Journal of Applied and Computational Mechanics
Micropolar Fluid Flow Induced due to a Stretching Sheet with Heat Source/Sink and Surface Heat Flux Boundary Condition Effects
Document Type : Research Paper
Authors
1 Department of Mathematics, Vaagdevi College of Engineering, Warangal -506005, Telangana, India
2 Department of Mathematics, B V Raju Institute of Technology, Medak-502313, Telangana, India
3 Department of Mathematics, SAS, Vellore institute of Technology (VIT University), Vellore-632014, Tamilnadu, India
Abstract
Computational and mathematical models provide an important compliment to experimental studies in the development of solar energy engineering in case of electro-conductive magnetic micropolar polymers. Inspired by further understanding the complex fluid dynamics of these processes, we examine herein the non-linear steady, hydromagnetic micropolar flow with radiation and heat source/sink effects included. The transformed non-dimensional governing partial differential equations are solved with the R-K fourth order with shooting technique subjected to appropriate boundary conditions. The characteristics of the embedded parameters are obtained and presented through graphs. Velocity and microrotation of the fluid decreased with enhancing values of material parameter and suction/injection parameter. Electric field parameter has ability to enhance velocity, but temperature shows opposite behaviour. Microrotation increases for both magnetic field and surface temperature parameters.
Keywords
- Micropolar Fluid
- Heat source/sink
- stretching Sheet
- Partial slip
- Surface heat flux boundary conditions
Main Subjects
[1] Eringen, A.C., Theory of micropolar fluids, Journal of Mathematics and Mechanics, 16, 1966, 1–18.
[2] Eringen, A.C., Theory of thermo Microfluids, Journal of Mathematical Analysis and Applications, 38, 1972, 480–96.
[3] Mirzaaghaian, A., Ganji, D.D., Application of differential transformation method in micro polar fluid flow and heat transfer through permeable walls, Alexandria Engineering Journal, 55, 2016, 2183–2191.
[4] Siddiqa, S., Faryad, A., Begum, N., Hossain, M.A., Rama Subba Reddy, G., Periodic magnetohydrodynamic natural convection flow of a micropolar fluid with radiation, International Journal of Thermal Science, 111, 2017, 215-222.
[5] Sui, J., Zhao, P., Cheng, Z., Doi, M., Influence of particulate thermophoresis on convection heat and mass transfer in a slip flow of a viscoelasticity-based micropolar fluid, International Journal of Heat Mass Transfer, 119, 2018, 40–51.
[6] Alizadeh, M., Dogonchi, A.S., Ganji, D.D., Micropolar nanofluid flow and heat transfer between penetrable walls in the presence of thermal radiation and magnetic field, Case Studies Thermal Engineering, 12, 2018, 319–332.
[7] Shamshuddin, MD., Satya Narayana, P.V., Primary and secondary flows on unsteady MHD free convective micropolar fluid flow past an inclined plate in a rotating system: a finite element analysis, Fluid Dynamic and Material Processing,14(1), 2018, 57-86.
[8] Miroshnichenko, I.V., Sheremet, M.A., Pop, I., Natural convection in a trapezoidal cavity filled with a micropolar fluid under the effect of a local heat source, International Journal of Mechanical Science, 120, 2017, 182–189.
[9] Abbas, M.A., Faraz, N., Bai, Y.Q., Khan, Y., Analytical study of the non-orthogonal stagnation point flow of a micro polar fluid, Journal of King Saud University- Engineering Science, 29, 2017, 126-132.
[10] Venkateswarlu, B., Satya Narayana, P.V., Effects of thermal radiation on unsteady MHD micropolar fluid past a vertical porous plate in the presence of radiation absorption, International Journal of Engineering Science and Computing, 6(9), 2016, 1-12.
[11] Chen, C.H., Effect of magnetic field and suction/injection on convection heat transfer of non-Newtonian power law fluids past a power-law stretched sheet with surface heat flux, International Journal of Thermal Science, 47(7), 2008, 954-961.
[12] Kumar, H., Heat transfer over a stretching porous sheet subjected to power law heat flux in presence of heat source, Thermal Science, 15, 2011, 187-194.
[13] Elbashbeshy, E.M.A., Aldawody, D.A., Heat transfer over an unsteady stretching surface with variable heat flux in the presence of a heat source or sink, Computer & Mathematics with Applications, 60(10), 2010, 2806-2811.
[14] Turkyilmazoglu, M., Mixed convection flow of magnetohydrodynamic micropolar fluid due to a porous heated/cooled deformable plate: Exact solutions, International Journal of Heat and Mass Transfer, 106, 2017, 127–134.
[15] Khan, M., Irfan, M., Khan, W.A., Impact of heat source/sink on radiative heat transfer to Maxwell nanofluid subject to revised mass flux condition, Results in Physics, 9, 2018, 81-857.
[16] Waqas, M., Farooq, M., Khan, M.I., Alsaedi, A., Hayat, T., Yasmeen, T., Magnetohydrodynamic (MHD) mixed convection flow of micropolar liquid due to nonlinear stretched sheet with convective condition, International Journal of Heat and Mass Transfer, 102, 2016, 766–772.
[17] Baag, S., Mishra, S.R., Dash, G.C., Acharya, M.R., Numerical investigation on MHD micropolar fluid flow toward a stagnation point on a vertical surface with heat source and chemical reaction, Journal of King Saud University-Engineering Science, 29, 2017, 75–83.
[18] Elbashbeshy, E.M.A.R., Abdelgaber, K.M., Asker, H.G., Unsteady flow of micropolar Maxwell fluid over stretching surface in the presence of magnetic field, International Journal of Electronic and Engineering Computer Science, 2(4), 2017, 28-34.
[19] Shaheen, A., Muhammad, A., Kashif, A., MHD flow and heat transfer analysis of micropolar fluid through a porous medium between two stretchable disks using Quasi-linearization method, Iranian Journal of Chemistry & Chemical Engineering, 36(4), 2017, 1-15.
[20] Mahmoud, M.A.A., Waheed, S.E., MHD flow and heat transfer of a micropolar fluid over a stretching surface with heat generation (absorption) and slip velocity, Journal of Egyptian Mathematical Society, 20, 2012, 20–27.
[21] Doh, D.H., Muthtamilselvan, M., Thermophoretic particle deposition on magnetohydrodynamic flow of micropolar fluid due to a rotating disk, International Journal of Mechanical Science, 130, 2017, 350–359.
[22] Ramzan, M., Farooq, M., Hayat, T., Chung, J.D., Radiative and Joule heating effects in the MHD flow of a micropolar fluid with partial slip and convective boundary condition, Journal of Molecular Liquids, 221, 2016, 394–400.
[23] Abbas, N., Saleem, A., Nadeem, S., Alderremy, A.A., Khan, A.U., On stagnation point flow of a micropolar nanofluid past a circular cylinder with velocity and thermal slip, Results in Physics, 9, 2018, 1224-1232.
[24] Pal, D., Biswas, S., Magnetohydrodynamic convective-radiative oscillatory flow of a chemically reactive micropolar fluid in a porous medium, Propulsion and Power Research, 7(2), 2018, 158-170.
[25] Sheikholeslami, M., Shehzad, S.A., Li, Z., Shafee, A., Numerical modeling for alumina nanofluid magnetohydrodynamic convective heat transfer in a permeable medium using Darcy law, International Journal of Heat and Mass Transfer, 127, 2018, 614-622.
[26] Shah, Z., Islam, S., Gul, T., Bonyan, E., Khan, M.A., The electrical MHD and hall current impact on micropolar nanofluid flow between rotating parallel plates, Results in Physics, 9, 2018, 1201-1214.
[27] Jusoh, R., Nazar, R., Pop, I., Magnetohydrodynamic rotating flow and heat transfer of ferrofluid due to an exponentially permeable stretching/shrinking sheet, Journal of Magnetism and Magnetic Materials, 465, 2018, 365-374.
[28] Gupta, D., Kumar, L., Bég, O.A., Singh, B., Finite element analysis of MHD flow of micropolar fluid over a shrinking sheet with a convective surface boundary condition, Journal of Engineering Thermophysics, 27(2), 2018, 202–220.
[29] Narla V.K., Tripathi, D., Bég, O.A., Kadir, A., Modeling transient magnetohydrodynamic peristaltic pumping of electro-conductive viscoelastic fluids through a deformable curved channel, Journal of Engineering Mathematics, 111, 2018,127–143.
[30] Din, S.T.M., Jan, S.U., Khan, U., Ahmed, N., MHD flow of radiative micropolar nanofluid in a porous channel: optimal and numerical solutions, Neural Computing & Applications, 29, 2018, 793–801.
[31] Soomro, F.A., Rizwan Ul Haq., Al-Mdallal, Q.M., Zhang, Q., Heat generation/absorption and nonlinear radiation effects on stagnation point flow of nanofluid along a moving surface, Results in Physics, 8, 2018, 404-414.
[32] Prabhakar, B., Rizwan Ul Haq., Shankar, B., Al-Mdallal, Q.M., Thermal radiation and slip effects on MHD stagnation point flow of non-Newtonian nanofluid over a convective stretching surface, Neural Computing and Applications, 31(1), 2017, 207-217.
[33] Qasim, M., Khan, Z.H., Khan, I., Al-Mdallal, Q.M., Analysis of entropy generation in flow of methanol-based nanofluid in a sinusoidal wavy channel, Entropy, 19(10), 2017, 409.
[34] Ganesh, N.V., Al-Mdallal, Q.M., Chamkha, A.J., A numerical investigation of Newtonian fluid flow with buoyancy, thermal slip of order two and entropy generation, Case Studies in Thermal Engineering, 13, 2019, Article ID:100376.
[35] Ganesh, N.V., Kameswaran, P.K., Al-Mdallal, Q.M., Hakeem, A.K.A., Ganga, B., Non-linear thermal radiative Marangoni boundary layer flow of gamma Al2O3 nanofluids past a stretching sheet, Journal of Nanofluids, 7(5), 2018, 944-950.
[36] Singh, K., Kumar, M., MHD slips flow of a micro-polar fluid due to moving plate in porous medium with chemical reaction and thermal radiation: A lie group analysis, International Journal of Applied and Computational Mathematics, 4, 2018, 1-17.
[37] Pradhan, B., Das, S.S., Paul, A.K., Dash, R.C., Unsteady free convection flow of a viscous incompressible polar fluid past a semi-infinite vertical porous moving plate, International Journal of Applied Engineering Research, 12(21), 2017, 10958-10963.
[38] Harish Babu, D., Satya Narayana, P.V., Influence of variable permeability and radiation absorption on heat and mass transfer in MHD micropolar flow over a vertical moving porous plate, ISRN Thermodynamics, Article ID: 953536, 2013, 1-17.
[39] Khan, M., Irfan, M., Khan, W.A., Thermophysical Properties of unsteady 3D flow of magneto Carreau fluid in the presence of chemical species: a numerical approach, Journal of Brazilian Society of Mechanical Sciences and Engineering, 40, 2018, 108.
[40] Irfan, M., Khan, W.A., Khan, M., Gulzar, M.M., Influence of Arrhenius activation energy in chemically reactive radiative flow of 3D Carreau nanofluid with nonlinear mixed convection, Journal of Physics and Chemistry of Solids, 12, 2019, 141-152.
[41] Hsiao, K.L., Micropolar nanofluid flow with MHD and viscous dissipation effects towards a stretching sheet with multimedia feature, International Journal of Heat and Mass Transfer, 112, 2017, 983-990.
[42] Hsiao, K.L., Stagnation electrical MHD nanofluid mixed convection with slip boundary on a stretching sheet, Applied Thermal Engineering, 98, 2016, 850-861.
[43] Hsiao, K.L., Combined electrical MHD heat transfer thermal extrusion system using Maxwell fluid with radiative and viscous dissipation effects, Applied Thermal Engineering, 112, 2017, 1281-1288.
[44] Hsiao, K.L., To promote radiation electrical MHD activation energy thermal extrusion manufacturing system efficiency by using Carreau-nanofluid with parameters control method, Energy, 130, 2017, 983-990.
[45] Mostafa, A.A.M., Shimaa, E.W., MHD flow and heat transfer of a micropolar fluid over a stretching surface with heat generation (absorption) and slip velocity, Journal of Egyptian Mathematical Society, 20, 2012, 20-27.
[46] Guram, G.S., Smith, A.C., Stagnation point flows of micropolar fluids with strong and weak interactions, Computers and Mathematics with Applications, 6, 1980, 231-233.
[47] Ahmadi, G., Self-similar solution of incompressible micropolar boundary layer flow over a semi-infinite plate, International Journal of Engineering Science, 14, 1976, 639-646.
[48] J. Peddieson, An application of the micropolar fluid model to the calculation of turbulent shear flow, International Journal of Engineering Science, 10, 1972, 23-32.
[49] Stokes, V.K., Theories of fluids with microstructure, Springer, New York, 1984.
[50] Modest, M.F., Radiation heat transfer, McGraw-Hill, New York, 1992.
[51] Brewster, M.Q., Thermal radiative transfer and properties, John Wiley, New York, 1992.
[52] Cortell, R., A numerical tackling on Sakiadis flow with thermal radiation, Chinese Physics Letters, 25, 2008, 1340-1342.
[53] Khan, W.A., Khan, M., Irfan, M., Alshomrani, A.S., Impact of melting heat transfer and nonlinear radiative heaty flux mechanism for the generalized Burgers fluids, Results in Physics, 7, 2017, 4025-4032.
[54] Thirupathi, T., Mishra, S.R., Effect of Viscous dissipation and Joule heating on MHD Jeffery nanofluid flow with and without multi slip boundary conditions, Journal of Nanofluids, 7(3), 2018, 516–526.
)
