NUMERICAL INVESTIGATION OF MHD CASSON NANOFLUID FLOW TOWARDS A NON LINEAR STRETCHING SHEET IN PRESENCE OF DOUBLE-DIFFUSIVE EFFECTS ALONG WITH VISCOUS AND OHMIC DISSIPATION
Year 2021,
, 1 - 17, 01.02.2021
Vinita Makkar
Vikas Poply
Rangoli Goyal
Naresh Sharma
Abstract
The intention behind carrying out this research work is to analyze the steady Magnetohydrodynamic (MHD) boundary layer flow with Casson nanofluid in presence of Viscous and Ohmic dissipation effects towards a non-linear stretching sheet. Two phase representation of nanofluid studied the consequence of Brownian motion along with thermophoresis. The major purpose of study is to investigates the significant role of prominent fluid parameters especially yield stress, slip velocity, thermophoresis, Brownian motion, Eckert number, Schmidt number, magnetic parameter and non-linear stretching parameter on profile of velocity, temperature distribution and concentration while keeping the other parameters under study constant. Runge-Kutta Fehlberg (RKF) approach was adopted to numerically solve the non-linear governing equations and the linked boundary conditions by use of shooting technique. In present study, we use MATLAB for finding the final outcomes and relating the concluding results for local Nusselt number -θ_δ^' (0) with extant outcomes in literature as a limiting case in the absence of thermophoresis and Brownian motion and an excellent agreement is noted. Over all the consequence of prominent fluid parameters are explained via graphs, whereas distinction of several valuable engineering quantities like skin friction coefficient, local Nusselt number and local Sherwood number are also tabulated. The finding of present study helps to control the rate of heat transportation as well as fluid velocity in any manufacturing processes and industrial applications to make desired quality of final product.
Thanks
First author (Vinita) would like to thank Mr. Madan Lal Makkar and Mrs. Neelam Makkar for their love, support and encouragement. Additionally, all authors appreciate the constructive and valuable comments of the reviewers, which improved the manuscript.
References
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- [23] Goyal R, Vinita, Sharma N, Bhargava R. GFEM analysis of MHD nanofluid flow toward a power‐law stretching sheet in the presence of thermodiffusive effect along with regression investigation. Heat Transfer 2020; 1–23. https://doi.org/10.1002/htj.21873.
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- [29] Poply V, Vinita (2021). Analysis of Outer Velocity and Heat Transfer of Nanofluid Past a Stretching Cylinder with Heat Generation and Radiation. In: Singh P., Gupta R.K., Ray K., Bandyopadhyay A. (eds) Proceedings of International Conference on Trends in Computational and Cognitive Engineering. Advances in Intelligent Systems and Computing, vol 1169. Springer, Singapore. https://doi.org/10.1007/978-981-15-5414-8_18
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- [34] Geridönmez BP. Numerical simulation of natural convection in a porous cavity filled with ferrofluid in presence of magnetic source. Journal of Thermal Engineering 2017; 4(2): 1756–1769, doi: 10.18186/journal-of-thermal-engineering.369169.
- [35] Poply V, Singh P, Yadav AK. A study of temperature-dependent fluid properties on mhd free stream flow and heat transfer over a non-linearly stretching sheet. Procedia Engineering 2015; 127: 391 – 397.
- [36] Singh P, Poply V. Impact of free stream velocity and variable heat flux over a permeable stretching surface. International Journal of Applied Engineering Research 2015; 10: 69-76.
- [37] Kameswaran PK, Shaw S, Sibanda P. Dual solutions of Casson fluid flow over a stretching or shrinking sheet. Sadhana 2014; 39: 1573–1583.
- [38] Khan MS, Karim I, Ali LE, Islam A. Unsteady MHD free convection boundary-layer flow of a nanofluid along a stretching sheet with thermal radiation and viscous dissipation effects. Int Nano Lett 2012; 2: 1–9.
- [39] Afify AA. The influence of slip boundary condition on Casson nanofluid flow over a stretching sheet in the presence of viscous dissipation and chemical reaction. Mathematical Problems in Engineering 2017; 2017: 1–12.
- [40] Mustafa M, Khan JA. Model for flow of Casson nanofluid past a non-linearly stretching sheet considering magnetic field effects. AIP Advances 2015; 5: 1-11.
- [41] Usman M, Soomro FA, Haq RUI, Wang W, Defterli O. Thermal and velocity slip effects on Casson nanofluid flow over an inclined permeable stretching cylinder via collocation method. International Journal of Heat and Mass Transfer 2018; 122: 1255–1263.
- [42] Gireesha B, Srinivasa C, Shashikumar N, Macha M, Singh J, Mahanthesh B. Entropy generation and heat transport analysis of Casson fluid flow with viscous and Joule heating in an inclined porous microchannel. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering 2019; 233: 1173–1184.
- [43] Seth GS, Bhattacharyya A, Kumar R, Chamkha AJ. Entropy generation in hydro-magnetic nanofluid flow over a non-linear stretching sheet with Naviers velocity slip and convective heat transfer. Physics of Fluids 2018; 30: 1-15.
Year 2021,
, 1 - 17, 01.02.2021
Vinita Makkar
Vikas Poply
Rangoli Goyal
Naresh Sharma
References
- [1] Crane LJ. Flow past a stretching plate. Zeitschrift fr angewandte Mathematik und Physik ZAMP 1970; 21: 645–647.
- [2] Gupta PS, Gupta AS. Heat and mass transfer on a stretching sheet with suction or blowing. The Canadian Journal of Chemical Engineering 1977; 55: 744–746.
- [3] Yoon BB, Rao RS, Kikuchi N. Sheet stretching: A theoretical-experimental comparison. International Journal of Mechanical Sciences 1989; 31: 579–590.
- [4] Sarma MS, Rao BN. Heat transfer in a viscoelastic fluid over a stretching sheet. Journal of Mathematical Analysis and Applications 1998; 222: 268–275.
- [5] Vajravelu K. Viscous flow over a nonlinearly stretching sheet. Appl. Math. Comput. 2001; 124: 281–288.
- [6] Cortell R. Viscous flow and heat transfer over a nonlinearly stretching sheet. Applied Mathematics and Computation 2007; 184: 864–873.
- [7] Nadeem S, Hussain A, Vajravelu K. Effects of heat transfer on the stagnation flow of a third order fluid over a shrinking sheet. Zeitschrift fr Naturforschung A 2010; 65: 969–994.
- [8] Prasad K, Vajravelu K, Datti P. Mixed convection heat transfer over a non-linear stretching surface with variable fluid properties. International Journal of Non-Linear Mechanics 2010; 45: 320– 330.
- [9] Choi SUS, Eastman JA. Enhancing thermal conductivity of fluids with nanoparticles. ASME International Mechanical Engineering Congress and Exposition 1995: 1-9.
- [10] Buongiorno J. Convective transport in nanofluids. Journal of Heat Transfer 2006; 128: 240–250.
- [11] Kuznetsov A, Nield D. Natural convective boundary-layer flow of a nanofluid past a vertical plate. International Journal of Thermal Sciences 2010; 49: 243–247.
- [12] Mamaloukas C, Spartalis S, Mazumdar HP. MHD flow of a Newtonian fluid over a stretching sheet: an approximate solution. International journal of Computational and Numerical Analysis and Applications 2002; 1: 299–310.
- [13] Tamizharasi R, Kumaran V. Pressure in MHD/Brinkman flow past a stretching sheet. Communications in Nonlinear Science and Numerical Simulation 2011; 16: 4671–4681.
- [14] Hayat T, Qasim M, Mesloub S. MHD flow and heat transfer over permeable stretching sheet with slip conditions. International Journal for Numerical Methods in Fluids 2011; 66: 963–975.
- [15] Hussain A, Malik M, Salahuddin T, Bilal S, Awais M. Combined effects of viscous dissipation and joule heating on MHD sisko nanofluid over a stretching cylinder. Journal of Molecular Liquids 2017; 231: 341–352.
- [16] Vajravelu K and Cannon J. Fluid flow over a nonlinearly stretching sheet. Applied Mathematics and Computation 2006; 181: 609–618.
- [17] Matin MH, Nobari MRH, Jahangiri P. Entropy Analysis in Mixed Convection MHD flow of Nanofluid over a Non-linear Stretching Sheet. Journal of Thermal Science and Technology 2012; 7(1): 104–119.
- [18] Shawky HM, Eldabe NTM, Kamel KA, Abd-Aziz EA. MHD flow with heat and mass transfer of Williamson nanofluid over stretching sheet through porous medium. Microsystem Technologies 2019; 25: 1155–1169.
- [19] Basir MFMd, Uddin MJ, Ismail AIMd, Bg OA. Nanofluid slip flow over a stretching cylinder with schmidt and pclet number effects. AIP Advances 2016; 6: 1-15.
- [20] Pandey AK, Kumar M. Boundary layer flow and heat transfer analysis on cu-water nanofluid flow over a stretching cylinder with slip 2017; 56(4): 671–677.
- [21] Vinita V, Poply V. Impact of outer velocity MHD slip flow and heat transfer of nanofluid past a stretching cylinder. Materials Today: Proceedings 2020; 26: 3429-3435.
- [22] Vinita, Poply V, Goyal R, Sharma N. Analysis of the velocity, thermal, and concentration MHD slip flow over a nonlinear stretching cylinder in the presence of outer velocity. Heat Transfer 2020; 1–27. https://doi.org/10.1002/htj.21941.
- [23] Goyal R, Vinita, Sharma N, Bhargava R. GFEM analysis of MHD nanofluid flow toward a power‐law stretching sheet in the presence of thermodiffusive effect along with regression investigation. Heat Transfer 2020; 1–23. https://doi.org/10.1002/htj.21873.
- [24] Poply V, Singh P, Choudhary KK. Analysis of laminar boundary layer flow along a stretching cylinder in the presence of thermal radiation. WSEAS Trans Fluid Mech. 2013; 8: 159-164.
- [25] Rana P, Bhargava R. Flow and heat transfer of a nanofluid over a nonlinearly stretching sheet: A numerical study. Communications in Nonlinear Science and Numerical Simulation 2012; 17: 212– 226.
- [26] Casson N. In rheology of dispersed system, pergamon press, oxford, uk, 1959,” 1959.
- [27] Mustafa M, Hayat T, Pop I, Aziz A. Unsteady boundary layer flow of a Casson fluid due to an impulsively started moving flat plate. Heat Trans. Asian Res. 2011; 40: 563–576.
- [28] Nadeem S, Mehmood R, Akbar NS. Optimized analytical solution for oblique flow of a Casson nano fluid with convective boundary conditions. International Journal of Thermal Sciences 2014; 78: 90–100.
- [29] Poply V, Vinita (2021). Analysis of Outer Velocity and Heat Transfer of Nanofluid Past a Stretching Cylinder with Heat Generation and Radiation. In: Singh P., Gupta R.K., Ray K., Bandyopadhyay A. (eds) Proceedings of International Conference on Trends in Computational and Cognitive Engineering. Advances in Intelligent Systems and Computing, vol 1169. Springer, Singapore. https://doi.org/10.1007/978-981-15-5414-8_18
- [30] Oyelakin IS, Mondal S, Sibanda P. Unsteady Casson nanofluid flow over a stretching sheet with thermal radiation, convective and slip boundary conditions. Alexandria Engineering Journal 2016; 55: 1025–1035.
- [31] Oyelakin I, Mondal S, Sibanda P. Unsteady MHD three dimensional Casson nanofluid flow over a porous linear stretching sheet with slip condition. Frontiers in Heat and Mass Transfer 2017; 8: 1-9.
- [32] Oyelakin IS, Mondal S, Sibanda P. Nonlinear radiation in bio-convective Casson nanofluid flow. Int. J. Appl. Comput. Math 2019; 5: 1-20.
- [33] Almakki̇ M, Mondal H, Sibanda P. Entropy generation in MHD flow of viscoelastic nanofluids with homogeneous-heterogeneous reaction, partial slip and nonlinear thermal radiation. Journal of Thermal Engineering 2020; 327–345, doi: 10.18186/thermal.712452.
- [34] Geridönmez BP. Numerical simulation of natural convection in a porous cavity filled with ferrofluid in presence of magnetic source. Journal of Thermal Engineering 2017; 4(2): 1756–1769, doi: 10.18186/journal-of-thermal-engineering.369169.
- [35] Poply V, Singh P, Yadav AK. A study of temperature-dependent fluid properties on mhd free stream flow and heat transfer over a non-linearly stretching sheet. Procedia Engineering 2015; 127: 391 – 397.
- [36] Singh P, Poply V. Impact of free stream velocity and variable heat flux over a permeable stretching surface. International Journal of Applied Engineering Research 2015; 10: 69-76.
- [37] Kameswaran PK, Shaw S, Sibanda P. Dual solutions of Casson fluid flow over a stretching or shrinking sheet. Sadhana 2014; 39: 1573–1583.
- [38] Khan MS, Karim I, Ali LE, Islam A. Unsteady MHD free convection boundary-layer flow of a nanofluid along a stretching sheet with thermal radiation and viscous dissipation effects. Int Nano Lett 2012; 2: 1–9.
- [39] Afify AA. The influence of slip boundary condition on Casson nanofluid flow over a stretching sheet in the presence of viscous dissipation and chemical reaction. Mathematical Problems in Engineering 2017; 2017: 1–12.
- [40] Mustafa M, Khan JA. Model for flow of Casson nanofluid past a non-linearly stretching sheet considering magnetic field effects. AIP Advances 2015; 5: 1-11.
- [41] Usman M, Soomro FA, Haq RUI, Wang W, Defterli O. Thermal and velocity slip effects on Casson nanofluid flow over an inclined permeable stretching cylinder via collocation method. International Journal of Heat and Mass Transfer 2018; 122: 1255–1263.
- [42] Gireesha B, Srinivasa C, Shashikumar N, Macha M, Singh J, Mahanthesh B. Entropy generation and heat transport analysis of Casson fluid flow with viscous and Joule heating in an inclined porous microchannel. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering 2019; 233: 1173–1184.
- [43] Seth GS, Bhattacharyya A, Kumar R, Chamkha AJ. Entropy generation in hydro-magnetic nanofluid flow over a non-linear stretching sheet with Naviers velocity slip and convective heat transfer. Physics of Fluids 2018; 30: 1-15.