Araştırma Makalesi
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Yıl 2023, Cilt: 7 Sayı: 1, 61 - 81, 31.03.2023
https://doi.org/10.31197/atnaa.1187342

Öz

Kaynakça

  • [1] L. Liu, L. Feng, Q. Xu, L. Zheng and F. Liu, Flow and heat transfer of generalized Maxwell fluid over a moving plate with distributed order time fractional constitutive models, Int. Commun. Heat Mass Transf., 116 (2020) 104-679.
  • [2] S. Yang, L. Liu, Z. Long and L. Feng, Unsteady natural convection boundary layer flow and heat transfer past a vertical flat plate with novel constitution models, Appl. Math. Lett., 120 (2021) 107-335.
  • [3] S.U. Choi and J.A. Eastman, Enhancing thermal conductivity of fluids with nanoparticles, Argonne National Lab, (1995).
  • [4] B. Mahanthesh, Flow and heat transport of nanomaterial with quadratic radiative heat flux and aggregation kinematics of nanoparticles, Int. Commun. Heat Mass Transf., 127 (2021) 105-521.
  • [5] P. Rana, B. Mahanthesh, J. Mackolil and W. Al-Kouz, Nanofluid flow past a vertical plate with nanoparticle aggregation kinematics, thermal slip and significant buoyancy force effects using modified Buongiorno model, Waves in Random and Complex Media, (2021) 1-25.
  • [6] K. Swain and B. Mahanthesh, Thermal enhancement of radiating magneto-nanoliquid with nanoparticles aggregation and joule heating: a three-dimensional flow, Arab J. Sci. Eng., 46(6) (2021) 5865-5873.
  • [7] B. Mahanthesh, B.J. Gireesha, R. Gorla, F.M. Abbasi and S.A. Shehzad, Numerical solutions for magnetohydrodynamic flow of nanofluid over a bidirectional non-linear stretching surface with prescribed surface heat flux boundary, J. Magn. Magn., 417 (2016) 189-196.
  • [8] A.S. Sabu, J. Mackolil, B. Mahanthesh and A. Mathew, Nanoparticle aggregation kinematics on the quadratic convective magnetohydrodynamic flow of nanomaterial past an inclined flat plate with sensitivity analysis, P I MECH. ENG. E-J PRO., (2021).
  • [9] F. Ahmed, M.A. Abir, M. Fuad, F. Akter, P.K. Bhowmik, S.B. Alam and D. Kumar, Numerical investigation of the thermo-hydraulic performance of water-based nanofluids in a dimpled channel flow using Al2O3, CuO, and hybrid Al2O3 CuO as nanoparticles, J. Heat Transfer, 50(5) (2021) 5080-5105.
  • [10] P.S. Reddy and P. Sreedevi, Effect of thermal radiation and volume fraction on carbon nanotubes based nanofluid flow inside a square chamber, Alex. Eng. J., 60(1) (2021) 1807-1817.
  • [11] Z. Ahmed, S. Saleem, S. Nadeem and A.U. Khan, Squeezing flow of Carbon nanotubes-based nanofluid in channel consid- ering temperature-dependent viscosity: a numerical approach, Arab. J. Sci. Eng., 46(3) (2021) 2047-2053.
  • [12] T. Gul, M. Bilal, W. Alghamdi, M.I. Asjad and T. Abdeljawad, Hybrid nanofluid flow within the conical gap between the cone and the surface of a rotating disk, Sci. Rep., 11(1) (2021) 1-19.
  • [13] I. Zari, A. Shafiq, T.S. Khan and S. Haq, Marangoni Convective Flow of GO-kerosene-and GO-water-based Casson Nano- liquid Toward a Penetrable Riga Surface, Braz. J. Phys., (2021) 1-16.
  • [14] T. Gul, B. Ali, W. Alghamdi, S. Nasir, A. Saeed, P. Kumam and M. Jawad, Mixed convection stagnation point flow of the blood based hybrid nanofluid around a rotating sphere, Sci. Rep., 11(1) (2021) 1-15.
  • [15] M.I. Khan, Transportation of hybrid nanoparticles in forced convective Darcy-Forchheimer flow by a rotating disk, Int. Commun. Heat Mass Transf., 122 (2021) 105-177.
  • [16] D.R.V.S.R.K. Sastry, A.S.N. Murti and T.P. Kantha, The effect of heat transfer on MHD Marangoni boundary layer flow past a flat plate in nanofluid, Int. J. Eng. Math., (2013).
  • [17] D.R.V.S.R.K. Sastry, Thermosolutal MHD marangoni convective flow of a nanofluid past a flat plate with viscous dissipation and radiation effects, WSEAS Trans. Math., 15 (2016) 271-279.
  • [18] D.R.V.S.R.K. Sastry, P.K. Kameswaran, P. Sibanda and P. Sudhagar, Soret and Dufour Effects on Hydromagnetic Marangoni Convection Boundary Layer Nanofluid Flow Past a Flat Plate, Appl. Math. Comput., (2019) 439-449.
  • [19] D.R.V.S.R.K. Sastry and P.K. Kameswaran, MHD and Viscous Dissipation Effects in Marangoni Mixed Flow of a Nanofluid over an Inclined Plate in the Presence of Ohmic Heating, Fluid Dyn. Mater. Proce., 17 (2021).
  • [20] T. Gul, M.Z. Ullah, A.K. Alzahrani, Z. Zaheer and I.S. Amiri, MHD thin film flow of kerosene oil based CNTs nano?uid under the Influence of Marangoni convection, Phys. Scr., 95(1) (2020) 15-702.
  • [21] Y. Zhang, Y. Zhang, Y. Bai, B. Yuan and L. Zheng, Flow and heat transfer analysis of a maxwell-power-law fluid film with forced thermal Marangoni convective, Int. Commun. Heat Mass Transf., 121 (2021) 105-162.
  • [22] T. Gul, H. Anwar, M.A. Khan, I. Khan and P. Kumam, Integer and non-integer order study of the GO-W/GO-EG nanofluids flow by means of Marangoni convection, Symmetry, 11(5) (2019) 640.
  • [23] S. Qayyum, Dynamics of Marangoni convection in hybrid nanofluid flow submerged in ethylene glycol and water base ?uids, Int. Commun. Heat Mass Transf., 119 (2020) 104-962.
  • [24] A. Gailitis, On the possibility to reduce the hydrodynamic drag of a plate in an electrolyte, Rep. Inst. Phys. Riga 13 (1961) 143-146.
  • [25] H. Vaidya, K.V. Prasad, I. Tlili, O.D. Makinde, C. Rajashekhar, S.U. Khan and D.L. Mahendra, Mixed convective nanofluid flow over a non linearly stretched Riga plate, Case Stud. Therm. Eng., 24 (2021) 100-828.
  • [26] N.S. Khashi'ie, N.M. Arifin, I. Pop and N.S. Wahid, Effect of suction on the stagnation point flow of hybrid nanofluid toward a permeable and vertical Riga plate, Heat Trans., 50(2) (2021) 1895-1910.
  • [27] M. Nazeer, M.I. Khan, M.U. Rafiq and N.B. Khan, Numerical and scale analysis of Eyring-Powell nanofluid towards a magnetized stretched Riga surface with entropy generation and internal resistance, I. Commun. Heat and Mass Trans., 119 (2020) 104-968.
  • [28] M.M. Bhatti and E.E. Michaelides, Study of Arrhenius activation energy on the thermo-bioconvection nanofluid flow over a Riga plate, J. Therm. Anal. Calorim. 143(3) (2021) 2029-2038.
  • [29] Z. Iqbal, E. Azhar, Z. Mehmood and E.N. Maraj, Melting heat transport of nanofluidic problem over a Riga plate with erratic thickness: use of Keller Box scheme, Results Phys. 7 (2017) 3648-3658.
  • [30] S. Nadeem, N. Abbas and M.Y. Malik, Heat transport in CNTs based nanomaterial flow of non-Newtonian fluid having electro magnetize plate, Alex. Eng. J., 59(5) (2020) 3431-3442.
  • [31] F.O.M. Mallawi, M. Bhuvaneswari, S. Sivasankaran and S. Eswaramoorthi, Impact of double-stratification on convective flow of a non-Newtonian liquid in a Riga plate with Cattaneo-Christov double-flux and thermal radiation, Ain Shams Eng. J., 12(1) (2021) 969-981.
  • [32] B. Ali, P.K. Pattnaik, R.A. Naqvi, H. Waqas and S. Hussain, Brownian motion and thermophoresis effects on bioconvection of rotating Maxwell nanofluid over a Riga plate with Arrhenius activation energy and Cattaneo-Christov heat flux theory, Therm. Sci. Eng. Prog., 23 (2021) 100-863.
  • [33] J.K. Madhukesh, G.K. Ramesh, E.H. Aly and A.J. Chamkha, Dynamics of water conveying SWCNT nanoparticles and swimming microorganisms over a Riga plate subject to heat source/sink, Alex. Eng. J., (2021).
  • [34] L. Noeiaghdam, S. Noeiaghdam and D. Sidorov, Dynamical control on the homotopy analysis method for solving nonlinear shallow water wave equation, J. Phys., 1847(1) (2021) 100-112.
  • [35] B.M. Yambiyo, F. Norouzi and G.M. Guerekata, A study of an epidemic SIR model via Homotopy Analysis Method in the sense of Caputo-fractional system, Stud. Evol. Eqs. STEAM-H series, (2021).
  • [36] H. Chen and Y. Wang, Homotopy Analysis Method for a Conservative Nonlinear Oscillator with Fractional Power, J. Appl. Math. Phys., 9(1) (2021) 31.
  • [37] C.L. Ejikeme, M.O. Oyesanya, D.F. Agbebaku and M.B. Okofu, Discussing a Solution to Nonlinear Duffing Oscillator with Fractional Derivatives Using Homotopy Analysis Method (HAM), T. Prac. Math. Comp. Sci., 6 (2021) 57-81.
  • [38] Z. Odibat and A. Sami Bataineh, An adaptation of homotopy analysis method for reliable treatment of strongly nonlinear problems: construction of homotopy polynomials, Mathemat. Methods Appl. Sci., 38(5) (2015) 991-1000.
  • [39] K. Hosseini, K. Sadri, M. Mirzazadeh, A. Ahmadian, Y.M. Chu and S. Salahshour, Reliable methods to look for analytical and numerical solutions of a nonlinear differential equation arising in heat transfer with the conformable derivative, Mathemat. Methods Appl. Sci., (2021).
  • [40] S. Chaudhary and K.M. Kanika, Radiation heat transfer on SWCNT and MWCNT based magnetohydrodynamic nanofluid flow with marangoni convection, Physica Scripta 95(2) (2019).
  • [41] I. Zari, A. Shafiq and T.S. Khan, Simulation study of Marangoni convective flow of kerosene oil based nanofluid driven by a porous surface with suction and injection, I. Communs. Heat and Mass Trans., 127 (2021) 105-493.
  • [42] I. Zari, A. Shafiq, G. Rasool, T.N. Sindhu and T.S. Khan, Double-stratified Marangoni boundary layer flow of Casson nanoliquid: probable error application, J. Thermal Analy. Calorimetry, 147(12) (2022) 6913-6929.
  • [43] A. Shafiq, I. Zari, I. Khan, T.S. Khan, A.H. Seikh and E.S.M. Sherif, Marangoni driven boundary layer flow of carbon nanotubes toward a Riga plate, Front. Phys., 7 (2020) 215.
  • [44] C.L. Ejikeme, M.O. Oyesanya, D.F. Agbebaku and M.B. Okofu, Discussing a Solution to Nonlinear Duffing Oscillator with Fractional Derivatives Using Homotopy Analysis Method (HAM), T. P. Math. Comp. Sci., 6 (2021) 57-81.
  • [45] H. Singh, Analysis of drug treatment of the fractional HIV infection model of CD4+ T-cells, Chaos, Sols. Fra., 146 (2021) 110-868.
  • [46] L. Noeiaghdam, S. Noeiaghdam and D. Sidorov, Dynamical control on the homotopy analysis method for solving nonlinear shallow water wave equation, I.J.Phys., 1847(1) (2021).
  • [47] Y. Chen, S. Dong, Z. Zang, C. Ao, H. Liu, M. Gao and J. Cao, Buckling analysis of subsea pipeline with idealized corrosion defects using homotopy analysis method, Ocean Eng., (2021) 108-865.
  • [48] Z. Zhunussova, Nonlinear PDE as immersions, Trends in Mathematics, 2 (2015) 289-297.
  • [49] A.F.A. Elbarghthi, H.M. Yousef, D. Václav; Heat Transfer Analysis between R744 and HFOs inside Plate Heat Exchangers Entropy 24(8) (2022) 11-50.
  • [50] R.I. Khrapko, Lorentz force in the absence of charges and currents. J. Modern. Opt. 69(18) (2022) 1060-1061.
  • [51] U. Khan, A. Zaib, A. Ishak, S.A. Bakar, M. Taseer Numerical simulations of bio-convection in the stream-wise and cross-flow directions comprising nanofluid conveying motile microorganism: analysis of multiple solutions. Int. J. Comput. Methods 19(1) (2022) 32.

Heat transfer analysis of Radiative-Marangoni Convective flow in nanofluid comprising Lorentz forces and porosity effects

Yıl 2023, Cilt: 7 Sayı: 1, 61 - 81, 31.03.2023
https://doi.org/10.31197/atnaa.1187342

Öz

The present work investigates the impacts of the Lorentz forces, porosity factor, viscous dissipation and radiation in thermo-Marangoni convective flow of a nanofluids (comprising two distinct kinds of carbon nanotubes ($CNT_{s}$)), in water ($H_{2}O$). Heat transportation developed by Marangoni forces happens regularly in microgravity situations, heat pipes, and in crystal growth. Therefore, Marangoni convection is considered in the flow model. A nonlinear system is constructed utilizing these assumptions which further converted to ordinary differential equations (ODEs) by accurate similarity transformations. The homotopic scheme is utilized to compute the exact solution for the proposed system. The study reveals that higher estimations of Hartmann number and Marangoni parameter speed up the fluid velocity while the opposite behavior is noted for porosity factor. Further, the rate of heat transfer shows upward trend for the Hartmann number, Marangoni parameter, nanoparticle solid volume fraction, radiation parameter whereas a downward trend is followed by the Brinkman number and porosity factor. It is fascinating to take observe that contemporary analytical outcomes validate the superb convergence with previous investigation.

Kaynakça

  • [1] L. Liu, L. Feng, Q. Xu, L. Zheng and F. Liu, Flow and heat transfer of generalized Maxwell fluid over a moving plate with distributed order time fractional constitutive models, Int. Commun. Heat Mass Transf., 116 (2020) 104-679.
  • [2] S. Yang, L. Liu, Z. Long and L. Feng, Unsteady natural convection boundary layer flow and heat transfer past a vertical flat plate with novel constitution models, Appl. Math. Lett., 120 (2021) 107-335.
  • [3] S.U. Choi and J.A. Eastman, Enhancing thermal conductivity of fluids with nanoparticles, Argonne National Lab, (1995).
  • [4] B. Mahanthesh, Flow and heat transport of nanomaterial with quadratic radiative heat flux and aggregation kinematics of nanoparticles, Int. Commun. Heat Mass Transf., 127 (2021) 105-521.
  • [5] P. Rana, B. Mahanthesh, J. Mackolil and W. Al-Kouz, Nanofluid flow past a vertical plate with nanoparticle aggregation kinematics, thermal slip and significant buoyancy force effects using modified Buongiorno model, Waves in Random and Complex Media, (2021) 1-25.
  • [6] K. Swain and B. Mahanthesh, Thermal enhancement of radiating magneto-nanoliquid with nanoparticles aggregation and joule heating: a three-dimensional flow, Arab J. Sci. Eng., 46(6) (2021) 5865-5873.
  • [7] B. Mahanthesh, B.J. Gireesha, R. Gorla, F.M. Abbasi and S.A. Shehzad, Numerical solutions for magnetohydrodynamic flow of nanofluid over a bidirectional non-linear stretching surface with prescribed surface heat flux boundary, J. Magn. Magn., 417 (2016) 189-196.
  • [8] A.S. Sabu, J. Mackolil, B. Mahanthesh and A. Mathew, Nanoparticle aggregation kinematics on the quadratic convective magnetohydrodynamic flow of nanomaterial past an inclined flat plate with sensitivity analysis, P I MECH. ENG. E-J PRO., (2021).
  • [9] F. Ahmed, M.A. Abir, M. Fuad, F. Akter, P.K. Bhowmik, S.B. Alam and D. Kumar, Numerical investigation of the thermo-hydraulic performance of water-based nanofluids in a dimpled channel flow using Al2O3, CuO, and hybrid Al2O3 CuO as nanoparticles, J. Heat Transfer, 50(5) (2021) 5080-5105.
  • [10] P.S. Reddy and P. Sreedevi, Effect of thermal radiation and volume fraction on carbon nanotubes based nanofluid flow inside a square chamber, Alex. Eng. J., 60(1) (2021) 1807-1817.
  • [11] Z. Ahmed, S. Saleem, S. Nadeem and A.U. Khan, Squeezing flow of Carbon nanotubes-based nanofluid in channel consid- ering temperature-dependent viscosity: a numerical approach, Arab. J. Sci. Eng., 46(3) (2021) 2047-2053.
  • [12] T. Gul, M. Bilal, W. Alghamdi, M.I. Asjad and T. Abdeljawad, Hybrid nanofluid flow within the conical gap between the cone and the surface of a rotating disk, Sci. Rep., 11(1) (2021) 1-19.
  • [13] I. Zari, A. Shafiq, T.S. Khan and S. Haq, Marangoni Convective Flow of GO-kerosene-and GO-water-based Casson Nano- liquid Toward a Penetrable Riga Surface, Braz. J. Phys., (2021) 1-16.
  • [14] T. Gul, B. Ali, W. Alghamdi, S. Nasir, A. Saeed, P. Kumam and M. Jawad, Mixed convection stagnation point flow of the blood based hybrid nanofluid around a rotating sphere, Sci. Rep., 11(1) (2021) 1-15.
  • [15] M.I. Khan, Transportation of hybrid nanoparticles in forced convective Darcy-Forchheimer flow by a rotating disk, Int. Commun. Heat Mass Transf., 122 (2021) 105-177.
  • [16] D.R.V.S.R.K. Sastry, A.S.N. Murti and T.P. Kantha, The effect of heat transfer on MHD Marangoni boundary layer flow past a flat plate in nanofluid, Int. J. Eng. Math., (2013).
  • [17] D.R.V.S.R.K. Sastry, Thermosolutal MHD marangoni convective flow of a nanofluid past a flat plate with viscous dissipation and radiation effects, WSEAS Trans. Math., 15 (2016) 271-279.
  • [18] D.R.V.S.R.K. Sastry, P.K. Kameswaran, P. Sibanda and P. Sudhagar, Soret and Dufour Effects on Hydromagnetic Marangoni Convection Boundary Layer Nanofluid Flow Past a Flat Plate, Appl. Math. Comput., (2019) 439-449.
  • [19] D.R.V.S.R.K. Sastry and P.K. Kameswaran, MHD and Viscous Dissipation Effects in Marangoni Mixed Flow of a Nanofluid over an Inclined Plate in the Presence of Ohmic Heating, Fluid Dyn. Mater. Proce., 17 (2021).
  • [20] T. Gul, M.Z. Ullah, A.K. Alzahrani, Z. Zaheer and I.S. Amiri, MHD thin film flow of kerosene oil based CNTs nano?uid under the Influence of Marangoni convection, Phys. Scr., 95(1) (2020) 15-702.
  • [21] Y. Zhang, Y. Zhang, Y. Bai, B. Yuan and L. Zheng, Flow and heat transfer analysis of a maxwell-power-law fluid film with forced thermal Marangoni convective, Int. Commun. Heat Mass Transf., 121 (2021) 105-162.
  • [22] T. Gul, H. Anwar, M.A. Khan, I. Khan and P. Kumam, Integer and non-integer order study of the GO-W/GO-EG nanofluids flow by means of Marangoni convection, Symmetry, 11(5) (2019) 640.
  • [23] S. Qayyum, Dynamics of Marangoni convection in hybrid nanofluid flow submerged in ethylene glycol and water base ?uids, Int. Commun. Heat Mass Transf., 119 (2020) 104-962.
  • [24] A. Gailitis, On the possibility to reduce the hydrodynamic drag of a plate in an electrolyte, Rep. Inst. Phys. Riga 13 (1961) 143-146.
  • [25] H. Vaidya, K.V. Prasad, I. Tlili, O.D. Makinde, C. Rajashekhar, S.U. Khan and D.L. Mahendra, Mixed convective nanofluid flow over a non linearly stretched Riga plate, Case Stud. Therm. Eng., 24 (2021) 100-828.
  • [26] N.S. Khashi'ie, N.M. Arifin, I. Pop and N.S. Wahid, Effect of suction on the stagnation point flow of hybrid nanofluid toward a permeable and vertical Riga plate, Heat Trans., 50(2) (2021) 1895-1910.
  • [27] M. Nazeer, M.I. Khan, M.U. Rafiq and N.B. Khan, Numerical and scale analysis of Eyring-Powell nanofluid towards a magnetized stretched Riga surface with entropy generation and internal resistance, I. Commun. Heat and Mass Trans., 119 (2020) 104-968.
  • [28] M.M. Bhatti and E.E. Michaelides, Study of Arrhenius activation energy on the thermo-bioconvection nanofluid flow over a Riga plate, J. Therm. Anal. Calorim. 143(3) (2021) 2029-2038.
  • [29] Z. Iqbal, E. Azhar, Z. Mehmood and E.N. Maraj, Melting heat transport of nanofluidic problem over a Riga plate with erratic thickness: use of Keller Box scheme, Results Phys. 7 (2017) 3648-3658.
  • [30] S. Nadeem, N. Abbas and M.Y. Malik, Heat transport in CNTs based nanomaterial flow of non-Newtonian fluid having electro magnetize plate, Alex. Eng. J., 59(5) (2020) 3431-3442.
  • [31] F.O.M. Mallawi, M. Bhuvaneswari, S. Sivasankaran and S. Eswaramoorthi, Impact of double-stratification on convective flow of a non-Newtonian liquid in a Riga plate with Cattaneo-Christov double-flux and thermal radiation, Ain Shams Eng. J., 12(1) (2021) 969-981.
  • [32] B. Ali, P.K. Pattnaik, R.A. Naqvi, H. Waqas and S. Hussain, Brownian motion and thermophoresis effects on bioconvection of rotating Maxwell nanofluid over a Riga plate with Arrhenius activation energy and Cattaneo-Christov heat flux theory, Therm. Sci. Eng. Prog., 23 (2021) 100-863.
  • [33] J.K. Madhukesh, G.K. Ramesh, E.H. Aly and A.J. Chamkha, Dynamics of water conveying SWCNT nanoparticles and swimming microorganisms over a Riga plate subject to heat source/sink, Alex. Eng. J., (2021).
  • [34] L. Noeiaghdam, S. Noeiaghdam and D. Sidorov, Dynamical control on the homotopy analysis method for solving nonlinear shallow water wave equation, J. Phys., 1847(1) (2021) 100-112.
  • [35] B.M. Yambiyo, F. Norouzi and G.M. Guerekata, A study of an epidemic SIR model via Homotopy Analysis Method in the sense of Caputo-fractional system, Stud. Evol. Eqs. STEAM-H series, (2021).
  • [36] H. Chen and Y. Wang, Homotopy Analysis Method for a Conservative Nonlinear Oscillator with Fractional Power, J. Appl. Math. Phys., 9(1) (2021) 31.
  • [37] C.L. Ejikeme, M.O. Oyesanya, D.F. Agbebaku and M.B. Okofu, Discussing a Solution to Nonlinear Duffing Oscillator with Fractional Derivatives Using Homotopy Analysis Method (HAM), T. Prac. Math. Comp. Sci., 6 (2021) 57-81.
  • [38] Z. Odibat and A. Sami Bataineh, An adaptation of homotopy analysis method for reliable treatment of strongly nonlinear problems: construction of homotopy polynomials, Mathemat. Methods Appl. Sci., 38(5) (2015) 991-1000.
  • [39] K. Hosseini, K. Sadri, M. Mirzazadeh, A. Ahmadian, Y.M. Chu and S. Salahshour, Reliable methods to look for analytical and numerical solutions of a nonlinear differential equation arising in heat transfer with the conformable derivative, Mathemat. Methods Appl. Sci., (2021).
  • [40] S. Chaudhary and K.M. Kanika, Radiation heat transfer on SWCNT and MWCNT based magnetohydrodynamic nanofluid flow with marangoni convection, Physica Scripta 95(2) (2019).
  • [41] I. Zari, A. Shafiq and T.S. Khan, Simulation study of Marangoni convective flow of kerosene oil based nanofluid driven by a porous surface with suction and injection, I. Communs. Heat and Mass Trans., 127 (2021) 105-493.
  • [42] I. Zari, A. Shafiq, G. Rasool, T.N. Sindhu and T.S. Khan, Double-stratified Marangoni boundary layer flow of Casson nanoliquid: probable error application, J. Thermal Analy. Calorimetry, 147(12) (2022) 6913-6929.
  • [43] A. Shafiq, I. Zari, I. Khan, T.S. Khan, A.H. Seikh and E.S.M. Sherif, Marangoni driven boundary layer flow of carbon nanotubes toward a Riga plate, Front. Phys., 7 (2020) 215.
  • [44] C.L. Ejikeme, M.O. Oyesanya, D.F. Agbebaku and M.B. Okofu, Discussing a Solution to Nonlinear Duffing Oscillator with Fractional Derivatives Using Homotopy Analysis Method (HAM), T. P. Math. Comp. Sci., 6 (2021) 57-81.
  • [45] H. Singh, Analysis of drug treatment of the fractional HIV infection model of CD4+ T-cells, Chaos, Sols. Fra., 146 (2021) 110-868.
  • [46] L. Noeiaghdam, S. Noeiaghdam and D. Sidorov, Dynamical control on the homotopy analysis method for solving nonlinear shallow water wave equation, I.J.Phys., 1847(1) (2021).
  • [47] Y. Chen, S. Dong, Z. Zang, C. Ao, H. Liu, M. Gao and J. Cao, Buckling analysis of subsea pipeline with idealized corrosion defects using homotopy analysis method, Ocean Eng., (2021) 108-865.
  • [48] Z. Zhunussova, Nonlinear PDE as immersions, Trends in Mathematics, 2 (2015) 289-297.
  • [49] A.F.A. Elbarghthi, H.M. Yousef, D. Václav; Heat Transfer Analysis between R744 and HFOs inside Plate Heat Exchangers Entropy 24(8) (2022) 11-50.
  • [50] R.I. Khrapko, Lorentz force in the absence of charges and currents. J. Modern. Opt. 69(18) (2022) 1060-1061.
  • [51] U. Khan, A. Zaib, A. Ishak, S.A. Bakar, M. Taseer Numerical simulations of bio-convection in the stream-wise and cross-flow directions comprising nanofluid conveying motile microorganism: analysis of multiple solutions. Int. J. Comput. Methods 19(1) (2022) 32.
Toplam 51 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Islam Zari Bu kişi benim 0000-0003-1757-2163

Taza Gul Bu kişi benim 0000-0003-1376-8345

Karlygash Dosmagulova 0000-0001-8289-6573

Tahir Saeed Khan Bu kişi benim 0000-0001-6523-9299

Safia Haq Bu kişi benim 0000-0002-8432-252X

Yayımlanma Tarihi 31 Mart 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 7 Sayı: 1

Kaynak Göster