Theoretical Investigation of Viscosity and Thermal Conductivity ‎of a Gas along a Non-isothermal Vertical Surface in Porous ‎Environment with Dissipative Heat: Numerical Technique

Document Type : Research Paper

Authors

Department of Mathematics, Rajiv Gandhi University, Arunachal Pradesh, India

Abstract

The prime objective of the current investigation is to explore the variation of viscosity and thermal conductivity impacts on MHD convective flow over a moving non-isothermal vertical plate in presence of the viscous-dissipative heat and thermal-radiation. The compatible transformation of similarity are employed to obtain the non-linear ODE with the appropriate boundary conditions from the governing equations and the numerical solution of the boundary value problem so obtained are solved via MATLAB bvp4c solver. Naturally, the fluid viscosity and thermal-conductivity may vary from liquid to metal with temperatures and therefore, the impact of viscosity and thermal-conductivity in this investigation is quite significant. The physical parameters along with several influences on momentum, temperature, and concentration are explicated and portrayed with graphs. In addition, the velocity, temperature and concentration gradients at the surface are evaluated and displayed in tabular form. A decent agreement is found in the present outcomes with previously issued work. Furthermore, it is found that the growth of the thermal-radiation increases the gas temperature. The present study is useful for various industrial applications like metal and polymer extrusion, continuous casting, cooling process, nuclear plant and many more.

Keywords

Main Subjects

[1] Chakrabarti, A., Gupta, A.S., Hydromagnetic flow and heat transfer over a stretching sheet, Quarterly of Applied Mathematics, 37, 1979, 73–80.
[2] Sakiadis, B.C., Boundary layer behaviour on continuous solid surface: I. Boundary-layer equations for two-dimensional and axisymmetric flow, Journal of American Institute of Chemical Engineers, 7, 1961, 26–28.
[3] Cheesewright, R., Natural Convection from a plate, vertical surface in non-isothermal surroundings, International Journal of Heat and Mass Transfer, 10, 1967, 1847-1859.
[4] Helmy, K.A., MHD Unsteady Free Convection flow past a vertical porous plate, Zeitschrift für Angewandte Mathematik und Mechanik, 78, 1998, 255-270.
[5] Molla, M.M., Hossain, M.A., Yao, L.S., Radiation effect on mixed convection laminar flow along a vertical wavy surface, International Journal of Thermal Science, 43, 2004, 157-163.
[6] Pop, I., Soundalgekar, V.M., Viscous Dissipation effects on Unsteady Free Convective Flow past an infinite vertical porous plate with variable Suction, International Journal of Heat and Mass Transfer, 17(1), 1962, 85-92.
[7] Zueco, J., Ahmed, S., López-González, L.M., 2-D Unsteady Free Convective Heat and Mass Transfer Newtonian Hartmann Flow with Thermal Diffusion and Soret Effects: Network Model and Finite Differences, International Journal of Heat and Mass Transfer, 110, 2017, 467–475.
[8] Ahmed, S., Zueco, J., López-González, L.M., Numerical and analytical solutions for magneto-hydrodynamic 3D flow through two parallel porous plates, International Journal of Heat and Mass Transfer, 108, 2017, 322–331.
[9] Bansal, J.L., Viscous Fluid Dynamics, Oxford & IBH Pub. Co., New Delhi, India, 1977.
[10] Herwing, H., Gersten, K., The effect variable properties on Laminar boundary layer Flow, Warme Stoffubertrag, 20, 1986, 47–57.
[11] Lai, F.C., Kulacki, F.A., The effect of variable viscosity on convective heat transfer along a vertical surface in a saturated porous medium, International Journal of Heat and Mass Transfer, 33, 1990, 1028–31.
[12] Pop, I., Gorla, R.S.R., Rashidi, M.M., The effect of variable viscosity on flow and heat transfer to a continuous moving flat plate, International Journal of Engineering Science, 30(1), 1992, 1–6.
[13] Abel, M.S., Khan, S.K., Prasad, K.V., Study of Visco-elastic fluid and heat transfer over a stretching sheet with variable viscosity, International Journal of Non-linear Mechanics, 37, 2002, 81–88.
[14] Salem, A.M., Variable viscosity and thermal conductivity effects on MHD flow and heat transfer in viscoelastic fluid over a stretching sheet, Physics Letter A, 369(4), 2007, 315–22.
[15] Chiam, T.C., Heat transfer in a fluid with variable thermal conductivity over a linearly stretching sheet, Acta Mechanica, 129, 1998, 63–72.
[16] Pantokratoras, A., Further results on the variable viscosity on the flow and heat transfer to a continuous moving flat plate, International Journal of Engineering Science, 42, 2004, 1891–96.
[17] Mukhopadhyay, S., Layek, G.C., Effect of thermal radiation and variable fluid viscosity on free convective and heat transfer past a porous stretching surface, International Journal of Heat and Mass Transfer, 51, 2008, 2167–78.
[18] Mahanti, N.C., Gaur, P., Effect of varying viscosity and thermal conductivity on steady free convective flow and heat transfer along an isothermal vertical plate in the presence of heat sink, Journal of Applied Fluid Mechanics, 2(1), 2009, 23-28.
[19] Sarma, U., Hazarika, G.C., Effect of variable viscosity and thermal conductivity on heat and mass transfer flow along a vertical plate in the presence of magnetic field, International Journal of Physical Education, 8(3), 2009, 45–54.
[20] Seddeek, M.A., Salem, A.M., Laminar mixed convection adjacent to vertical continuously stretching sheet with variable viscosity and variable thermal diffusivity, Heat and Mass Transfer, 41, 2005, 1048-1055.
[21] Chaim, T.C., Heat transfer in a fluid with variable thermal conductivity over stretching sheet, Acta Mechanica, 129, 1998, 63-72.
[22] Chamkha, A.J., Khaled, A.R.A., Similarity solutions for hydromagnetic simultaneous heat and mass transfer by natural convection from an inclined plate with internal heat generation or absorption, Heat and Mass Transfer, 37, 2001, 117-123.
[23] Subhakar, M.J., Gangadhar, K., Reddy, N.B., Soret and Dufour effects on MHD convective flow of heat and mass transfer over a moving non-isothermal vertical plate with heat generation/absorption, Advances in Applied Science Research, 3(5), 2012, 3165-3184.
[24] Hazarika, G.C., Phukan, B., Ahmed, S., The effect of variable viscosity and thermal conductivity on unsteady free convective flow of a micropolar fluid past a vertical cone, Journal of Engineering Physics and Thermophysics, 93, 2020, 184-191.
[25] Schlichting, H., Boundary Layer Theory, McGraw-Hill Book Co., New York, 1968.
[26] Sheikholeslami, M., Jafaryar, M., Sheremet, M.A., Shafee, A., Babazadeh, H., Nanomaterial thermal performance within a pipe in presence of turbulator, Applied Nanoscience, 10, 2020, 3421–3430.
[27] Wang, G., Yao, Y., Chen, Z., Hu, P., Thermodynamic and optical analyses of a hybrid solar CPV/T system with high solar concentrating uniformity based on spectral beam splitting technology, Energy, 166, 2019, 256-266.
[28] Yu, H., Dai, W., Qian, G., Gong, X., Zhou, D., Li, X., Zhou, X., The NOx Degradation Performance of Nano-TiO2 Coating for Asphalt Pavement, Nanomaterials, 10(5), 2020, 897.
[29] Guo, C., Hu, M., Li, Z., Duan, F., He, L., Zhang, Z., Du, M., Structural hybridization of bimetallic zeolitic imidazolate framework (ZIF) nanosheets and carbon nanofibers for efficiently sensing α-synuclein oligomers, Sensors and Actuators B: Chemical, 309, 2020, 127821.
[30] Liu, C., Huang, X., Wu, Y., Deng, X., Liu, J., Zheng, Z., Hui, D., Review on the research progress of cement-based and geopolymer materials modified by graphene and graphene oxide, Nanotechnology Reviews, 9(1), 155-169, 2020.
[31] Yan, H., Xue, X., Chen, W., Wu, X., Dong, J., Liu, Y., Wang, Z., Reversible Na+ insertion/extraction in conductive polypyrrole-decorated NaTi2(PO4)3 nanocomposite with outstanding electrochemical property, Applied Surface Science, 530, 2020, 147295.
[32] Luo, X., Hu, H., Pan, Z., Pei, F., Qian, H., Miao, K., Feng, G., Efficient and stable catalysis of hollow Cu9S5 nanospheres in the Fenton-like degradation of organic dyes, Journal of Hazardous Materials, 396, 2020, 122735.
[33] He, L., Liu, J., Liu, Y., Cui, B., Hu, B., Wang, M., Du, M., Titanium dioxide encapsulated carbon-nitride nanosheets derived from MXene and melamine-cyanuric acid composite as a multifunctional electrocatalyst for hydrogen and oxygen evolution reaction and oxygen reduction reaction, Applied Catalysis B: Environmental, 248, 2019, 366-379.
[34] Feng, Q., Li, Y., Wang, N., Hao, Y., Chang, J., Wang, Z., Wang, L., A Biomimetic Nanogenerator of Reactive Nitrogen Species Based on Battlefield Transfer Strategy for Enhanced Immunotherapy, Small, 16(25), 2020, e2002138.
[35] Liu, Y., Zhang, Q., Xu, M., Yuan, H., Chen, Y., Zhang, J., You, B., Novel and efficient synthesis of Ag-ZnO nanoparticles for the sunlight-induced photocatalytic degradation, Applied Surface Science, 476, 2019, 632-640.
[36] Liu, J., Wang, C., Sun, H., Wang, H., Rong, F., He, L., Du, M., CoOx/CoNy nanoparticles encapsulated carbon-nitride nanosheets as an efficiently trifunctional electrocatalyst for overall water splitting and Zn-air battery, Applied Catalysis B: Environmental, 279, 2020, 119407.
[37] Ahmed, S., Hazarika, G.C., Gogoi, G., Investigation of variable viscosity and thermal conductivity on MHD mass transfer flow problem over a moving non-isothermal vertical plate, Journal of Naval Architecture and Marine Engineering, 17, 2020, 183-197.
[38] Hazarika, S., Ahmed, S., Yao, S.W., Investigation of Cu–water nano-fluid of natural convection hydro-magnetic heat transport in a Darcian porous regime with diffusion-thermo, Applied Nanoscience, 2021, https://doi.org/10.1007/s13204-020-01655-w.
[39] Hazarika, S., Ahmed, S., Study of Carbon Nanotubes with Casson Fluid in a Vertical Channel of Porous Media for Hydromagnetic Drag Force and Diffusion-Thermo, Journal of Scientific Research, 13(1), 2021, 31–45.
[40] Ludwig, C., Sitz. ber. Math.-Naturw. Clas. Kais. Akad. Wiss. 20, 1856, 539.
[41] Soret, C., Arch. Sci. Phys. Nat., 2, 1879, 48.
[42] Hartmann, J., Hg-Dynamics-I, Theory of the laminar flow of an electrically conducting liquid in a homogeneous magnetic field, Kgl, Danske Videnskab. Selskab Mat-Fys. Medd, 15(6), 1937, 1-28.
[43] Lorentz, H.A., La Théorie electromagnétique de Maxwell et son application aux corps mouvants, Archives Néerlandaises des Sciences Exactes et Naturelles, 25, 1892, 363–552.