3D Casson nanofluid flow over slendering surface in a suspension of gyrotactic microorganisms with Cattaneo-Christov heat flux

doi:10.1007/s10483-018-2331-6

摘要/Abstract

摘要：

A mathematical model is proposed to execute the features of the non-uniform heat source or sink in the chemically reacting magnetohydrodynamic (MHD) Casson fluid across a slendering sheet in the presence of microorganisms and Cattaneo-Christov heat flux. Multiple slips (diffusion, thermal, and momentum slips) are applied in the modeling of the heat and mass transport processes. The Runge-Kutta based shooting method is used to find the solutions. Numerical simulation is carried out for various values of the physical constraints when the Casson index parameter is positive, negative, or infinite with the aid of plots. The coefficients of the skin factors, the local Nusselt number, and the Sherwood number are estimated for different parameters, and discussed for engineering interest. It is found that the gyrotactic microorganisms are greatly encouraged when the dimensionless parameters increase, especially when the Casson fluid parameter is negative. It is worth mentioning that the velocity profiles when the Casson fluid parameter is positive are higher than those when the Casson fluid parameter is negative or infinite, whereas the temperature and concentration fields show exactly opposite phenomena.

关键词: Casson fluid, Stroh’s formalism, eigenvalue, stress intensity factors, microorganisms, Cattaneo-Christov heat flux, slendering sheet, multiple slip

Abstract:

Key words: multiple slip, Stroh’s formalism, eigenvalue, stress intensity factors, Cattaneo-Christov heat flux, microorganisms, slendering sheet, Casson fluid

中图分类号:

76B75

V. NAGENDRAMMA, C. S. K. RAJU, B. MALLIKARJUNA, S. A. SHEHZAD, A. LEELARATHNAM. 3D Casson nanofluid flow over slendering surface in a suspension of gyrotactic microorganisms with Cattaneo-Christov heat flux[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(5): 623-638.

参考文献

[1] Choi, S. U. S. Enhancing thermal conductivity of fluids with nanoparticle. Proceedings of the ASME International Mechanical Engineering Congress and Exposition, 231, 99-105(1995)
[2] Zhu, J., Zheng, L., Zheng, L. C., and Zhang, X. X. Second-order slip MHD flow and heat transfer of nanofluids with thermal radiation and chemical reaction. Applied Mathematics and Mechanics (English Edition), 36(9), 1131-1146(2015) https://doi.org/10.1007/s10483-015-1977-6
[3] Hsiao, K. Stagnation electrical MHD nanofluid mixed convection with slip boundary on a stretching sheet. Applied Thermal Engineering, 98, 850-861(2016)
[4] Hayat, T., Asad, S., and Alsaedi, A. Flow of Casson fluid with nanoparticles. Applied Mathematics and Mechanics (English Edition), 37(4), 459-470(2016) https://doi.org/10.1007/s10483-016-2047-9
[5] Sheikholeslami, M. and Rokni, H. B. Numerical modeling of nanofluid natural convection in a semi annulus in existence of Lorentz force. Computer Methods in Applied Mechanics and Engineering, 317, 419-430(2017)
[6] Sheikholeslami, M. Influence of Coulomb forces on Fe₃O₄-H₂O nanofluid thermal improvement. International Journal of Hydrogen Energy, 42, 821-829(2017)
[7] Zhu, J., Wang, S. N., Zheng, L. C., and Zhang, X. X. Heat transfer of nanofluids considering nanoparticle migration and second-order slip velocity. Applied Mathematics and Mechanics (English Edition), 38, 125-136(2017) https://doi.org/10.1007/s10483-017-2155-6
[8] Sheikholeslami, M. Influence of magnetic field on nanofluid free convection in an open porous cavity by means of Lattice Boltzmann method. Journal of Molecular Liquids, 234, 364-374(2017)
[9] Mahanthesh, B., Gireesha, B. J., Shehzad, S. A., Abbasi, F. M., and Gorla, R. S. R. Nonlinear three-dimensional stretched flow of an Oldroyd-B fluid with convective condition, thermal radiation, and mixed convection. Applied Mathematics and Mechanics (English Edition), 38(7), 969-980(2017) https://doi.org/10.1007/s10483-017-2219-6
[10] Hayat, T., Mumtaz, M., Shafiq, A., and Alsaedi, A. Stratified magnetohydrodynamic flow of tangent hyperbolic nanofluid induced by inclined sheet. Applied Mathematics and Mechanics (English Edition), 38(2), 271-288(2017) https://doi.org/10.1007/s10483-017-2168-9
[11] Oyelakin, I. S., Mondal, S., and Sibanda, P. Unsteady Casson nanofluid flow over a stretching sheet with thermal radiation, convective and slip boundary conditions. Alexandria Engineering Journal, 55, 1025-1035(2016)
[12] Cattaneo, C. Sulla conduzione del calore. Some Aspects of Diffusion Theory (ed. Pignedoli, A.), Springer, Berlin, Heidelberg, 83-101(1948)
[13] Christov, C. I. On frame in different formulation of the Maxwell-Cattaneo model of finite-speed heat conduction. Mechanics Research Communication, 36, 481-486(2009)
[14] Straughan, B. Thermal convection with the Cattaneo-Christov model. International Journal of Heat and Mass Transfer, 53, 95-98(2010)
[15] Li, J., Zheng, L., and Liu, L. MHD viscoelastic flow and heat transfer over a vertical stretching sheet with Cattaneo-Christov heat flux effects. Journal of Molecular Liquids, 221, 19-25(2016)
[16] Hayat, T., Khan, M. I., Farooq, M., Yasmeen, T., and Alsaedi, A. Stagnation point flow with Cattaneo-Christov heat flux and homogeneous-heterogeneous reactions. Journal of Molecular Liquids, 220, 49-55(2016)
[17] Liu, L., Zheng, L., Liu, F., and Zhang, X. An improved heat conduction model with Riesz fractional Cattaneo-Christov flux. International Journal of Heat and Mass Transfer, 103, 1191-1197(2016)
[18] Hayat, T., Qayyum, S., Imtiaz, M., and Alsaedi, A. Impact of Cattaneo-Christov heat flux in Jeffrey fluid flow with homogeneous-heterogeneous reactions. PLoS One, 11, e0148662(2016)
[19] Hayat, T., Qayyum, S., Imtiaz, M., and Alsaedi, A. Flow between two stretchable rotating disks with Cattaneo-Christov heat flux model. Results in Physics, 7, 126-133(2017)
[20] Hayat, T., Kiran, A., Imtiaz, M., and Alsaedi, A. Unsteady flow of carbon nanotubes with chemical reaction and Cattaneo-Christov heat flux model. Results in Physics, 7, 823-831(2017)
[21] Hashim and Khan, M. On Cattaneo-Christov heat flux model for Carreau fluid flow over a slendering sheet. Results in Physics, 7, 310-319(2017)
[22] Malik, M. Y., Khan, M., Salahuddin, T., and Khan, I. Variable viscosity and MHD flow in Casson fluid with Cattaneo-Christov heat flux model:using Keller box method. Engineering Science and Technology, an International Journal, 19, 1985-1992(2016)
[23] Muhammad, N., Nadeem, S., and Mustafa, M. Squeezed flow of a nanofluid with CattaneoChristov heat and mass fluxes. Results in Physics, 7, 862-869(2017)
[24] Mustafa, M. Cattaneo-Christov heat flux model for rotating flow and heat transfer of upper convected Maxwell fluid. AIP Advances, 5, 047109(2015)
[25] Shehzad, S. A., Abbasi, F. M., Hayat, T., and Alsaedi, A. Cattaneo-Christov heat flux model for Darcy-Forchheimer flow of an Oldroyd-B fluid with variable conductivity and non-linear convection. Journal of Molecular Liquids, 224, 274-278(2016)
[26] Rubab, K. and Mustafa, M. Cattaneo-Christov heat flux model for MHD three-dimensional flow of Maxwell fluid over a stretching sheet. PLoS One, 11, e0153481(2015)
[27] Abbasi, F. M., Hayat, T., Shehzad, S. A., and Alsaedi, A. Impact of Cattaneo-Christov heat flux on flow of two-types viscoelastic fluid in Darcy-Forchheimer porous medium. International Journal of Numerical Methods for Heat and Fluid Flow, 27, 1955-1966(2017)
[28] Meraj, M. A., Shehzad, S. A., Hayat, T., Abbasi, F. M., and Alsaedi, A. Darcy-Forchheimer flow of variable conductivity Jeffrey liquid with Cattaneo-Christov heat flux theory. Applied Mathematics and Mechanics (English Edition), 38(4), 557-566(2017) https://dor.org/10.1007/s10483-017-2188-6
[29] Devi, S. P. A. and Prakash, M. Temperature dependent viscosity and thermal conductivity effects on hydromagnetic flow over a slendering stretching sheet. Journal of the Nigerian Mathematical Society, 34, 318-330(2015)
[30] Devi, S. P. A. and Prakash, M. Slip flow effects over hydromagnetic forced convective flow over a slandering stretching sheet. Journal of Applied Fluid Mechanics, 9, 683-692(2016)
[31] Babu, M. J. and Sandeep, N. MHD non-Newtonian fluid flow over a slendering stretching sheet in the presence of cross-diffusion effects. Alexandria Engineering Journal, 55, 2193-2201(2016)
[32] Khan, M. and Khan, W. A. Three-dimensional flow and heat transfer to burgers fluid using Cattaneo-Christov heat flux model. Journal of Molecular Liquids, 221, 651-657(2016)
[33] Hayat, T., Muhammad, T., Alsaedi, A., and Ahmad, B. Three-dimensional flow of nanofluid with Cattaneo-Christov double diffusion. Results in Physics, 6, 897-903(2016)
[34] Raju, C. S. K., Sekhar, K. R., Ibrahim, S. M., Lorentzini, G., Reddy, G. W., and Lorentzini, E. Variable viscosity on unsteady dissipative Carreau fluid over a truncated cone filled with titanium alloy nanoparticles. Continuum Mechanics and Thermodynamics, 29, 699-713(2017)
[35] Raju, C. S. K., Ibrahim, S. M., Anuradha, S., and Priyadharshini, P. Bio-convection on the nonlinear radiative flow of a Carreau fluid over a moving wedge with suction or injection. The European Physical Journal Plus, 131, 409(2016)
[36] Hayat, T., Khan, M. I., Farooq, M., Alsaedi, A., Waqas, M., and Yasmeen, T. Impact of CattaneoChristov heat flux model in flow of variable thermal conductivity fluid over a variable thicked surface. International Journal of Heat and Mass Transfer, 99, 702-710(2016)
[37] Mamatha, S. U., Mahesha, and Raju, C. S. K. Cattaneo-Christov on heat and mass transfer of unsteady Eyring Powell dusty nanofluid over sheet with heat and mass flux conditions. Informatics Medicine Unlocked, 9, 76-85(2017)
[38] Hsiao, K. To promote radiation electrical MHD activation energy thermal extrusion manufacturing system efficiency by using Carreau-Nanofluid with parameters control method. Energy, 130, 486-499(2017)
[39] Ramesh, G. K., Gireesha, B. J., Shehzad, S. A., and Abbasi, F. M. Analysis of heat transfer phenomenon in magnetohydrodynamic Casson fluid flow through Cattaneo-Christov heat diffusion theory. Communications in Theoretical Physics, 68, 91-95(2017)
[40] Hsiao, K. Combined electrical MHD heat transfer thermal extrusion system using Maxwell fluid with Radiative and viscous dissipation effects. Applied Thermal Engineering, 112, 1281-1288(2017)
[41] Kumar, N. S., Prasad, P. D., Raju, C. S. K., Varma, S. V. K., and Shehzad, S. A. Partial slip and dissipation on MHD radiative ferro-fluid over a non-linear permeable convectively heated stretching sheet. Results in Physics, 7, 1940-1949(2017)
[42] Ramesh, G. K., Kumar, K. G., Shehzad, S. A., and Gireesha, B. J. Enhancement of radiation on hydromagnetic Casson fluid flow towards a stretched cylinder with suspension of liquid-particles. Canadian Journal of Physics, 96, 18-24(2018)
[43] Hsiao, K. Micropolar nanofluid flow with MHD and viscous dissipation effects towards a stretching sheet with multimedia feature. International Journal of Heat and Mass Transfer, 112, 983-990(2017)
[44] Ramesh, G. K., Prasannakumara, B. C., Gireesha, B. J., and Rashidi, M. M. Casson fluid flow near the stagnation point over a stretching sheet with variable thickness and radiation. Journal of Applied Fluid Mechanics, 9, 1115-1122(2016)
[45] Hsiao, K. Stagnation electrical MHD nanofluid mixed convection with slip boundary on a stretching sheet. Applied Thermal Engineering, 98, 850-861(2016)
[46] Ramesh, G. K. Numerical study of the influence of heat source on stagnation point flow towards a stretching surface of a Jeffrey nanoliquid. Journal of Engineering, 2015, 382061(2015)