Heat transfer characteristics in Williamson fluid flow in a vertical channel with chemical reaction and entropy production
Abstract
This research endeavor investigates the natural convection flow of Williamson fluid in the region between two vertical parallel flat plates via porous medium. Impacts of viscous dissipation, joule heating, exponential space-and thermal-dependent heat sources (ESHS/THS) are invoked. Mass transfer is also studied accounting chemical reaction impact. The governing non-linear PDEs are reduced to ODEs in non-dimensional form under adequate transformation relations. The numerical technique, namely, Runge–Kutta fourth-order is utilized to tackle the problem with shooting method. Additionally, second law analysis is presented in terms of entropy production. The effects of numerous regulating parameters occurred in the problem relevant to flow, heat and mass transport, and entropy production are discussed via graphical mode of representation. Moreover, the quantities of physical significance are computed, displayed in graphical form, and discussed. For verification of acquired results, a comparison is also made using HPM with prior research and found to be in excellent agreement. It is concluded that the fluid temperature field enhances with upsurging values of pertinent parameters. The influence of the convective surface parameter and order of reaction are found to make augmentation in mass diffusion. Further, effect of Joule heating is noticed to rise rate of heat transfer while reverse scenario observed with upsurging values of heat source parameters. The influence of viscous dissipation is seen to grow entropy production.
References
Bruce RW, Na TY. Natural convection flow of Powell-Eyring fluids between two vertical flat plates. ASME; 1967.
Aung W, Fletcher LS, Sernas V. Developing laminar free convection between vertical flat plates with asymmetric heating. Int. J. Heat Mass Transf. 1972; 15(11): 2293-2308. doi: 10.1016/0017-9310(72)90048-8
Vajravelu K, Sastri KS. Fully developed laminar free convection flow between two parallel vertical walls-I. Int. J. Heat Mass Transf. 1977; 20(6): 655-660. doi: 10.1016/0017-9310(77)90052-7
Rajagopal KR, Na TY. Natural convection flow of a non-Newtonian fluid between two vertical flat plates. Acta Mechanica. 1985; 54(3-4): 239-246. doi: 10.1007/bf01184849
Cheng CH, Kou HS, Huang WH. Flow reversal and heat transfer of fully developed mixed convection in vertical channels. Journal of Thermophysics and Heat Transfer. 1990; 4(3): 375-383. doi: 10.2514/3.190
Ziabakhsh Z, Domairry G. Analytic solution of natural convection flow of a non-Newtonian fluid between two vertical flat plates using homotopy analysis method. Communications in Nonlinear Science and Numerical Simulation. 2009; 14(5): 1868-1880. doi: 10.1016/j.cnsns.2008.09.022
Narahari M, Dutta BK. Free convection flow and heat transfer between two vertical parallel plates with variable temperature at one boundary. Acta Tech. 2011; 56: 103-113.
Kargar A, Akbarzade M. Analytic solution of natural convection flow of a non-newtonian fluid between two vertical flat plates using homotopy perturbation method (HPM). World Appl. Sci. J. 2012; 20(11): 1459-1465. doi: 10.5829/idosi.wasj.2012.20.11.1707
Rashidi MM, Abelman S, Freidooni Mehr N. Entropy generation in steady MHD flow due to a rotating porous disk in a nanofluid. International Journal of Heat and Mass Transfer. 2013; 62: 515-525. doi: 10.1016/j.ijheatmasstransfer.2013.03.004
Hatami M, Hatami J, Jafaryar M, et al. Differential transformation method for Newtonian and Non-Newtonian fluids flow analysis: comparison with HPM and numerical solution. Journal of the Brazilian Society of Mechanical Sciences and Engineering. 2015; 38(2): 589-599. doi: 10.1007/s40430-014-0275-3
Raptis A, Massalas C, Tzivanidis G. Hydromagnetic free convection flow through a porous medium between two parallel plates. Phys. Lett. A 1982; 90(6): 288-289. doi: 10.1016/0375-9601(82)90118-9
Chamkha AJ. Non-Darcy fully developed mixed convection in a porous medium channel with heat generation/absorption and hydromagnetic effects. Numer. Heat Transf.; A: Appl. 1997; 32(6): 653-675. doi: 10.1080/10407789708913911
Singh KD, Pathak R. Effect of rotation and Hall current on mixed convection MHD flow through a porous medium filled in a vertical channel in presence of thermal radiation. Indian J. Pure Appl. Phys. 2012; 50: 77-85.
Das S, Jana RN, Makinde OD. An oscillatory MHD convective flow in a vertical channel filled with porous medium with Hall and thermal radiation effects. Spec. Top. Rev. Porous Media 2014; 5(1): 63-82. doi: 10.1615/SpecialTopicsRevPorousMedia.v5.i1.60
Asha SK, Sunitha G. Effect of joule heating and MHD on peristaltic blood flow of Eyring–Powell nanofluid in a non-uniform channel. J. Taibah Uni. Sci. 2019; 13(1): 155-168. doi: 10.1080/16583655.2018.1549530
Swain, BK, Parida BC, Kar S, et al. Viscous dissipation and joule heating effect on MHD flow and heat transfer past a stretching sheet embedded in a porous medium. Heliyon 2020; 6(10): e05338. doi: 10.1016/j.heliyon.2020.e05338
Ramesh K, Riaz A, Dar ZA. Simultaneous effects of MHD and Joule heating on the fundamental flows of a Casson liquid with slip boundaries. Propulsion and Power Research 2021; 10(2): 118-129. doi: 10.1016/j.jppr.2021.05.002
Ali A, Ahammad NA, Tag-Eldin E, et al. MHD williamson nanofluid flow in the rheology of thermal radiation, joule heating, and chemical reaction using the Levenberg–Marquardt neural network algorithm. Frontiers in Energy Research. 2022; 10. doi: 10.3389/fenrg.2022.965603
Williamson RV. The Flow of Pseudoplastic Materials. Industrial & Engineering Chemistry. 1929; 21(11): 1108-1111. doi: 10.1021/ie50239a035
Vasudev, R. Peristaltic Pumping of Williamson fluid through a porous medium in a horizontal channel with heat transfer. American Journal of Scientific and Industrial Research. 2010; 1(3): 656-666. doi: 10.5251/ajsir.2010.1.3.656.666
Subramanyam S, Reddy MVS, Reddy BJ. Influence of Magnetic Field on Fully Developed Free Convective Flow of a Williamson Fluid through a Porous Medium in a Vertical Channel. JAMFM. 2013; 5(1): 33-44.
Swaroopa B, Prasad KR. Influence of Radiation on MHD free Convective flow of a Williamson Fluid in a Vertical Channel. Int. J. Eng. Tech. Research. 2016; 5(2): 73-77.
Ajibade OA, Jha BK, Jibril HM, et al. Effects of dynamic viscosity and nonlinear thermal radiation on free convective flow through a vertical porous channel. Int. J. Thermofluids. 2021; 9: 100062. doi: 10.1016/j.ijft.2020.100062
Qawasmeh BR, Duwairi HM, Alrbai M. Non-Darcian forced convection heat transfer of Williamson fluid in porous media. J. Porous Media. 2021; 24(8): 23-35. doi: 10.1615/JPorMedia.2021025540
Pattanaik PC, Mishra SR, Jena S, et al. Impact of radiative and dissipative heat on the Williamson nanofluid flow within a parallel channel due to thermal buoyancy. Proc. Inst. Mech. Eng. 2022; 236(1-2): 3-18. doi: 10.1177/23977914221080046
Usman, Shaheen S, Arain MB, et al. A case study of heat transmission in a Williamson fluid flow through a ciliated porous channel: A semi-numerical approach. Case Stud. Therm. Eng. 2023; 41: 102523. doi: 10.1016/j.csite.2022.102523
Grosan T, Pop R, Pop I. Thermophoretic deposition of particles in fully developed mixed convection flow in a parallel-plate vertical channel. Heat Mass Transf. 2009; 45(4): 503-509. doi: 10.1007/s00231-008-0443-z
Ibrahim FS, Hady FM, Abdel-Gaied SM, et al. Influence of chemical reaction on heat and mass transfer of non-Newtonian fluid with yield stress by free convection from vertical surface in porous medium considering Soret effect. Appl. Math. Mech.-Engl. 2010; 31: 675-684. doi: 10.1007/s10483-010-1302-9
Uwanta IJ, Hamza MM. Effect of suction/injection on unsteady hydromagnetic convective flow of reactive viscous fluid between vertical porous plates with thermal diffusion. Int. Sch. Res. Notices. 2014; 2014. doi: 10.1155/2014/980270
Prasannakumara BC, Gireesha BJ, Gorla R, et al. Effects of chemical reaction and nonlinear thermal radiation on Williamson nanofluid slip flow over a stretching sheet embedded in a porous medium. J. Aerosp. Eng. 2015; 29(5): 04016019. doi: 10.1061/(ASCE)AS.1943-5525.0000578
Singh K, Kumar M. Influence of chemical reaction on heat and mass transfer flow of a micropolar fluid over a permeable channel with radiation and heat generation. J. Thermodyn. 2016; 2016: 8307980. doi: 10.1155/2016/8307980
Mallikarjun P, Murthy RV, Mahabaleshwar US, et al. Finite-Element Analysis of Fully Developed Mixed Convection through a Vertical Channel in the Presence of Heat Generation/Absorption with a First-Order Chemical Reaction. Defect Diffus. Forum. 2018; 388: 394-406. doi: 10.4028/www.scientific.net/DDF.388.394
Loganathan P, Dhivya M. Heat and mass transfer analysis of a convective Williamson fluid flow over a cylinder. Int. J. Fluid Mech. Res. 2020; 47(2): 171-189. doi: 10.1615/InterJFluidMechRes.2020027371
Huang JS. Chemical reaction and activation energy on heat and mass transfer for convective flow along an inclined surface in Darcy porous medium with Soret and Dufour effects. J. Mech. 2023; 39: 88-104. doi: 10.1093/jom/ufad006
Nazir S, Kashif M, Zeeshan A, et al. A study of heat and mass transfer of non-Newtonian fluid with surface chemical reaction. J. Indian Chem. Soc. 2022; 99(5): 100434. doi: 10.1016/j.jics.2022.100434
Olkha A, Kumar M. Casson fluid flow in a vertical annulus through porous medium with heat transfer characteristics and chemical reaction: An exact solution. IJMPC. 2022; 34(6): 2350078. doi: 10.1142/S012918312350078X
Olkha A, Kumar M. Heat transfer characteristics in non‐Newtonian fluid flow due to a naturally permeable curved surface and chemical reaction. Heat Transf. 2023; 52: 5431–5453. doi: 10.1002/htj.22934
Srinivas S, Malathy T, Reddy AS. A note on thermal-diffusion and chemical reaction effects on MHD pulsating flow in a porous channel with slip and convective boundary conditions. JKSUES. 2016; 28(2): 213-221. doi: 10.1016/j.jksues.2014.03.011
Oyelakin IS, Mondal S, Sibanda P. Unsteady Casson nanofluid flow over a stretching sheet with thermal radiation, convective and slip boundary conditions. Alex. Eng. J. 2016; 55(2): 1025-1035. doi: 10.1016/j.aej.2016.03.003
Sharada K, Shankar B. Effect of partial slip and convective boundary condition on MHD mixed convection flow of Williamson fluid over an exponentially stretching sheet in the presence of joule heating. Glob. J. Pure Appl. 2017; 13(9): 5965-5975.
Zeeshan A, Shehzad N, Ellahi R. Analysis of activation energy in Couette-Poiseuille flow of nanofluid in the presence of chemical reaction and convective boundary conditions. Results Phys. 2018; 8: 502-512. doi: 10.1016/j.rinp.2017.12.024
Neeraja A, Devi RR, Devika B, et al. Effects of viscous dissipation and convective boundary conditions on magnetohydrodynamics flow of casson liquid over a deformable porous channel. RINENG. 2019; 4: 100040. doi: 10.1016/j.rineng.2019.100040.
Jagadeesh S, Reddy MCK. Convection of 3D MHD non-Newtonian couple stress nanofluid flow via stretching surface. Heat Transf. 2022; 52(2): 1081-1096. doi: 10.1002/htj.22730
Zia QZ, Ullah I, Waqas MA, et al. Cross diffusion and exponential space dependent heat source impacts in radiated three-dimensional (3D) flow of Casson fluid by heated surface. Results Phys.2018; 8: 1275-1282. doi: 10.1016/j.rinp.2018.01.001
Thriveni K, Mahanthesh B, Giulio L et al. Significance of induced magnetic field and exponential space dependent heat source on quadratic convective flow of Casson fluid in a micro-channel via HPM. Math. Model. Eng. Probl. 2019; 6(3): 369-384. doi: 10.18280/mmep.060308
Mahanthesh B, Lorenzini G, Oudina FM, et al. Significance of exponential space-and thermal-dependent heat source effects on nanofluid flow due to radially elongated disk with Coriolis and Lorentz forces. J. Therm. Anal. Calorim. 2020; 141: 37-44. doi: 10.1007/s10973-019-08985-0
Nagaraja B, Gireesha BJ. Exponential space-dependent heat generation impact on MHD convective flow of Casson fluid over a curved stretching sheet with chemical reaction. J. Therm. Anal. Calorim.2021; 143(6): 4071-4079. doi: 10.1007/s10973-020-09360-0
Swain K, Animasaun IL, Ibrahim SM. Influence of exponential space-based heat source and Joule heating on nanofluid flow over an elongating/shrinking sheet with an inclined magnetic field. Int. J. Ambient Energy 2021; 43(1): 1-13. doi: 10.1080/01430750.2021.1873854
Hasibi A, Gholami A, Asadi Z et al. Importance of Induced Magnetic Field and Exponential Heat Source on Convective Flow of Casson Fluid in a Micro-channel via AGM. Theor. Appl. Mech. 2022; 12(3): 100342. doi: 10.1016/j.taml.2022.100342
Sharma BK, Kumar A, Gandhi R, et al. Exponential space and thermal-dependent heat source effects on electro-magneto-hydrodynamic Jeffery fluid flow over a vertical stretching surface. Int. J. Mod. Phys. B 2022; 36(30): 2250220. doi: 10.1142/S0217979222502204
Yessef M, Bossoufi B, Taoussi M, et al. Improving the maximum power extraction from wind turbines using a second-generation CRONE controller. Energies. 2022; 15(10): 3644. doi: 10.3390/en15103644
Chojaa H, Derouich A, Zamzoum O, et al. Robust control of DFIG-based WECS integrating an energy storage system with intelligent MPPT under a real wind profile. IEEE Access. 2023; 11: 90065-90083. doi: 10.1109/ACCESS.2023.3306722
Loulijat A, Chojaa H, El marghichi M, et al. Enhancement of LVRT Ability of DFIG Wind Turbine by an Improved Protection Scheme with a Modified Advanced Nonlinear Control Loop. Processes. 2023; 11(5): 1417. doi: 10.3390/pr11051417
Hamid C, Aziz D, Zamzoum O, et al. Robust Control System for DFIG-Based WECS and Energy Storage in reel Wind Conditions. EAI Endorsed Transactions on Energy Web. 2024; 11. doi: 10.4108/ew.4856
Bejan A. A study of entropy generation in fundamental convective heat transfer. J. Heat Transf. 1979; 101(4): 718-725. doi: 10.1115/1.3451063
Bejan A. Short Communication Notes on the History of the Method of Entropy Generation Minimization (Finite Time Thermodynamics). J. Non-Equilib. Thermodyn. 1996; 21(3): 239-242. doi: 10.1515/jnet.1996.21.3.239
Baytas AC. Entropy generation for natural convection in an inclined porous cavity. Int. J. Heat Mass Transf. 2000; 43(12): 2089-2099. doi: 10.1016/S0017-9310(99)00291-4
Makinde OD, Eegunjobi AC. Entropy generation in a couple stress fluid flow through a vertical channel filled with saturated porous media. Entropy 2013; 15(11): 4589-4606. doi: 10.3390/e15114589
Das S, Banu AS, Jana RN, et al. Entropy analysis on MHD pseudo-plastic nanofluid flow through a vertical porous channel with convective heating. Alex. Eng. J. 2015; 54(3): 325-337. doi: 10.1016/j.aej.2015.05.003
Maskaniyan M, Nazari M, Rashidi S, et al. Natural convection and entropy generation analysis inside a channel with a porous plate mounted as a cooling system. TSEP 2018; 6: 186-193. doi: 10.1016/j.tsep.2018.04.003
Yusuf TA, Mabood F, Prasannakumara BC et al. Magneto-bioconvection flow of Williamson nanofluid over an inclined plate with gyrotactic microorganisms and entropy generation. Fluids. 2021; 6(3): 109. doi: 10.3390/fluids6030109
Olkha A, Dadheech A. Second Law Analysis for Radiative Magnetohydrodynamics Slip Flow for Two Different Non-Newtonian Fluid with Heat Source. J. Nanofluids. 2021; 10(3): 447-461. doi: 10.3390/fluids6030109
Reddy PBA, Salah T, Jakeer S, et al. Entropy generation due to magneto-natural convection in a square enclosure with heated corners saturated porous medium using Cu/water nanofluid. Chin. J. Phys. 2022; 77: 1863-1884. doi: 10.1016/j.cjph.2022.01.012
Raje A, Bhise AA, Kulkarni A. Entropy analysis of the MHD Jeffrey fluid flow in an inclined porous pipe with convective boundaries. Int. J. Thermofluids. 2023; 17: 100275. doi: 10.1016/j.ijft.2022.100275
Balamurugan KS, Varma NU, Prasad JLR. Entropy generation analysis on forced and free convection flow in a vertical porous channel with aligned magnetic field and Navier slip. Heat Transf. 2023. doi: 10.1002/htj.22897
He JH. Homotopy perturbation technique. Comp. Methods Appl. Mech. Eng. 1999; 178(3-4): 257-262. doi: 10.1016/S0045-7825(99)00018-3
He JH. Homotopy perturbation method: a new nonlinear analytical technique. Appl. Math. Comp. 2003; 135(1): 73-79. doi: 10.1016/S0096-3003(01)00312-5
He JH. An elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering. Int. J. Mod. Phy. B. 2008; 22(21): 3487-3578. doi: 10.1142/s0217979208048668
Singh AK and Paul T. Transient natural convection between two vertical walls heated/cooled asymmetrically. Int. J. Appl. Mech. 2006; 11(1): 143-154.
Copyright (c) 2024 Amala Olkha, Mukesh Kumar
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors contributing to this journal agree to publish their articles under the Creative Commons Attribution 4.0 International License, allowing third parties to share their work (copy, distribute, transmit) and to adapt it for any purpose, even commercially, under the condition that the authors are given credit. With this license, authors hold the copyright.