Journal of Applied and Computational Mechanics
Magneto Casson-Carreau Fluid Flow through a Circular Porous Cylinder with Partial Slip
Document Type : Research Paper
Authors
1 Department of Mathematics, Sri Sai Institute of Technology and Science, Rayachoty, A.P., 516270, India
2 Department of Mathematics, Walchand Institute of Technology, Solapur, M.H., 413006, India
3 Laboratory of Mechanics, Faculty of Sciences, Hassan II University, BP, Maarif Casablanca, 5366, Morocco
4 Department of Mathematics, Sreenivasa Institute of Technology and Management Studies, Chittoor, A.P., 517125, India
5 Department of Mathematics, K.L.E Society’s J.T. College, Gadag, Karnataka, 582101, India
Abstract
In the current study, a comparative analysis of two-dimensional heat transfer by the free convective flow of non-Newtonian Casson and Carreau fluid in electro-conductive polymer on the outside surface of a horizontal circular cylinder under slip and radial magnetic field effects is regarded. The Casson and Carreau fluid model formulation were first developed for the problem of the boundary layer of the horizontal circular cylinder and by using non-similarity transformations, the combined governing partial differential equations are translated into ordinary differential equations. The differential equations obtained are resolved by the Keller Box Method (KBM). The impact of the key parameters, the rate of heat transfer and skin friction is evaluated through graphs and tables. The result reveals that an increase in magnetic number decreases the velocity field of both Casson and Carreau fluid also Casson fluid is higher values when compared to Carreau fluid in variation of magnetic number.
Keywords
Main Subjects
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[1] Livescu, S., Mathematical Modeling of Thixotropic Drilling Mud and Crude Oil Flow in Wells and Pipelines–A review, Journal of Petroleum Science and Engineering, 98/99, 2012, 174–184.
[2] Hron, J., Málek, J., Pustějovská, P., Rajagopal, K.R., On the Modelling of the Synovial Fluid, Advances in Tribology, 2010, Article ID 104957.
[3] Loix, F., Orgéas, L., Geindreau, C., Badel, P., Boisse, P., Bloch, J.F., Flow of Non-Newtonian Liquid Polymers Through Deformed Composites Reinforcements, Composites Science and Technology, 69, 2009, 612–619.
[4] Kechichian, V., Crivellari, G.P., Gut, J.A.W., Tadini, C.C., Modelling of Continuous Thermal Processing of a Non-Newtonian Liquid Food under Diffusive Laminar Flow in a Tubular System, International Journal of Heat and Mass Transfer, 55, 2012, 5783–5792.
[5] Mukhopadhyay, S., Casson Fluid Flow and Heat Transfer over a Non-Linearly Stretching Surface, Chinese Physics B, 22(7), 2013, 1–5.
[6] Eldabe, N.T., Saddeck, G., Elsayed, A.F., Heat Transfer of MHD Non-Newtonian Casson Fluid Flow between Two Rotating Cylinders, Mechanics and Mechanical Engineering, 64, 1995, 41–64.
[7]Pramanik, S., Casson Fluid Flow and Heat Transfer Past an Exponentially Porous Stretching Surface in Presence of Thermal Radiation, Ain Shams Engineering Journal, 5, 2014, 205–212.
[8] Ghannam, G., Esmail, N., Flow Behavior of Enhanced Oil Recovery Alcoflood Polymers, Journal of Applied Polymer Science, 85 (14), 2002, 2896–2904.
[9] Tassaddiq, A., Khan, I., Nisar, K.S., Singh, J., MHD Flow of a generalized Casson Fluid with Newtonian Heating: A Fractional Model with MIttag-Leffler Memory, Alexandria Engineering Journal, 59(5), 2020, 3049–3059.
[10] Ramzan, M., Shaheen, N., Chung, J.D., Kadry, S., Chu, Y.M., Howari, F., Impact of Newtonian Heating and Fourier and Fick’s Laws on a Magnetohydrodynamic Dusty Casson Nanofluid Flow with Variable Heat Source/Sink over a Stretching Cylinder, Scientific Reports, 11, 2021, 2357.
[11] Nazeer, M., Ahmad, F., Ali, W., Saleem, M.I., Khaliq, Z., Chu, Y.M., Perturbation and Numerical Solutions of Non-Newtonian Fluid Bounded with in a Porous Channel: Applications of Pseudo-Spectral Collocation Method, Numerical Methods for Partial Differential Equations, 2020, 1-15.
[12] Nazeer, M., Khan, M.I., Kadry, S., Chu, Y.M, Ahmad, F., Ali, W., Irfan, M., Shaheen, M., Regula Perturbation Solution of Couette Flow (Non-Newtonian) between Two Porous Plates: A Numerical Analysis with Irreversibility, Applied Mathematics and Mechanics (English Edition), 42, 2021, 127–142.
[13] Ansari, MD. S., Otegbeye, O., Trivedi, M., Goqo, S.P., Magnetohydrodynamic Bio-Convective Casson Nanofluid Flow: A Numerical Simulation by Paired Quasilinearization, Journal of Applied and Computational Mechanics, 5(4), 2021, 2024-2039.
[14] Trivedi, M., Otegbeye, O., Ansari, MD.S., Motsa, S.S., A Paired Quasilinearization on Magnetohydrodynamic Flow and Heat Transfer of Casson Nanofluid with Hall Effects, Journal of Applied and Computational Mechanics, 5(5), 2019, 849-860.
[15] Venkateswarlu, B., Satya Narayana, P.V., Cu-Al2O3/H2O Hybrid Nanofluid Flow past a Porous Stretching Sheet due to Temperature Dependent Viscosity and Viscous Dissipation, Heat Transfer, 50(1), 2021, 432-449.
[16] Venkateswarlu, B., Satya Narayana, P.V., Variable Wall Concentration and Slip Effects on MHD Nanofluid Flow Past a Porous Vertical Plate, Journal of Nanofluids, 8(4), 2019, 838-844.
[17] Casson, N., A Flow Equation for Pigment Oil-Suspensions of the Printing Ink Type, In: Mill, C.C., Ed., Rheology of Disperse Systems (C.C. Mill, ed.), Pergamon Press, London, 1959, 84–104.
[18] Bird, R.R., Dai, G.C., Yarusso, B.J., The Rheology and Flow of Viscoplastic Materials, Review in Chemical Engineering, 1, 1983, 1–83.
[19] Hayat, T., Pop., I., Hendi, A.A., Stagnation-point Flow and Heat Transfer of a Casson Fluid Towards a Stretching Sheet, Zeitschrift fur Naturforschung A, 67, 2012, 70–76.
[20] Nasir, M.S., Butt, A.S., Ali, A., Unsteady Chemically-Reacting Casson Fluid Flow in an Irregular Channel with Convective Boundary, Zeitschrift fur Naturforschung A, 70(8), 2015, 10–18.
[21] Venkateswarlu, B., Satya Narayana, P.V., Influence of Variable Thermal Conductivity on MHD Casson Fluid Flow over a Stretching Sheet with Dissipation, Soret and Dufour Effects, Frontiers in Heat and Mass Transfer, 7, 3016, 1-16.
[22] Venkateswarlu, B., Satya Narayana, P.V., Chemical Reaction and Radiation Absorption Effects on the Flow and Heat Transfer of Nanofluid in a Rotating System, Applied Nanoscience, 5(3), 2015, 351-360.
[23] Khellaf, K., Lauriat, G., Numerical Study of Heat Transfer in a Non-Newtonian Carreau-Fluid between Rotating Concentric Vertical Cylinders, Journal of Non-Newtonian Fluid Mechanics, 89, 2000, 45–61.
[24] Khan, M., Hashim, Hussain, M., Azam, M., Magnetohydrodynamic Flow of Carreau Fluid over a Convectively Heated Surface in the Presence of Non-Linear Radiation, Journal of Magnetism and Magnetic Materials, 412, 2016, 63–68.
[25] Raju, C.S.K., Sandeep, N., Falkner-Skan Flow of a Magnetic-Carreau Fluid Past a Wedge in the Presence of Cross Diffusion Effects, The European Physical Journal Plus, 131, 2016, 267.
[26] Akbar, N.S., Nadeem, S., Ul Haq, R., Ye, S., MHD Stagnation Point Flow of Carreau Fluid toward a Permeable Shrinking Sheet: Dual Solutions, Ain Shams Engineering Journal, 5(4), 2014, 1233–1239.
[27] Abbas, T., Rehman, S., Ali, R.S, Idrees, M., Qayyum, M., Analysis of MHD Carreau Fluid Flow over a Stretching Permeable Sheet with Variable Viscosity and Thermal Conductivity, Physica A: Statistical Mechanics and its Applications, 551, 2020, 124225.
[28] Azam, M., Xu, T., Mabood, F., Khan, M., Non-linear Radiative Bioconvection Flow of Cross Nano-material with Gyrotactic Microorganism and Activation Energy, International Communication in Heat and Mass Transfer, 127, 2021, 105530
[29] Song, Y.Q., Waqas, H., Al-Khaled, K., Farooq, U., Khan, S.U., Khan, M.I., Chu, Y.M., Qayyum, S., Bioconvection Analysis for Sutter by Nanofluid over an Axially Rigid Cylinder with Melting Heat Transfer and Variable Thermal Features: A Marangoni and Solutal Model, Alexandria Engineering Journal, 60, 2021, 4663-4675.
[30] Malik, M.K., Salahuddin, T., Hussain, A., Bilal, S., Awais, M., Homogeneous-Heterogeneous Reactions in Williamson Fluid Model over a Stretching Cylinder by using Keller Box Method, AIP Advances, 5, 2015, 107227.
[31] Azam, M., Xu, T., Shakoor, A., Khan, M., Effects of Arrhenius Activation Energy in Development of Covalent Bonding in Axisymmetric Flow of Radiative-Cross Nanofluid, International Communication in Heat and Mass Transfer, 113, 2020, 104547.
[32] Azam, M., Mabood, F., Xu, T., Waly, M., Tlili, I., Entropy Optimized Radiative Heat Transportation in Axisymmetric Flow of Williamson Nanofluid with Activation Energy, Results in Physics, 19(3), 2020, 103576.
[33] Rehman, K.U. Khan, A.A., Malik, M.Y., Ali, U., Naseer, M., Numerical Analysis Subject to Double Stratification and Chemically Reactive Species on Williamson Dual Convection Fluid Flow Yield by an Inclined Stretching Cylindrical Surface, Chinese Journal of Physics, 55, 2017, 1637-1652.
[34] Alsemiry, R.D., Sayed, H.M., Amin, N., Mathematical Analysis of Carreau Fluid Flow and Heat transfer within an Eccentric Catheterized Artery, Alexandria Engineering Journal, 61(1), 2022, 523-539.
[35] Afzal, S., Siddique, I., Jarad, F., Ali, R., Abdal, S., Hussain, S., Significance of Double Diffusion for Unsteady Carreau Micropolar Nanofluid Transportation Across an Extending Sheet with Thermo-Radiation and Uniform Heat Source, Case Studies in Thermal Engineering, 28, 2021, 101397
[36] Bilal, M., Saeed, A., Gul, T., Rehman, M., Khan, A., Thin Film Flow of Carreau Fluid over a Stretching Surface Including the Couple Stress and Uniform Magnetic Field, Partial Differential Equations in Applied Mathematics, 4, 2021, 100162.
[37] Shehzad, S.A., Madhu, M., Shashi Kumar, N.S., Gireesha, B.J., Mahanthesh, B., Thermal and Entropy Generation of Non-Newtonian Magneto-Carreau Fluid Flow in Microchannel, Journal of Thermal Analysis and Calorimetry, 143, 2021, 2717-2727.
[38] Noreen, S., Kausar, T., Tripathi, D., Ul Ain, Q., Lu, D.C., Heat Transfer Analysis on Creeping Flow Carreau Fluid Driven by Peristaltic Pumping in an Inclined Asymmetric Channel, Thermal Science and Engineering Progress, 17(1), 2020, 100486.
[39] Raza, J., Thermal Radiation and Slip Effects on Magnetohydrodynamic (MHD) Stagnation Point Flow of Casson Fluid over a Convective Stretching Sheet, Propulsion and Power Research, 8(2), 2019, 138–146.
[40] Santoshi, P.N., Ramana Reddy, G.V., Padma, P., Numerical Scrutinization of Three Dimensional Casson-Carreau Nanofluid Flow, Journal of Applied and Computational Mechanics, 6(2), 2020, 531-542.
[41] Nagendra, N., Amanulla, CH., Sudhakar Reddy, M., Slip Effects on MHD Flow of a Williamson Fluid from an Isothermal Sphere: A Numerical Study, Modelling Measurement and Control B, 86(3), 2017, 782-807.
[42] Amanulla, CH., Wakif, A., Saleem, S., Numerical Study of a Williamson Fluid Past a Semi-Infinite Vertical Plate with Convective Heating and Radiation Effects, Diffusion Foundations, 28, 2020, 1-15.
[43] Liu, Y., Gehde, M., Effects of Surface Roughness and Processing Parameters on Heat Transfer Coefficient between Polymer and Cavity Wall During Injection Molding, International Journal of Advanced Manufacturing Technology, 84, 2016, 1325–1333.
[44] Hatzikiriakos, S.G., Mitsoulis, E., Slip Effects in Tapered Dies, Polymer Engineering and Science, 49(10), 2009, 1960–1969.
[45] Sparrow, E.M., Lin, S.H., Laminar Heat Transfer in Tubes under Slip-Flow Conditions, ASME Journal of Heat Transfer, 84, 1962, 363–639.
[46] Subba Rao, A., Prasad, V.R., Bhaskar Reddy, N., Bég, O.A., Heat Transfer in a Casson Rheological Fluid from a Semi-Infinite Vertical Plate with Partial Slip, Heat Transfer Asian Research, 44(3), 2015, 272–291.
[47] Uddin, MD.J., Khan, W.A., Ismail, A.I.MD., Bég, O.A., Computational Study of Three-Dimensional Stagnation Point Nanofluid Bio-Convection Flow on a Moving Surface with Anisotropic Slip and Thermal Jump Effects, ASME Journal of Heat Transfer, 138(10), 2016, 104502.
[48] Madhu, M., Mahanthesh, B., Shashi Kumar, N.S., Shehzad, S.A., Khan, S.U., Gireesha, B.J., Performance of Second Law in Carreau Fluid Flow by an Inclined Microchannel with Radiative Heated Convective Condition, International Communications in Heat and Mass Transfer, 117, 2020, 104761.
[49] Salahuddin, T., Carreau Fluid Model towards a Stretching Cylinder: Using Keller Box and Shooting Method, Ain Shams Engineering Journal, 11(2), 2020, 495–500.
[50] Mahanthesh, B., Animasaun, I.L., Gorji, M.R., Alarifi, I.M., Quadratic Convective Transport of Dust Casson and Dusty Carreau Fluids Past a Stretched Surface with Nonlinear Thermal Radiation, Convective Condition and Non-Uniform Heat Source/Sink, Physica A: Statistical Mechanics and its Applications, 535(1), 2019, 122471.
[51] Amanulla, CH., Wakif, A., Boulahia, Z., Reddy, M.S., Nagendra, N., Numerical Investigations on Magnetic Field Modeling for Carreau Non-Newtonian Fluid Flow Past an Isothermal Sphere, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40, 2018, 462.
[52] Gireesha, B.J., Kumar, P.B.S., Mahanthesh, M., Shehzad, S.A., Rauf, A., Nonlinear 3D Flow of Casson-Carreau Fluids with Homogeneous-Heterogeneous Reactions: A Comparative Study, Results in Physics, 7, 2017, 2762–2770.
[53] Khan, M., Irfan, M., Khan, W.A., Alshomrani, A.S., A New Modeling for 3D Carreau Fluid Flow Considering Nonlinear Thermal Radiation, Results in Physics, 7, 2017, 2692–2704.
[54] Rao, A.S., Nagendra, N., Amanulla, C.H., Surya Narayana Reddy, M., Beg, O.A., Computational Analysis of Non-Newtonian Boundary Layer Flow of Nanofluid Past a Vertical Plate with Partial Slip, Modelling, Measurement and Control B, 86(1), 2017, 271-295.
[55] Beg, O.A., Rao, A.S., Amanulla, C.H., Nagendra, N., Suryanarayana Reddy, M., Kadir, A., Numerical Study of Hydromagnetic Non-Newtonian Nanofluid Transport Phenomena from a Horizontal Cylinder with Thermal Slip: Aerospace Nanomaterial Enrobing Simulation, Journal of Nanofluids, 7(1), 2018, 115–128.
[56] Cebeci, T., Bradshaw, P., Physical and Computational Aspects of Convective Heat Transfer, Springer, New York, 1984.
[57] Keller, H.B., A New Difference Method for Parabolic Problems, In: Bramble J (Ed) Numerical Methods for Partial Differential Equations, Academic Press, New York, 1970.
[58] Merkin, Free Convection Boundary Layer on an Isothermal Horizontal Circular Cylinders, ASME/AIChE, Heat Transfer Conference, St. Louis, Mo., U.S.A., 1976, 9–11.
[59] Molla, M.M., Saha, S.C., Khan, M.A.I., Hossain, M.A., Radiation Effects on Natural Convection Laminar Flow From a Horizontal Circular Cylinder, Desalination and Water Treatment, 30(1-3), 2011, 89–97.
[60] Javed, T., Majeed, A., Mustafa, I., MHD Effects on Natural Convection Laminar Flow from a Horizontal Circular Cylinder in Presence of Radiation, Revista Mexicana de Fisica, 61, 2015, 450–457.
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