A modelling of bioconvective flow existing with tiny particles and quartic autocatalysis reaction across stratified upper horizontal surface of a paraboloid of revolution
Year 2023,
, 74 - 100, 31.03.2023
Nehad Ali Shah
Amos Oladele Popoola
Tosin Oreyeni
Emmanuel Omokhuale
Muhammad Muhammad Altine
Abstract
The study considers the case of the unequal diffusion coefficients of reactant $A$ (bulk fluid) and reactant $B$ (catalyst at the wall) with the dispersion of both nanoparticles and gyrotactic microorganisms of Erying-Powell fluid flow over a surface with non-uniform thickness in the presence of variable fluid properties and stratification. The numerical solution of the transformed governing equations is obtained by using the Runge-Kutta method and shooting techniques. The outcome of this study is that the increasing values of temperature-dependent thermal conductivity parameter lead to the augmentation of the kinetic energy which thereafter causes a significant enhancement of the fluid temperature.
References
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- Tamilzharasan, B.M., Karthikeyan, S., Kaabar, M.K., Yavuz, M. and Özköse, F. Magneto mixed convection of Williamson nanofluid flow through a double stratified porous medium in attendance of activation energy. Mathematical and Computational Applications, 27(3), 46, (2022).
- Jagan, K. and Sivasankaran, S. Soret & Dufour and Triple stratification effect on MHD flow with velocity slip towards a stretching cylinder. Mathematical and Computational Applications, 27(2), 25, (2022).
- Rehman, S., Anjum, A., Farooq, M., Hashim and Malik, M.Y. Melting heat phenomenon in thermally stratified fluid reservoirs (Powell-Eyring fluid) with joule heating. International Communications in Heat and Mass Transfer, 137, 106196, (2022).
- Oreyeni, T., Ramesh, K., Nayak, M.K. and Oladele, P.A. Triple stratification impacts on an inclined hydromagnetic bioconvective flow of micropolar nanofluid with exponential space-based heat generation. Waves in Random and Complex Media.
- Fayz-Al-Asad, M., Oreyeni, T., Yavuz, M. and Olanrewaju, P.O. Analytic simulation of MHD boundary layer flow of a chemically reacting upper-convected Maxwell fluid past a vertical surface subjected to double stratifications with variable properties. The European Physical Journal Plus, 137, 813, (2022).
- Khan, W.A., Anjum, N., Waqas, M., Abbas, S.Z., Irfan, M. and Muhammad, T. Impact of stratification phenomena on a nonlinear radiative flow of sutterby nanofluid. Journal of Materials Research and Technology, 15, 306-314, (2021).
- Chen, S.B., Shahmir, N., Ramzan, M., Sun, Y.L., Aly, A.A. and Malik, M.Y. Thermophoretic particle deposition in the flow of dual stratified Casson fluid with magnetic dipole and generalized Fourier’s and Fick’s laws. Case Studies in Thermal Engineering, 26, 101186, (2021).
- Dawar, A., Shah, Z., Alshehri, H. M., Islam, S. and Kumam, P. Magnetized and nonmagnetized Casson fluid flow with gyrotactic microorganisms over a stratified stretching cylinder. Scientific Reports, 11, 16376, (2021).
- Verma, A.K., Bhattacharyya, K., Rajput, S., Mandal, M.S., Chamkha, A.J. and Yadav, D. Buoyancy driven non-Newtonian Prandtl-Eyring nanofluid flow in Darcy-Forchheimer porous medium over inclined non-linear expanding sheet with double stratification. Waves in Random and Complex Media, (2022).
- Mahmood, Z., Alhazmi, S.E., Alhowaity, A., Marzouki, R., Al-Ansari, N. and Khan, U. MHD mixed convective stagnation point flow of nanofluid past a permeable stretching sheet with nanoparticles aggregation and thermal stratification. Scientific Reports, 12, 16020, (2022).
- Koriko, O.K., Shah, N.A., Saleem, S., Chung, J.D., Omowaye, A.J. and Oreyeni, T. Exploration of bioconvection flow of MHD thixotropic nanofluid past a vertical surface coexisting with both nanoparticles and gyrotactic microorganisms. Scientific Reports, 11, 16627, (2021).
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- Nadeem, S., Fuzhang, W., Alharbi, F.M., Sajid, F., Abbas, N., El-Shafay, A.S. and Al-Mubaddel, F.S. Numerical computations for Buongiorno nano fluid model on the boundary layer flow of viscoelastic fluid towards a nonlinear stretching sheet. Alexandria Engineering Journal, 61(2), 1769-1778, (2022).
- Rao, A.S., Ramaiah, K.D., Kotha, G., Rao, M.V.S. and Chamkha, A.J. A Spectral Relaxation approach for boundary layer flow of nanofluid past an exponentially stretching surface with variable suction in the presence of heat source/sink with viscous dissipation. Arabian Journal for Science and Engineering, 46, 7509-7520, (2021).
- Ur Rasheed, H., AL-Zubaidi, A., Islam, S., Saleem, S., Khan, Z. and Khan, W. Effects of Joule heating and viscous dissipation on magnetohydrodynamic boundary layer flow of Jeffrey nanofluid over a vertically stretching cylinder. Coatings, 11(3), 353, (2021).
- Abbas, Z., Abdal, S., Hussain, N., Hussain, F., Adnan, M., Ali, B., ... & Younas, S. (2019). Mhd boundary layer flow and heat transfer of nanofluid over a vertical stretching sheet in the presence of a heat source. Scientific Inquiry and Review, 3(4), 60-73, (2019).
- Rasool, G., Shafiq, A. and Durur, H. Darcy-Forchheimer relation in magnetohydrodynamic Jeffrey nanofluid flow over stretching surface. Discrete & Continuous Dynamical Systems Series S, 14(7), 2497-2515, (2021).
- Kebede, T., Haile, E., Awgichew, G. and Walelign, T. Heat and mass transfer in unsteady boundary layer flow of Williamson nanofluids. Journal of Applied Mathematics, 1890972, (2020).
- Swain, K., Mahanthesh, B. and Mebarek-Oudina, F. Heat transport and stagnation-point flow of magnetized nanoliquid with variable thermal conductivity, Brownian moment, and thermophoresis aspects. Heat Transfer, 50(1), 754-767, (2021).
- Qureshi, M.A. Numerical simulation of heat transfer flow subject to MHD of Williamson nanofluid with thermal radiation. Symmetry, 13(1), 10, (2021).
- Sravanthi, C.S., Mabood, F., Nabi, S. G. and Shehzad, S.A. Heterogeneous and homogeneous reactive flow of magnetite-water nanofluid over a magnetized moving plate. Propulsion and Power Research, 11(2), 265-275, (2022).
- Alzahrani, F., Growda, R.J.P., Kumar, R.N. and Khan, M.I. Dynamics of thermosolutal Marangoni convection and nanoparticle aggregation effects on Oldroyd-B nanofluid past a porous boundary with homogeneous-heterogeneous catalytic reactions. Journal of the Indian Chemical Society, 99(6), 100458, (2022).
- Sarojamma, G., Lakshmi, R.V., Narayana, P.V.S. and Animasaun, I.L. Exploration of the significance of autocatalytic chemical reaction and Cattaneo-Christov heat flux on the dynamics of a micropolar fluid. Journal of Applied and Computational Mechanics, 6(1), 77-89, (2020).
- Animasaun, I.L., Mahanthesh, B., Sarojamma, G. and Damisa, J.S. Significance of thickness of paraboloid of revolution and buoyancy forces on the dynamics of Erying-Powel fluid subject to equal diffusivity kind of quartic autocatalysis. Physica A: Statistical Mechanics and its Applications, 549, 124047, (2020).
- Hayat, T., Hussain, Z., Muhammad, T. and Alsaedi, A. Effects of homogeneous and heterogeneous reactions in flow of nanofluids over a nonlinear stretching surface with variable surface thickness. Journal of Molecular Liquids, 221, 1121-1127, (2016).
- Zhao, Q., Xu, H. and Tao, L. Homogeneous-heterogeneous reactions in boundary-layer flow of a nanofluid near the forward stagnation point of a cylinder. Journal of Heat Transfer, 139(3), 034502, (2016).
- Platt, J.R. Bioconvection patterns in cultures of free-swimming organisms. Science, 133(3466), 1766-1767, (1961).
- Ramzan, M., Shamshad, U., Rehman, S., Saeed, A., Kumam, P. and Watthayu, W. Compuation of MHD flow of three-dimensional mixed convection non-Newtonian viscoelastic fluid with the physical aspect of gyrotactic microorganism. Waves in Random and Complex Media, 1-23, (2022).
- Zhang, L., Puneeth, V., Ijaz Khan, M., El-Zahar, E.R., Manjunath, N., Shah, N.A., Chung, J.D., Khan, S.U. and Khan, M.I. Applications of bioconvection for tiny particles due to two concentric cylinders when role of Lorentz force is significant. Plos One, 17(5), e0265026, (2022).
- Rao, M.V.S., Gangadhar, K., Chamkha, A.J. and Surekha, P. Bioconvection in a convectional nanofluid flow containing gyrotactic microorganisms over an isothermal vertical cone embedded in a porous surface with chemical reactive species. Arabian Journal for Science and Engineering, 46, 2493-2503, (2021).
- Sankad, G., Ishwar, M. and Dhange, M. Varying wall temperature and thermal radiation effects on MHD boundary layer liquid flow containing gyrotactic microorganisms. Partial Differential Equations in Applied Mathematics, 4, 100092, (2021).
- Parveen, N., Awais, M., Awan, S.E., Shah, S.A., Yuan, A., Nawaz, M., Akhtar, R. and Malik, M.Y. Thermophysical properties of chemotactic microorganisms in bio-convective peristaltic rheology of nano-liquid with slippage, Joule heating and viscous dissipation. Cases in Thermal Engineering, 27, 101285, (2021).
- Naganthran, K., Md Basir, M.F., Thumma, T., Ige, E.O., Nazar, R. and Tlili, I. Scaling group analysis of bioconvective micropolar fluid flow and heat transfer in a porous medium. Journal of Thermal Analysis and Calorimetry, 143, 1943-1955, (2021).
- Ramzan, M., Bilal, M., Kanwal, S. and Chung, J.D. Effects of variable thermal conductivity and non-linear thermal radiation past an Eyring Powell nanofluid with chemical reaction. Communications in Theoretical Physics, 67(6), 723-731, (2017).
- Hayat, T., Iqbal, Z., Qasim, M. and Alsaedi, A. Flow of an Eyring-Powell fluid with convective boundary conditions. Journal of Mechanics, 29(2), 217-224, (2013).
- Animasaun, L. and Koriko, O.K. New similarity solution of micropolar fluid flow problem over an UHSPR in the presence of quartic kind of autocatalytic chemical reaction. Frontiers in Heat and Mass Transfer, 8(26), (2017).
- Kuznetsov, A.V. and Nield, D.A. Double-diffusive natural convective boundary layer flow of a nanofluid past a vertical plate. International Journal of Thermal Sciences, 50(5), 712-717, (2011).
- Raees, A., Xu, H., Sun, Q. and Pop, I. Mixed convection in gravity-driven nanoliquid film containing both nanoparticles and gyrotactic microorganisms. Applied Mathematics and Mechanics, 36(2), 163-178, (2015).
- Chaudhary, M.A. and Merkin, J.H. A simple isothermal model for homogeneousheterogeneous reaction in boundary-layer flow. I Equal diffusivities. Fluid Dynamics Research, 16(6), 311-333, (1995).
- Koriko, O.K., Omowaye, A.J., Sandeep, N. and Animasaun, I.L. Analysis of boundary layer formed on an upper horizontal surface of a paraboloid of revolution within nanofluid flow in the presence of thermophoresis and Brownian motion of 29 nm CuO. International Journal of Mechanical Sciences, 124-125, 22-36, (2017).
- Kuznetsov, A.V. The onset of nanofluid bioconvection in a suspension containing both nanoparticles and gyrotactic microorganisms. International Communications in Heat and Mass Transfer, 37(10), 1421-1425, (2010).
- Batchelor, G.K. An Introduction to Fluid Dynamics. Cambridge University Press: London, (1987).
- Charraudeau, J. Influence de gradients de proprietes physiques en convection forceeapplication au cas du tube. International Journal of Heat and Mass Transfer, 18(1), 87-95, (1975).
- Oreyeni, T., Shah, N.A., Popoola, A.O., Elzahar, E.R. and Yook, S.J. The significance of exponential space-based heat generation and variable thermophysical properties on the dynamics of Casson fluid over a stratified surface with non-uniform thickness. Waves in Random and Complex Media, (2022).
- Oreyeni, T. and Omokhuale, E. Optimal homotopy analysis of MHD natural convection flow of thixotropic fluid under subjection of thermal stratification: Boundary layer analysis. American Journal of Computational Mathematics, 9(02), 116-131, (2019).
- Koriko, O.K., Animasaun, I.L., Omowaye, A.J. and Oreyeni, T. The combined influence of nonlinear thermal radiation and thermal stratification on the dynamics of micropolar fluid along a vertical surface. Multidiscipline Modeling in Materials and Structures, 15(1), 133-155, (2019).
- Koriko, O.K., Oreyeni, T., Omowaye, A.J. and Animasaun, I.L. Homotopy analysis of MHD free convective micropolar fluid flow along a vertical surface embedded in non-darcian thermally-stratified medium. Open Journal of Fluid Dynamics, 6(3), 198-221, (2016).
Year 2023,
, 74 - 100, 31.03.2023
Nehad Ali Shah
Amos Oladele Popoola
Tosin Oreyeni
Emmanuel Omokhuale
Muhammad Muhammad Altine
References
- Shamshuddin, M.D., Shahzad, F., Jamshed, W., Bég, O.A., Eid, M.R. and Bég, T.A. Thermosolutal stratification and chemical reaction effects on radiative magnetized nanofluid flow along an exponentially stretching sensor plate: Computational analysis. Journal of Magnetism and Magnetic Materials, 565, 170286, (2023).
- Tamilzharasan, B.M., Karthikeyan, S., Kaabar, M.K., Yavuz, M. and Özköse, F. Magneto mixed convection of Williamson nanofluid flow through a double stratified porous medium in attendance of activation energy. Mathematical and Computational Applications, 27(3), 46, (2022).
- Jagan, K. and Sivasankaran, S. Soret & Dufour and Triple stratification effect on MHD flow with velocity slip towards a stretching cylinder. Mathematical and Computational Applications, 27(2), 25, (2022).
- Rehman, S., Anjum, A., Farooq, M., Hashim and Malik, M.Y. Melting heat phenomenon in thermally stratified fluid reservoirs (Powell-Eyring fluid) with joule heating. International Communications in Heat and Mass Transfer, 137, 106196, (2022).
- Oreyeni, T., Ramesh, K., Nayak, M.K. and Oladele, P.A. Triple stratification impacts on an inclined hydromagnetic bioconvective flow of micropolar nanofluid with exponential space-based heat generation. Waves in Random and Complex Media.
- Fayz-Al-Asad, M., Oreyeni, T., Yavuz, M. and Olanrewaju, P.O. Analytic simulation of MHD boundary layer flow of a chemically reacting upper-convected Maxwell fluid past a vertical surface subjected to double stratifications with variable properties. The European Physical Journal Plus, 137, 813, (2022).
- Khan, W.A., Anjum, N., Waqas, M., Abbas, S.Z., Irfan, M. and Muhammad, T. Impact of stratification phenomena on a nonlinear radiative flow of sutterby nanofluid. Journal of Materials Research and Technology, 15, 306-314, (2021).
- Chen, S.B., Shahmir, N., Ramzan, M., Sun, Y.L., Aly, A.A. and Malik, M.Y. Thermophoretic particle deposition in the flow of dual stratified Casson fluid with magnetic dipole and generalized Fourier’s and Fick’s laws. Case Studies in Thermal Engineering, 26, 101186, (2021).
- Dawar, A., Shah, Z., Alshehri, H. M., Islam, S. and Kumam, P. Magnetized and nonmagnetized Casson fluid flow with gyrotactic microorganisms over a stratified stretching cylinder. Scientific Reports, 11, 16376, (2021).
- Verma, A.K., Bhattacharyya, K., Rajput, S., Mandal, M.S., Chamkha, A.J. and Yadav, D. Buoyancy driven non-Newtonian Prandtl-Eyring nanofluid flow in Darcy-Forchheimer porous medium over inclined non-linear expanding sheet with double stratification. Waves in Random and Complex Media, (2022).
- Mahmood, Z., Alhazmi, S.E., Alhowaity, A., Marzouki, R., Al-Ansari, N. and Khan, U. MHD mixed convective stagnation point flow of nanofluid past a permeable stretching sheet with nanoparticles aggregation and thermal stratification. Scientific Reports, 12, 16020, (2022).
- Koriko, O.K., Shah, N.A., Saleem, S., Chung, J.D., Omowaye, A.J. and Oreyeni, T. Exploration of bioconvection flow of MHD thixotropic nanofluid past a vertical surface coexisting with both nanoparticles and gyrotactic microorganisms. Scientific Reports, 11, 16627, (2021).
- Shah, N.A., Tosin, O., Shah, R., Salah, B. and Chung, J.D. Brownian motion and thermophoretic diffusion effects on the dynamics of MHD upper convected Maxwell nanofluid flow past a vertical surface. Physica Scripta, 96(12), 125722, (2021).
- Nadeem, S., Fuzhang, W., Alharbi, F.M., Sajid, F., Abbas, N., El-Shafay, A.S. and Al-Mubaddel, F.S. Numerical computations for Buongiorno nano fluid model on the boundary layer flow of viscoelastic fluid towards a nonlinear stretching sheet. Alexandria Engineering Journal, 61(2), 1769-1778, (2022).
- Rao, A.S., Ramaiah, K.D., Kotha, G., Rao, M.V.S. and Chamkha, A.J. A Spectral Relaxation approach for boundary layer flow of nanofluid past an exponentially stretching surface with variable suction in the presence of heat source/sink with viscous dissipation. Arabian Journal for Science and Engineering, 46, 7509-7520, (2021).
- Ur Rasheed, H., AL-Zubaidi, A., Islam, S., Saleem, S., Khan, Z. and Khan, W. Effects of Joule heating and viscous dissipation on magnetohydrodynamic boundary layer flow of Jeffrey nanofluid over a vertically stretching cylinder. Coatings, 11(3), 353, (2021).
- Abbas, Z., Abdal, S., Hussain, N., Hussain, F., Adnan, M., Ali, B., ... & Younas, S. (2019). Mhd boundary layer flow and heat transfer of nanofluid over a vertical stretching sheet in the presence of a heat source. Scientific Inquiry and Review, 3(4), 60-73, (2019).
- Rasool, G., Shafiq, A. and Durur, H. Darcy-Forchheimer relation in magnetohydrodynamic Jeffrey nanofluid flow over stretching surface. Discrete & Continuous Dynamical Systems Series S, 14(7), 2497-2515, (2021).
- Kebede, T., Haile, E., Awgichew, G. and Walelign, T. Heat and mass transfer in unsteady boundary layer flow of Williamson nanofluids. Journal of Applied Mathematics, 1890972, (2020).
- Swain, K., Mahanthesh, B. and Mebarek-Oudina, F. Heat transport and stagnation-point flow of magnetized nanoliquid with variable thermal conductivity, Brownian moment, and thermophoresis aspects. Heat Transfer, 50(1), 754-767, (2021).
- Qureshi, M.A. Numerical simulation of heat transfer flow subject to MHD of Williamson nanofluid with thermal radiation. Symmetry, 13(1), 10, (2021).
- Sravanthi, C.S., Mabood, F., Nabi, S. G. and Shehzad, S.A. Heterogeneous and homogeneous reactive flow of magnetite-water nanofluid over a magnetized moving plate. Propulsion and Power Research, 11(2), 265-275, (2022).
- Alzahrani, F., Growda, R.J.P., Kumar, R.N. and Khan, M.I. Dynamics of thermosolutal Marangoni convection and nanoparticle aggregation effects on Oldroyd-B nanofluid past a porous boundary with homogeneous-heterogeneous catalytic reactions. Journal of the Indian Chemical Society, 99(6), 100458, (2022).
- Sarojamma, G., Lakshmi, R.V., Narayana, P.V.S. and Animasaun, I.L. Exploration of the significance of autocatalytic chemical reaction and Cattaneo-Christov heat flux on the dynamics of a micropolar fluid. Journal of Applied and Computational Mechanics, 6(1), 77-89, (2020).
- Animasaun, I.L., Mahanthesh, B., Sarojamma, G. and Damisa, J.S. Significance of thickness of paraboloid of revolution and buoyancy forces on the dynamics of Erying-Powel fluid subject to equal diffusivity kind of quartic autocatalysis. Physica A: Statistical Mechanics and its Applications, 549, 124047, (2020).
- Hayat, T., Hussain, Z., Muhammad, T. and Alsaedi, A. Effects of homogeneous and heterogeneous reactions in flow of nanofluids over a nonlinear stretching surface with variable surface thickness. Journal of Molecular Liquids, 221, 1121-1127, (2016).
- Zhao, Q., Xu, H. and Tao, L. Homogeneous-heterogeneous reactions in boundary-layer flow of a nanofluid near the forward stagnation point of a cylinder. Journal of Heat Transfer, 139(3), 034502, (2016).
- Platt, J.R. Bioconvection patterns in cultures of free-swimming organisms. Science, 133(3466), 1766-1767, (1961).
- Ramzan, M., Shamshad, U., Rehman, S., Saeed, A., Kumam, P. and Watthayu, W. Compuation of MHD flow of three-dimensional mixed convection non-Newtonian viscoelastic fluid with the physical aspect of gyrotactic microorganism. Waves in Random and Complex Media, 1-23, (2022).
- Zhang, L., Puneeth, V., Ijaz Khan, M., El-Zahar, E.R., Manjunath, N., Shah, N.A., Chung, J.D., Khan, S.U. and Khan, M.I. Applications of bioconvection for tiny particles due to two concentric cylinders when role of Lorentz force is significant. Plos One, 17(5), e0265026, (2022).
- Rao, M.V.S., Gangadhar, K., Chamkha, A.J. and Surekha, P. Bioconvection in a convectional nanofluid flow containing gyrotactic microorganisms over an isothermal vertical cone embedded in a porous surface with chemical reactive species. Arabian Journal for Science and Engineering, 46, 2493-2503, (2021).
- Sankad, G., Ishwar, M. and Dhange, M. Varying wall temperature and thermal radiation effects on MHD boundary layer liquid flow containing gyrotactic microorganisms. Partial Differential Equations in Applied Mathematics, 4, 100092, (2021).
- Parveen, N., Awais, M., Awan, S.E., Shah, S.A., Yuan, A., Nawaz, M., Akhtar, R. and Malik, M.Y. Thermophysical properties of chemotactic microorganisms in bio-convective peristaltic rheology of nano-liquid with slippage, Joule heating and viscous dissipation. Cases in Thermal Engineering, 27, 101285, (2021).
- Naganthran, K., Md Basir, M.F., Thumma, T., Ige, E.O., Nazar, R. and Tlili, I. Scaling group analysis of bioconvective micropolar fluid flow and heat transfer in a porous medium. Journal of Thermal Analysis and Calorimetry, 143, 1943-1955, (2021).
- Ramzan, M., Bilal, M., Kanwal, S. and Chung, J.D. Effects of variable thermal conductivity and non-linear thermal radiation past an Eyring Powell nanofluid with chemical reaction. Communications in Theoretical Physics, 67(6), 723-731, (2017).
- Hayat, T., Iqbal, Z., Qasim, M. and Alsaedi, A. Flow of an Eyring-Powell fluid with convective boundary conditions. Journal of Mechanics, 29(2), 217-224, (2013).
- Animasaun, L. and Koriko, O.K. New similarity solution of micropolar fluid flow problem over an UHSPR in the presence of quartic kind of autocatalytic chemical reaction. Frontiers in Heat and Mass Transfer, 8(26), (2017).
- Kuznetsov, A.V. and Nield, D.A. Double-diffusive natural convective boundary layer flow of a nanofluid past a vertical plate. International Journal of Thermal Sciences, 50(5), 712-717, (2011).
- Raees, A., Xu, H., Sun, Q. and Pop, I. Mixed convection in gravity-driven nanoliquid film containing both nanoparticles and gyrotactic microorganisms. Applied Mathematics and Mechanics, 36(2), 163-178, (2015).
- Chaudhary, M.A. and Merkin, J.H. A simple isothermal model for homogeneousheterogeneous reaction in boundary-layer flow. I Equal diffusivities. Fluid Dynamics Research, 16(6), 311-333, (1995).
- Koriko, O.K., Omowaye, A.J., Sandeep, N. and Animasaun, I.L. Analysis of boundary layer formed on an upper horizontal surface of a paraboloid of revolution within nanofluid flow in the presence of thermophoresis and Brownian motion of 29 nm CuO. International Journal of Mechanical Sciences, 124-125, 22-36, (2017).
- Kuznetsov, A.V. The onset of nanofluid bioconvection in a suspension containing both nanoparticles and gyrotactic microorganisms. International Communications in Heat and Mass Transfer, 37(10), 1421-1425, (2010).
- Batchelor, G.K. An Introduction to Fluid Dynamics. Cambridge University Press: London, (1987).
- Charraudeau, J. Influence de gradients de proprietes physiques en convection forceeapplication au cas du tube. International Journal of Heat and Mass Transfer, 18(1), 87-95, (1975).
- Oreyeni, T., Shah, N.A., Popoola, A.O., Elzahar, E.R. and Yook, S.J. The significance of exponential space-based heat generation and variable thermophysical properties on the dynamics of Casson fluid over a stratified surface with non-uniform thickness. Waves in Random and Complex Media, (2022).
- Oreyeni, T. and Omokhuale, E. Optimal homotopy analysis of MHD natural convection flow of thixotropic fluid under subjection of thermal stratification: Boundary layer analysis. American Journal of Computational Mathematics, 9(02), 116-131, (2019).
- Koriko, O.K., Animasaun, I.L., Omowaye, A.J. and Oreyeni, T. The combined influence of nonlinear thermal radiation and thermal stratification on the dynamics of micropolar fluid along a vertical surface. Multidiscipline Modeling in Materials and Structures, 15(1), 133-155, (2019).
- Koriko, O.K., Oreyeni, T., Omowaye, A.J. and Animasaun, I.L. Homotopy analysis of MHD free convective micropolar fluid flow along a vertical surface embedded in non-darcian thermally-stratified medium. Open Journal of Fluid Dynamics, 6(3), 198-221, (2016).