Variable Thermal Conductivity of Sutterby Nanofluid flow: a Numerical Study

The current research focuses on the impact of variable thermal conductivity on electro-magnetohydrodynamic (EMHD) flow of a Sutterby nanofluid in a Darcy-Forchheimer porous media with a stretching sheet. The impacts of thermal radiation and Christov-Cattaneo heat flux model are also considered in the study. The similarity approach is used to transform the governing mathematical model into a set of nonlinear ODEs which are then numerically solved by applying the BVP4C method. The detailed parametric studies are performed to provide more insights into the fluid flow and heat transfer behavior. It is found that the increase in magnetic field and velocity slip parameters decreases the fluid velocity. Also, the rise in the variable thermal conductivity parameter increases the temperature profile. The impacts of several controlling parameters on the velocity, temperature, concentration, skin friction coefficient, heat transfer rate, and Nusselt number are discussed and illustrated graphically and in tabular form.

[1]   Sharma, G., Kumar, A., Sharma, S., Naushad, M., Dwivedi, R. P., ALOthman, Z. A., & Mola, G. T. (2019). Novel development of nanoparticles to bimetallic nanoparticles and their composites: a review. Journal of King Saud University-Science, 31(2), 257-269.

[2]   Su, F., Deng, Y., & Ma, H. (2015). Numerical analysis of ammonia bubble absorption in a binary nanofluid. Chemical Engineering Communications, 202(4), 500-507.

[3]   Zarifi, E., Jahanfarnia, G., & Veysi, F. (2013). Subchannel analysis of nanofluids application to VVER-1000 reactor. Chemical Engineering Research and Design, 91(4), 625-632.

[4]   Sreeremya, T. S., Krishnan, A., Mohamed, A. P., Hareesh, U. S., & Ghosh, S. (2014). Synthesis and characterization of cerium oxide based nanofluids: An efficient coolant in heat transport applications. Chemical Engineering Journal, 255, 282-289.

[5]   Tripathi, D., & Bég, O. A. (2014). Mathematical modelling of peristaltic pumping of nano-fluids. In Modelling and Simulation of Diffusive Processes (pp. 69-95). Springer, Cham.

[6]   Ali, B., Hussain, S., Naqvi, S. I. R., Habib, D., & Abdal, S. (2021). Aligned magnetic and bioconvection effects on tangent hyperbolic nanofluid flow across faster/slower stretching wedge with activation energy: Finite element simulation. International Journal of Applied and Computational Mathematics, 7(4), 1-20.

[7]   Ali, B., Rasool, G., Hussain, S., Baleanu, D., & Bano, S. (2020). Finite element study of magnetohydrodynamics (MHD) and activation energy in Darcy–Forchheimer rotating flow of Casson Carreau nanofluid. Processes, 8(9), 1185.

[8]   Choi, S. U., & Eastman, J. A. (1995). Enhancing thermal conductivity of fluids with nanoparticles (No. ANL/MSD/CP-84938; CONF-951135-29). Argonne National Lab., IL (United States).

[9]   Bachok, N., Ishak, A., & Pop, I. (2011). Stagnation-point flow over a stretching/shrinking sheet in a nanofluid. Nanoscale research letters, 6(1), 1-10.

[10]                   Ali, B., Thumma, T., Habib, D., & Riaz, S. (2022). Finite element analysis on transient MHD 3D rotating flow of Maxwell and tangent hyperbolic nanofluid past a bidirectional stretching sheet with Cattaneo Christov heat flux model. Thermal Science and Engineering Progress, 28, 101089.

[11]                   Hamad, M. A. A. (2011). Analytical solution of natural convection flow of a nanofluid over a linearly stretching sheet in the presence of magnetic field. International communications in heat and mass transfer, 38(4), 487-492.

[12]                   Ibrahim, W., Shankar, B., & Nandeppanavar, M. M. (2013). MHD stagnation point flow and heat transfer due to nanofluid towards a stretching sheet. International journal of heat and mass transfer, 56(1-2), 1-9.

[13]                   Sutterby, J. L. (1966). Laminar converging flow of dilute polymer solutions in conical sections: Part I. Viscosity data, new viscosity model, tube flow solution. AIChE Journal, 12(1), 63-68.

[14]                   Batra, R. L., & Eissa, M. (1994). Helical flow of a Sutterby model fluid. Polymer-Plastics Technology and Engineering, 33(4), 489-501.

[15]                   Ahmad, S., Farooq, M., Javed, M., & Anjum, A. (2018). Double stratification effects in chemically reactive squeezed Sutterby fluid flow with thermal radiation and mixed convection. Results in physics, 8, 1250-1259.

[16]                   Bilal, S., Sohail, M., Naz, R., & Malik, M. Y. (2020). Dynamical and optimal procedure to analyze the exhibition of physical attributes imparted by Sutterby magneto-nanofluid in Darcy medium yielded by axially stretched cylinder. Canadian Journal of Physics, 98(1), 1-10.

[17]                   Hayat, T., Bibi, F., Khan, A. A., & Alsaedi, A. (2021). Entropy production minimization and non-Darcy resistance within wavy motion of Sutterby liquid subject to variable physical characteristics. Journal of Thermal Analysis and Calorimetry, 143(3), 2215-2225.

[18]                   Mir, N. A., Farooq, M., Rizwan, M., Ahmad, F., Ahmad, S., & Ahmad, B. (2020). Analysis of thermally stratified flow of Sutterby nanofluid with zero mass flux condition. Journal of Materials Research and Technology, 9(2), 1631-1639.

[19]                   Bilal, S., Sohail, M., Naz, R., Malik, M. Y., & Alghamdi, M. (2019). Upshot of ohmically dissipated Darcy-Forchheimer slip flow of magnetohydrodynamic Sutterby fluid over radiating linearly stretched surface in view of Cash and Carp method. Applied Mathematics and Mechanics, 40(6), 861-876

[20]                   Forchheimer, P. (1901). Wasserbewegung durch boden. Z. Ver. Deutsch, Ing., 45, 1782-1788.

[21]                   Muskat, M. (1938). The flow of homogeneous fluids through porous media. Soil Science, 46(2), 169.

[22]                   Khan, M. I., Alzahrani, F., & Hobiny, A. (2020). Simulation and modeling of second order velocity slip flow of micropolar ferrofluid with Darcy–Forchheimer porous medium. Journal of Materials Research and Technology, 9(4), 7335-7340.

[23]                   Eid, M. R., & Mabood, F. (2021). Entropy analysis of a hydromagnetic micropolar dusty carbon NTs-kerosene nanofluid with heat generation: Darcy–Forchheimer scheme. Journal of Thermal Analysis and Calorimetry, 143(3), 2419-2436.

[24]                   Ramzan, M., Gul, H., & Zahri, M. (2020). Darcy-Forchheimer 3D Williamson nanofluid flow with generalized Fourier and Fick’s laws in a stratified medium. Bulletin of the Polish Academy of Sciences. Technical Sciences, 68(2).

[25]                   Cattaneo, C. (1948). Sulla conduzione del calore. Atti Sem. Mat. Fis. Univ. Modena, 3, 83-101.

[26]                   Straughan, B. (2010). Thermal convection with the Cattaneo–Christov model. International Journal of Heat and Mass Transfer, 53(1-3), 95-98.

[27]                   Tibullo, V., & Zampoli, V. (2011). A uniqueness result for the Cattaneo–Christov heat conduction model applied to incompressible fluids. Mechanics Research Communications, 38(1), 77-79.

[28]                   Han, S., Zheng, L., Li, C., & Zhang, X. (2014). Coupled flow and heat transfer in viscoelastic fluid with Cattaneo–Christov heat flux model. Applied Mathematics Letters, 38, 87-93.

[29]                   Hayat, T., Farooq, M., Alsaedi, A., & Al-Solamy, F. (2015). Impact of Cattaneo-Christov heat flux in the flow over a stretching sheet with variable thickness. Aip Advances, 5(8), 087159.

[30]                   Chiam, T. C. (1996). Heat transfer with variable conductivity in a stagnation-point flow towards a stretching sheet. International Communications in Heat and Mass Transfer, 23(2), 239-248.

[31]                   Chiam, T. (1998). Heat transfer in a fluid with variable thermal conductivity over a linearly stretching sheet. Acta mechanica, 129(1), 63-72.

[32]                   Gbadeyan, J. A., Titiloye, E. O., & Adeosun, A. T. (2020). Effect of variable thermal conductivity and viscosity on Casson nanofluid flow with convective heating and velocity slip. Heliyon, 6(1), e03076.

[33]                   Hamid, M., Usman, M., Zubair, T., Haq, R. U., & Wang, W. (2018). Shape effects of MoS2 nanoparticles on rotating flow of nanofluid along a stretching surface with variable thermal conductivity: A Galerkin approach. International Journal of Heat and Mass Transfer, 124, 706-714.

[34]                   Salawu, S. O., & Dada, M. S. (2016). Radiative heat transfer of variable viscosity and thermal conductivity effects on inclined magnetic field with dissipation in a non-Darcy medium. Journal of the Nigerian Mathematical Society, 35(1), 93-106.

[35]                   Subhas, A., Prasad, K. V., & Mahaboob, A. (2005). Buoyancy force and thermal radiation effects in MHD boundary layer viscoelastic flow over continuously moving stretching surface. Int. J. Therm. Sci, 44, 465-476.

[36]                   Resler Jr, E. L., & Sears, W. R. (1958). The prospects for magneto-aerodynamics. Journal of the Aerospace Sciences, 25(4), 235-245.

[37]                   Chakraborty, S., & Paul, D. (2006). Microchannel flow control through a combined electromagnetohydrodynamic transport. Journal of Physics D: Applied Physics, 39(24), 5364.

[38]                   Buren, M., Jian, Y., & Chang, L. (2014). Electromagnetohydrodynamic flow through a microparallel channel with corrugated walls. Journal of Physics D: Applied Physics, 47(42), 425501.

[39]                   Shah, Z., Bonyah, E., Islam, S., & Gul, T. (2019). Impact of thermal radiation on electrical MHD rotating flow of Carbon nanotubes over a stretching sheet. AIP Advances, 9(1), 015115.

[40]                   Laurent, O. J. (1996). Lobatto methods. URL: https://homepage. math. uiowa. edu/~ ljay/publications. dir/Lobatto.

[41]                   Ascher, U. M., Mattheij, R. M., & Russell, R. D. (1995). Numerical solution of boundary value problems for ordinary differential equations. Society for Industrial and Applied Mathematics.