Effects of Variable Thermal Conductivity on MHD Fluid Flow on Rotating Vertical Cone in the Presence of Darcy Forchheimer, Soret and Dufour Effects through a Porous Medium

I. J. Uwanta

Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Sokoto State, Nigeria.

I. D. Yale

Department of Mathematics, Kebbi State University of Science and Technology, Aleiro, Kebbi State, Nigeria.

A. Ahmed *

Department of Mathematics, Kebbi State Polytechnic, Dakingari, Kebbi State, Nigeria.

*Author to whom correspondence should be addressed.


Abstract

This research investigated the effects of Variable Thermal Conductivity on MHD fluid on a Rotating Vertical Cone in the Presence of Darcy Forchheimer, Soret and Dufour effects through a porous medium. The system of nonlinear differential equations were transformed into first order differential equations and solved using shooting technique in Matlab package Bvp4c.Furthermore, the effects of various parameters over the main physical quantities are shown graphically and also extensively discussed. The result shows that Thermal conductivity increases Tangential Velocity, Temperature and decreases Normal Velocity. Dufour increases Tangential Velocity and decreases Normal Velocity. Radiation parameter R enhances Tangential Velocity and Temperature.

Keywords: Darcy-forchheimer, soret, dufour, thermal conductivity


How to Cite

Uwanta , I. J., I. D. Yale, and A. Ahmed. 2024. “Effects of Variable Thermal Conductivity on MHD Fluid Flow on Rotating Vertical Cone in the Presence of Darcy Forchheimer, Soret and Dufour Effects through a Porous Medium”. Physical Science International Journal 28 (4):1-20. https://doi.org/10.9734/psij/2024/v28i4832.

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References

Anilkumar D, Roy S. Unsteady mixed convection flow on a rotating cone in a rotating fluid.Applied Mathematics and Computation. 2004;155: 545-561.

Chamkha AJ, Ali A. Unsteady heat and mass transfer from a rotating vertical cone with a magnetic field and heat generation or absorption effects. International Journal of Thermal Science. 2005;44:267-276.

Ece, CM. Free convection about a cone under mixed thermal boundary conditions and a magnetic field. AppliedMathematical Modelling. 2005;29:1121-1134.

Alim, MA, Alam, M Md, Chowdhury, MK. Pressure work effectson natural convection flow from a vertical circular cone with suction and non-uniform surface temperature. Journal of Mechanical Engineering. 2006;36:6-11.

Hazem, AA.Rotating disk flow and heat transfer of a conducting non newtonian fluid with suction injection and ohmic heating. Journal of the Braz. Soc. of Mech. Sci. and Eng. Xxix. 2007;2:168-173.

Award, FG, Sibanda, P. Motsa, SS, Makinde OD. Convection from an inverted cone in a porous medium with cross diffusion effects. Computer and Mathematics with Application. 2011;61: 1431-1441

Cheng, CY. Natural convection boundary layer flow in a micropolar fluid over a vertical permeable cone with variable wall temperature. International communications in Heat and Mass Transfer. 2011;38:429-433.

Kairi, RR, Murthy, PVSN. Effect of viscous dissipation on natural convection, heat and mass transfer from vertical cone in a non-Newtonian fluid saturated non-Darcy porous medium.Applied Mathematics and Computation. 2011;217:8100-8114.

Kabede T, Hoile E, Awgichew G, Walelign T. Heat and mass transfer in unsteady bounsary layer flow of Williamson nanofluid. Journal of Applied Mathematics. 2020:article ID 1890972, 13 pages.

Chamkha AJ, Rashad AM. Natural convection from a vertical permeable cone in a nano fluid saturated porous media for uniform heat and nano particles volume fraction fluxes. International Journal of Numerical Methods for Heat &Fluid Flow. 2012;22:1073-1085.

El-Kabeir SM, El-Sayed EA. Effects of thermal radiation and viscous dissipation on mhd viscoelastic free convection past a vertical isothermal cone surface with chemical reaction.International Journal of Energy and Technology. 2012;4: 1-7.

Kumar, M, Sivaraj, R. MHD viscoelastic fluid non-Darcy flow along a moving vertical cone. International Journal of Applied Mathematics and Mechanics. 2012;8;69-81.

Gilvert, M, Makinde OD. Precious S. Natural convection of viscoelastic fluid from a cone embedded in porous medium with viscous dissipation. Hindawi Mathematical problems in Engineering. 2013. Article ID 934712, 1- 11,

[Malikarjuna, B, Rashed, AM, Chamkha AJ. Chemical reaction on MHD convective heat and mass transfer flow past a rotating cone embedded in a variable porosity regime.African Mathematical Union. 2015;1-22. DOI10.1007/s13370-015-0372-1

Bilal, S, Khalil, UR, Raman, HJ, Malik, MY, Salahuddin, T: Dissipative slip flow along heat and mass transfer over a vertically rotating cone by way of chemical reaction with dufor and soret effects. API Advances. 2016;6:125-135 DOI.org/10.1063/1.4973307

Sulonocha, C, Ashwinkumar, GP, Sandeep N. Similarity solution of 3d casson nona fluid flow over a stretching sheet with convective boundary condition. Journal of Nigerian Mathematical Society. 2016;35: 128-141.

Pandit, KK, Sarma, D, Deka AK. Effects of hall current and rotation on unsteady MHD natural convection flow past a vertical flat plate with ramped wall temperature and heat absorption.British Journal of Mathematics and Computer Science. 2016;18(5):1-26 Article no.BJMCS 27221.

Khan WA, Irfan M. Khan, M. An improved heat conduction and mass diffusion models for rotating flow of an old royd-b fluid. Result in Physics. 2017;7:3583-3589.

Saleem S, Hunza R, Al-Qahtani A, Abd-El-Aziz M. Malik MY. Animasaun, IL. Magneto jeffrey nonafluid bioconvection over a rotating vertical cone due to gyrotatic microorganism. Mathematical problems in Engineering. Hindawi. 2019Art. ID 3478037:11.

Kabede T, Hoile E, Awgichew G, Walelign T. Heat and mass transfer analysis in unsteady flow of tangent hyperbplic nanofluid over a moving wedge with buoyancy and dissipation effects. Heliyon. 2020;6:e03776.

Sahzad A, Kashif A, Hina, B. Interaction of micropolar fluid structure with the porous media in the flow due to rotating cone.Alexndria Engineering Journal. 2021;60:1249-1257.

Cheng CY. Soret and dufour effects on natural convection boundary layer flow over a vertical cone in a porous medium with constant wall heat and mass fluxes.International Communications in Heat and Mass Transfer. 2011a;38:44-48.

Eswaramoothi S, Bhuvaneswari M, Sivasankaran S, Rajan S, Soret Dufour. Effects on viscoelastic boundary layer flow over a stretching surface with convective boundary condition with radiation and chemical reaction. Scientia Iranica, Transactions B: mechanical Engineering. 2016;23:2575-2586.

Sulonocha, C, Samrat, SP, Sandeep, N. Numerical investigation of magneto-hydrodynamic (mhd) radiative flow over a rotating cone in the presence of soret and chemical reaction. Propulsion and Power Research. (2018): 7, 91-101.

Krishnandan, V, Debozani, B, Sharma, BR. Soret and Dufor effects on MHD flow about a rotating vertical cone in the presence of radiation. Journal of Maths Comp. Sci. (2021): 11(3), 3188-3204.

Zeeshan, Khan, M. S.. Khan I., Eldin S. M., Hira. Numerical solution of hest and mass transfer using buingionro model through a porous stretching sheet impact of variable magnetic heat source and temperature conductivity. Science Progress. (2023): 106(3), 1-22.

Hayat, T, Muhammad, T, Al-Mezal, S. Liao, SJ. Forchheimer flow with variable thermal conductivity and cattaneo-christov heat flux. International Journal of Numerical Methods Heat Fluid Flow. (2016): 26, 2355-2369.

Hayat T, HaiderF, Muhammad T, Asaed A. Darcy-Forchheimer flow due to a curved stretching surface with cattaneo- christov double diffusion. A numerical study. Results Physics. 2017;7: 2663-2670.

Upreti, H, Pandey, AK, Kumar, M. Makinde, OD. Ohmic heating and a non-uniform source/sink roles on 3D Darcy-Forchheimer flow of CNTs nanofluid over a stretching surface. Arab Journal of Science Engineering. 2020;45: 7705-7717.

Sohail, AK, Hayat, T, Alsaedi, A. Irreversibility analysis in Darcy-Forchheimer flow of viscous fluid with Dufour and Soret effects via finite difference method.Case Studies in Thermal Engineering. 2021;26:101065.

Loganathan K, Nazek A, Fehaid A, Salem, A. Significances of Darcy-Forchheimer porous medium in third grade nanofluid with entropy features. European Physical Journal Special Topics. 2012;230: 1293-1305.

Eswaramoothi, S, Loganathan, K, Muhammad, F, Thongchai, B, Nehad, AS. Analytical and numerical investigation of darcy-forchheimer flow of a nonlinear radiative non newtonian fluid over a riga plate with entropy optimization. Ain Shams Engineering Journal. 2023;14:101887.

Elsayed ME, Nasser SE. Chebyshev finite difference method for effects of variable viscosity and variable thermal conductivity on heat transfer from moving surfaces with radiation. International Journal of Thermal Science. 2004;43:889-8899.

Zeeshan, Ahammad, N. A., Shah, N. A. Chung, J. D., Attaullah. Role of chemically magnetized nanofluid flow for energy transition over a porous stretching pipe with heat generation/absorption and its stability. Mathematics. 2023;11:1844 DOI.org/10.3390/math11081844.

Sharma, PR, Singh, G: Effect of variable thermal conductivity and heat source/sink on MHD flow near stagnation point on linear stretching sheet. Journal of Applied Fluid Mechanics. 2009;2(1):13-21.

Uwanta IJ, Usman H. Effect of variable thermal conductivity on heat and mass transfer flow over a vertical channel with magnetic field intensity. Applied and Computational Mathematics. 2014;3(2):48-56.

DOI; 10.11648/j.acm 20140302.12.

Bhuvanavijaya R, Mallikarjuna B. Effect of variable thermal conductivity on convective heat and mass transfer over a vertical plate in a rotating system with variable porosity regime. Journal Architecture and Marine Engineering; 2014. DOI.org/10.3329/jname.VIIil.16488

Mondal RK, Abdul-Kalam MA, Arifuzzaman SM, Hossain KE, Ahmed SF. Unsteady free convective flow along a vertical porous plate with variable viscosity and thermal conductivity. IOSR Journal of Mathematics. 2016;12(4): 64-71.

Ravichandra Babu, SR, Venkateswartu S, Jaya, LK: Effect of variable viscosity and thermal conductivity on heat and mass transfer flow of nano fluid over a vertical cone with chemical reaction. International Journal of Applied Engineering Research. 2018;13(18):13989-14002.

Muhammad A, Sarah F. A new shooting type method for nonlinear boundary value problems. Alexandria Engineering Journal. 2013;52:801-805.

Badradeen, A, Mohsin, HA, H. Shooting method in solving boundary value problems. International Journal Recent Research and Applied Studies. 2014; 21(1):8-30.

Summiya, P. Numerical solution of the falkner skan equation by using shooting techniques. IOSR Journal of Mathematics .(IOSR-JM). 2014;(10)6:78-83.

Chang, SH. Numerical solution of troesch's problem by simple shooting method. Applied Mathematics and Computation. 2010;216:3303-3306.

Uwanta, IJ, Yale, ID, Ahmed, A. Mathematical modelling of steady two dimension MHD fluid flow in a rotating vertical cone in the presence of forchheimer, soret and dufour through a porous medium. International Journal of Science and Applied Research. 2023; 10(2):14-35.