.2022.100323
|
| [67] |
F. H. Sani, M. Pourfallah, M. Gholinia, The effect of MoS2-Ag/H2O hybrid nanofluid on improving the performance of a solar collector by placing wavy strips in the absorber tube, Case Stud. Therm. Eng., 30 (2022), 101760. https://doi.org/10.1016/j.csite.2022.101760 doi: 10.1016/j.csite.2022.101760
|
| [68] |
A. H. Ghobadi, M. G. Hassankolaei, A numerical approach for MHD Al2O3-TiO2/H2O hybrid nanofluids over a stretching cylinder under the impact of shape factor, Heat Transf., 48 (2019), 4262-4282. https://doi.org/10.1002/htj.21591 doi: 10.1002/htj.21591
|
| [69] |
S. Shahlaei, M. G. Hassankolaei, MHD boundary layer of GO-H2O nanoliquid flow upon stretching plate with considering nonlinear thermal ray and Joule heating effect, Heat Transf., 48 (2019), 4152-4173. https://doi.org/10.1002/htj.21586 doi: 10.1002/htj.21586
|
| [70] |
A. H. Ghobadi, M. G. Hassankolaei, Numerical treatment of magneto Carreau nanofluid over a stretching sheet considering Joule heating impact and nonlinear thermal ray, Heat Transf., 48 (2019), 4133-4151. https://doi.org/10.1002/htj.21585 doi: 10.1002/htj.21585
|
Figures(5) / Tables(5)
M. S. Alqarni. Thermo-bioconvection flow of Walter's B nanofluid over a Riga plate involving swimming motile microorganisms[J]. AIMS Mathematics, 2022, 7(9): 16231-16248. doi: 10.3934/math.2022886
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