Gyrotactic Microorganisms Mixed Convection Nanofluid Flow along an Isothermal Vertical Wedge in Porous Media
The main objective of the present article is to explore the state of mixed convection nanofluid flow of gyrotactic microorganisms from an isothermal vertical wedge in porous medium. In our pioneering investigation, the easiest possible boundary conditions have been employed, in other words when the temperature, the nanofluid and motile microorganisms’ density have been considered to be constant on the wedge wall. Adding motile microorganisms to the nanofluid tends to enhance microscale mixing, mass transfer, and improve the nanofluid stability. Upon the Oberbeck–Boussinesq approximation and non-similarity transmutation, the paradigm of nonlinear equations are obtained and tackled numerically by using the R.K. Gill and shooting methods to obtain the dimensionless velocity, temperature, nanoparticle concentration and motile microorganisms density together with the reduced Sherwood, Nusselt, and numbers. Bioconvection parameters have strong effect upon the motile microorganism, heat, and volume fraction of nanoparticle transport rates. In the case when bioconvection is neglected, the obtained computations were found in very good agreement with the previous published data.
[1] P. Keblinski, S.R. Phillpot, S.U.-S. Choi, J.A. Eastman, Mechanisms of heat flow in suspensions of nano-sized particles (nanofluids), Int. J. Heat Mass Transfer 45 (4) (2002) 855–863.
[2] U. S. U. Choi, Enhancing thermal conductivity of fluids with nanoparticle. In: Siginer, D.A., Wang H.P. (eds.), Developments and Applications of Non-Newtonian Flows, ASME FED, 231/MD 66 (1995) 99–105.
[3] A. Mahdy, S. E. Ahmed, Laminar free convection over a vertical wavy surface embedded in a porous medium saturated with a nanofluid. Transp. Porous Med. 91 (2012) 423–435.
[4] W. Duangthongsuk, S. Wongwises, Effect of thermophysical properties models on the predicting of the convective heat transfer coefficient for low concentration nanofluid. Int. Commun. Heat Mass Transf. 35 (2008) 1320–1326.
[5] D. A. Nield, A. V. Kuznetsov, The Cheng-Minkowycz problem for natural convective boundary layer flow in a porous medium saturated by a nanofluid. Int. J. Heat Mass Transf. 52 (2009) 5792-5795.
[6] P. Cheng, W. J. Minkowycz, Free convection about a vertical flat plate embedded in a porous medium with application to heat transfer from a dike. J. Geophys. Res. 28 (1977) 2040-2044.
[7] J. Buongiorno, Convective transport in nanofluids. ASME J. Heat Transf. 128 (2006) 240–250.
[8] S. Lee, S. U. S. Choi, S. Li, J. A. Eastman, Measuring thermal conductivity of fluids containing oxide nanoparticles. ASME J. Heat Transfer Trans (1999) 121-280.
[9] J. A. Eastman, S. U. S. Choi, S. Li, W. Yu, L. J. Thompson, Anomalously increased effective thermal conductivity of ethylene glycol-based nanofluids containing copper nanoparticles. Appl. Phys. Lett. 78 (2001) 718–720.
[10] W. A. Khan, I. Pop, Free convection boundary layer flow past a horizontal flat plate embedded in a porous medium filled with a nanofluid. ASME J. Heat Transf. 133 (2011) 094501-1.
[11] E. Abu-Nada, Application of nanofluids for heat transfer enhancement of separated flows encountered in a backward facing step, Int. J. Heat Fluid Flow 29 (2008) 242–249.
[12] R. K. Tiwari, M. K. Das, Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids. Int. J. Heat Mass Transf. 50 (2007) 2002-2018.
[13] S. Kakać, A. Pramuanjaroenkij, Review of convective heat transfer enhancement with nanofluids, Int. J. Heat Mass Transf. 52 (2009) 3187–3196.
[14] D. Wen, G. Lin, S. Vafaei, K. Zhang, Review of nanofluids for heat transfer applications, Particuology 7 (2011) 141–150.
[15] P. M. Congedo, S. Collura, Modeling and analysis of natural convection heat transfer in nanofluids. In: Proc ASME Summer Heat Transfer Conf. 3 (2009) 569–579.
[16] A. Chamkha, S. R. G. Rama, G. Kaustubh, Non-similar Solution for Natural Convective Boundary Layer Flow Over a Sphere Embedded in a Porous Medium Saturated with a Nanofluid. Transp. Porous Med. 86 (2011) 13–22.
[17] M. A. A. Hamad, I. Pop, A. I. Ismail, Magnetic field effects on free convection flow of a nanofluid past a semi-infinite vertical flat plate. Nonlinear Analysis: Real World Appl. 12 (2011) 1338–1346.
[18] D. A. Nield, A. V. Kuznetsov, Thermal instability in a porous medium layer saturated by a nanofluid: Brinkman model. Transp. Porous media 81 (2010) 409–422.
[19] Y. Xuan, W. Roetzel, Conceptions for heat transfer correlation of nanofluids. Int. J. Heat Mass Transf. 43 (2000) 3701-3707.
[20] A. J. Chamkha, A. M Aly, H. Al-Mudhaf, Laminar MHD mixed convection flow of a nanofluid along a stretching permeable surface in the presence of heat generation or absorption effects. Int. J. Microscale Nanoscale Thermal Fluid Transp. Phenom. 2 (2011).
[21] M. Kumari, G. Nath, Radiation effect on mixed convection from a horizontal surface in a porous medium. Mech. Res. Commun. 31 (2004) 483–491.
[22] D. A. Nield, A. Bejan, Convection in Porous Media. 2nd edn. Springer, New York (2006).
[23] C-Y. Cheng, Soret Dufour effects on mixed convection heat and mass transfer from a vertical wedge in a porous medium with constant wall temperature and concentration, Transp. Porous Med. 94 (2012) 123-132.
[24] K. A. Yih, Radiation effect on mixed convection over an isothermal wedge in porous media: the entire regime. Heat Transf. Eng. 22 (2001) 26–32.
[25] J. C. Hsieh, T. S. Chen, B. F. Armaly, Mixed convection along a non-isothermal vertical plate embedded in a porous medium: the entire regime. Int. J. Heat Mass Transf. 36 (1993) 1819–1825.
[26] P. Geng, A. V. Kuznetsov, Settling of bidispersed small solid particles in a dilute suspension containing gyrotactic microorganisms. Int. J. Eng. Sci. 43 (2005) 992-1010.
[27] P. Geng, A. V. Kuznetsov, Effect of small solid particles on the development of bioconvection plumes. Int. Commun. Heat Mass Transfer 31 (2004) 629-638.
[28] P. Geng, A. V. Kuznetsov, Introducing the concept of effective diffusivity to evaluate the effect of bioconvection on small solid particles. Int. J. Transp. Phenom. 7 (1995) 321–338.
[29] W. A. Khan, M. J. Uddin, A. I. Ismail, Free convection of non-Newtonian nanofluids in porous media with gyrotactic microorganisms. Transp Porous Med. 97 (2013) 241–252.
[30] A. J. Hillesdon, T. j. Pedley, Bioconvection in suspensions of oxytactic bacteria: linear theory. J. Fluid Mech. 324 (1996) 223-259.
[31] A. Aziz, W. a. Khan, I. Pop, Free convection boundary layer flow past a horizontal flat plate embedded in porous medium filled by nanofluid containing gyrotactic microorganisms. Int. J. Thermal Sci. 56 (2012) 48–57.
[32] S. M. Becker, A. V. Kuznetsov, A. A. Avramenko, Numerical modeling of a falling bioconvection plume in a porous medium. Fluid Dyn. Res. 33 (2004) 323-339.
[33] W. N. Mutuku, O. D. Makinde, Hydromagnetic bioconvection of nanofluid over a permeable vertical plate due to gyrotactic microorganisms. Computers & Fluids 95 (2014) 88–97.
[34] S. Childress, M. Levandowsky, E. A. Spiegel, Pattern formation in a suspension of swimming microorganisms – equations and stability theory. J. Fluid Mech. 69 (1975) 591–613.
[35] A. A. Avramenko, A. V. Kuznetsov, Stability of a suspension of gyrotactic microorganisms in superimposed fluid and porous layers. Int. Commun. Heat Mass Transfer 31 (2004) 1057–1066.
[36] A. V. Kuznetsov, The onset of nanofluid bioconvection in a suspension containing both nanoparticles and gyrotactic microorganisms. Int. Commun. Heat Mass Transf. 37 (2010) 1421–1425.
[37] W. A. Khan, O. D. Makinde, Z. H. Khan, MHD boundary layer flow of a nanofluid containing gyrotactic microorganisms past a vertical plate with Navier slip. Int. J. Heat Mass Transf. 74 (2014) 285–291.
[38] A. Mahdy, Natural convection boundary layer flow due to gyrotactic microorganisms about a vertical cone in porous media saturated by a nanofluid. J. Braz. Soc. Mech. Sci. Eng. 38 (2016) 67-76.
[39] S. E. Ahmed, A. Mahdy, Laminar MHD natural convection of nanofluid containing gyrotactic microorganisms over vertical wavy surface saturated non-Darcian porous media, Applied Mathematics and Mechanics 37 (2016) 471-484.
[40] A. V. Kuznetsov, The onset of thermo-bioconvection in a shallow fluid saturated porous layer heated from below in a suspension of oxytactic microorganisms. Eur. J. Mech. – B/Fluids 25 (2006) 223–233.
[41] A. V. Kuznetsov, Bio-thermal convection induced by two different species of microorganisms. Int. Commun. Heat Mass Transf. 38 (2011) 548–553.
[42] A. V. Kuznetsov, Nanofluid bioconvection in water-based suspensions containing nanoparticles and oxytactic microorganisms: oscillatory instability. Nanoscale Res. Lett. 6 (2011) 1-13.
[43] T. Cebeci, P. Bradshaw, Physical and computational aspects of convective heat transfer, Berlin-Heidelberg-New york- Springer-Verlag (1984).
[1] P. Keblinski, S.R. Phillpot, S.U.-S. Choi, J.A. Eastman, Mechanisms of heat flow in suspensions of nano-sized particles (nanofluids), Int. J. Heat Mass Transfer 45 (4) (2002) 855–863.
[2] U. S. U. Choi, Enhancing thermal conductivity of fluids with nanoparticle. In: Siginer, D.A., Wang H.P. (eds.), Developments and Applications of Non-Newtonian Flows, ASME FED, 231/MD 66 (1995) 99–105.
[3] A. Mahdy, S. E. Ahmed, Laminar free convection over a vertical wavy surface embedded in a porous medium saturated with a nanofluid. Transp. Porous Med. 91 (2012) 423–435.
[4] W. Duangthongsuk, S. Wongwises, Effect of thermophysical properties models on the predicting of the convective heat transfer coefficient for low concentration nanofluid. Int. Commun. Heat Mass Transf. 35 (2008) 1320–1326.
[5] D. A. Nield, A. V. Kuznetsov, The Cheng-Minkowycz problem for natural convective boundary layer flow in a porous medium saturated by a nanofluid. Int. J. Heat Mass Transf. 52 (2009) 5792-5795.
[6] P. Cheng, W. J. Minkowycz, Free convection about a vertical flat plate embedded in a porous medium with application to heat transfer from a dike. J. Geophys. Res. 28 (1977) 2040-2044.
[7] J. Buongiorno, Convective transport in nanofluids. ASME J. Heat Transf. 128 (2006) 240–250.
[8] S. Lee, S. U. S. Choi, S. Li, J. A. Eastman, Measuring thermal conductivity of fluids containing oxide nanoparticles. ASME J. Heat Transfer Trans (1999) 121-280.
[9] J. A. Eastman, S. U. S. Choi, S. Li, W. Yu, L. J. Thompson, Anomalously increased effective thermal conductivity of ethylene glycol-based nanofluids containing copper nanoparticles. Appl. Phys. Lett. 78 (2001) 718–720.
[10] W. A. Khan, I. Pop, Free convection boundary layer flow past a horizontal flat plate embedded in a porous medium filled with a nanofluid. ASME J. Heat Transf. 133 (2011) 094501-1.
[11] E. Abu-Nada, Application of nanofluids for heat transfer enhancement of separated flows encountered in a backward facing step, Int. J. Heat Fluid Flow 29 (2008) 242–249.
[12] R. K. Tiwari, M. K. Das, Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids. Int. J. Heat Mass Transf. 50 (2007) 2002-2018.
[13] S. Kakać, A. Pramuanjaroenkij, Review of convective heat transfer enhancement with nanofluids, Int. J. Heat Mass Transf. 52 (2009) 3187–3196.
[14] D. Wen, G. Lin, S. Vafaei, K. Zhang, Review of nanofluids for heat transfer applications, Particuology 7 (2011) 141–150.
[15] P. M. Congedo, S. Collura, Modeling and analysis of natural convection heat transfer in nanofluids. In: Proc ASME Summer Heat Transfer Conf. 3 (2009) 569–579.
[16] A. Chamkha, S. R. G. Rama, G. Kaustubh, Non-similar Solution for Natural Convective Boundary Layer Flow Over a Sphere Embedded in a Porous Medium Saturated with a Nanofluid. Transp. Porous Med. 86 (2011) 13–22.
[17] M. A. A. Hamad, I. Pop, A. I. Ismail, Magnetic field effects on free convection flow of a nanofluid past a semi-infinite vertical flat plate. Nonlinear Analysis: Real World Appl. 12 (2011) 1338–1346.
[18] D. A. Nield, A. V. Kuznetsov, Thermal instability in a porous medium layer saturated by a nanofluid: Brinkman model. Transp. Porous media 81 (2010) 409–422.
[19] Y. Xuan, W. Roetzel, Conceptions for heat transfer correlation of nanofluids. Int. J. Heat Mass Transf. 43 (2000) 3701-3707.
[20] A. J. Chamkha, A. M Aly, H. Al-Mudhaf, Laminar MHD mixed convection flow of a nanofluid along a stretching permeable surface in the presence of heat generation or absorption effects. Int. J. Microscale Nanoscale Thermal Fluid Transp. Phenom. 2 (2011).
[21] M. Kumari, G. Nath, Radiation effect on mixed convection from a horizontal surface in a porous medium. Mech. Res. Commun. 31 (2004) 483–491.
[22] D. A. Nield, A. Bejan, Convection in Porous Media. 2nd edn. Springer, New York (2006).
[23] C-Y. Cheng, Soret Dufour effects on mixed convection heat and mass transfer from a vertical wedge in a porous medium with constant wall temperature and concentration, Transp. Porous Med. 94 (2012) 123-132.
[24] K. A. Yih, Radiation effect on mixed convection over an isothermal wedge in porous media: the entire regime. Heat Transf. Eng. 22 (2001) 26–32.
[25] J. C. Hsieh, T. S. Chen, B. F. Armaly, Mixed convection along a non-isothermal vertical plate embedded in a porous medium: the entire regime. Int. J. Heat Mass Transf. 36 (1993) 1819–1825.
[26] P. Geng, A. V. Kuznetsov, Settling of bidispersed small solid particles in a dilute suspension containing gyrotactic microorganisms. Int. J. Eng. Sci. 43 (2005) 992-1010.
[27] P. Geng, A. V. Kuznetsov, Effect of small solid particles on the development of bioconvection plumes. Int. Commun. Heat Mass Transfer 31 (2004) 629-638.
[28] P. Geng, A. V. Kuznetsov, Introducing the concept of effective diffusivity to evaluate the effect of bioconvection on small solid particles. Int. J. Transp. Phenom. 7 (1995) 321–338.
[29] W. A. Khan, M. J. Uddin, A. I. Ismail, Free convection of non-Newtonian nanofluids in porous media with gyrotactic microorganisms. Transp Porous Med. 97 (2013) 241–252.
[30] A. J. Hillesdon, T. j. Pedley, Bioconvection in suspensions of oxytactic bacteria: linear theory. J. Fluid Mech. 324 (1996) 223-259.
[31] A. Aziz, W. a. Khan, I. Pop, Free convection boundary layer flow past a horizontal flat plate embedded in porous medium filled by nanofluid containing gyrotactic microorganisms. Int. J. Thermal Sci. 56 (2012) 48–57.
[32] S. M. Becker, A. V. Kuznetsov, A. A. Avramenko, Numerical modeling of a falling bioconvection plume in a porous medium. Fluid Dyn. Res. 33 (2004) 323-339.
[33] W. N. Mutuku, O. D. Makinde, Hydromagnetic bioconvection of nanofluid over a permeable vertical plate due to gyrotactic microorganisms. Computers & Fluids 95 (2014) 88–97.
[34] S. Childress, M. Levandowsky, E. A. Spiegel, Pattern formation in a suspension of swimming microorganisms – equations and stability theory. J. Fluid Mech. 69 (1975) 591–613.
[35] A. A. Avramenko, A. V. Kuznetsov, Stability of a suspension of gyrotactic microorganisms in superimposed fluid and porous layers. Int. Commun. Heat Mass Transfer 31 (2004) 1057–1066.
[36] A. V. Kuznetsov, The onset of nanofluid bioconvection in a suspension containing both nanoparticles and gyrotactic microorganisms. Int. Commun. Heat Mass Transf. 37 (2010) 1421–1425.
[37] W. A. Khan, O. D. Makinde, Z. H. Khan, MHD boundary layer flow of a nanofluid containing gyrotactic microorganisms past a vertical plate with Navier slip. Int. J. Heat Mass Transf. 74 (2014) 285–291.
[38] A. Mahdy, Natural convection boundary layer flow due to gyrotactic microorganisms about a vertical cone in porous media saturated by a nanofluid. J. Braz. Soc. Mech. Sci. Eng. 38 (2016) 67-76.
[39] S. E. Ahmed, A. Mahdy, Laminar MHD natural convection of nanofluid containing gyrotactic microorganisms over vertical wavy surface saturated non-Darcian porous media, Applied Mathematics and Mechanics 37 (2016) 471-484.
[40] A. V. Kuznetsov, The onset of thermo-bioconvection in a shallow fluid saturated porous layer heated from below in a suspension of oxytactic microorganisms. Eur. J. Mech. – B/Fluids 25 (2006) 223–233.
[41] A. V. Kuznetsov, Bio-thermal convection induced by two different species of microorganisms. Int. Commun. Heat Mass Transf. 38 (2011) 548–553.
[42] A. V. Kuznetsov, Nanofluid bioconvection in water-based suspensions containing nanoparticles and oxytactic microorganisms: oscillatory instability. Nanoscale Res. Lett. 6 (2011) 1-13.
[43] T. Cebeci, P. Bradshaw, Physical and computational aspects of convective heat transfer, Berlin-Heidelberg-New york- Springer-Verlag (1984).
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:75731", author = "A. Mahdy", title = "Gyrotactic Microorganisms Mixed Convection Nanofluid Flow along an Isothermal Vertical Wedge in Porous Media ", abstract = "The main objective of the present article is to explore the state of mixed convection nanofluid flow of gyrotactic microorganisms from an isothermal vertical wedge in porous medium. In our pioneering investigation, the easiest possible boundary conditions have been employed, in other words when the temperature, the nanofluid and motile microorganisms’ density have been considered to be constant on the wedge wall. Adding motile microorganisms to the nanofluid tends to enhance microscale mixing, mass transfer, and improve the nanofluid stability. Upon the Oberbeck–Boussinesq approximation and non-similarity transmutation, the paradigm of nonlinear equations are obtained and tackled numerically by using the R.K. Gill and shooting methods to obtain the dimensionless velocity, temperature, nanoparticle concentration and motile microorganisms density together with the reduced Sherwood, Nusselt, and numbers. Bioconvection parameters have strong effect upon the motile microorganism, heat, and volume fraction of nanoparticle transport rates. In the case when bioconvection is neglected, the obtained computations were found in very good agreement with the previous published data.
", keywords = "Bioconvection, wedge, gyrotactic microorganisms, porous media, nanofluid, mixed. ", volume = "11", number = "4", pages = "840-11", }
