Analysis of Tangent Hyperbolic over a Vertical Porous Sheet of Carreau Fluid and Heat Transfer
DOI:
https://doi.org/10.37934/cfdl.15.5.8696Keywords:
Carreau Fluid, heat transfer, power index, laminar flow, magnetic fieldAbstract
The purpose of this study is to investigate the boundary layer of Carreau fluid and heat transfer over an exponentially stretching plate derived in a vertical porous with variable surface thermal flux. The partial differential equations that represent the momentum equation and heat equation are commuted into nonlinear ODEs by applying similarity transformations and results found numerically. The impact of several emerging dimensionless parameters labelled the Weissenberg number (We), the power-law index ( ), Velocity slip ( ), Thermal jump ( ), and Prandtl number ( ) on the velocity profile and heat transfer on the boundary layer are showed in detail. In more detail, also the influence of physical parameters on local skin friction and Sherwood number are studied. The shooting method with the explicit technique is used to find the solution and all results are illustrated graphically and numerically. We noted that by increasing power index, radiation parameter and velocity slip, the velocity profile increases, and the temperature profile decreases. Furthermore, it is deduced that rising the thermal radiation parameter reduces the local Nusselt number.
Downloads
References
Hayat, T., S. A. Shehzad, M. Qasim, and S. Obaidat. "Radiative flow of Jeffery fluid in a porous medium with power law heat flux and heat source." Nuclear Engineering and Design 243 (2012): 15-19. https://doi.org/doi:10.1016/J.NUCENGDES.2011.11.005
Prasad, Vallampati R., Buddakkagari Vasu, Bég Osman Anwar, and Rana Parshad. "Unsteady free convection heat and mass transfer in a Walters-B viscoelastic flow past a semi-infinite vertical plate: a numerical study." Thermal Science 15, no. suppl. 2 (2011): 291-305. https://doi.org/10.2298/TSCI101102002P
Tripathi, Dharmendra, O. Anwar Bég, and Jose Luis Curiel-Sosa. "Homotopy semi-numerical simulation of peristaltic flow of generalised Oldroyd-B fluids with slip effects." Computer methods in biomechanics and biomedical engineering 17, no. 4 (2014): 433-442. http://dx.doi.org/10.1080/10255842.2012.688109
Wilson, Laurie L., R. Alex Speers, and Marvin A. Tung. "Yield stresses in molten chocolates." Journal of texture studies 24, no. 3 (1993): 269-286. http://dx.doi.org/10.1111/J.1745-4603.1993.TB01284.X
Hossain, M. Anwar, Khalil Khanafer, and Kambiz Vafai. "The effect of radiation on free convection flow of fluid with variable viscosity from a porous vertical plate." International Journal of Thermal Sciences 40, no. 2 (2001): 115-124. https://doi.org/10.1016/S1290-0729(00)01200-X
Harris, S. D., D. B. Ingham, and I. Pop. "Unsteady mixed convection boundary-layer flow on a vertical surface in a porous medium." International journal of heat and mass transfer 42, no. 2 (1999): 357-372. https://doi.org/10.1016/S0017-9310(98)00209-9
Ibrahim, F. S., and I. A. Hassanien. "Mixed convection boundary layer flow of a micropolar fluid on a horizontal flat plate with power law variation in surface temperature." International journal of thermal sciences 39, no. 3 (2000): 360-373. https://doi.org/10.1016/S1290-0729(00)00221-0
Temam, Roger, and Xiaoming Wang. "Boundary layers in channel flow with injection and suction." Applied mathematics letters 14, no. 1 (2001): 87-91. https://doi.org/10.1016/S0893-9659(00)00117-8
Mureithi, Eunice W., and David P. Mason. "On the stability of a forced-free boundary layer flow with viscous heating." Fluid dynamics research 31, no. 1 (2002): 65. https://doi.org/10.1016/S0169-5983(02)00088-6
Lok, Yian Yian, Norsarahaida Amin, and Ioan Pop. "Unsteady boundary layer flow of a micropolar fluid near the rear stagnation point of a plane surface." International Journal of Thermal Sciences 42, no. 11 (2003): 995-1001. https://doi.org/10.1016/S1290-0729(03)00079-6
Nazar, Roslinda, Norsarahaida Amin, Diana Filip, and Ioan Pop. "Unsteady boundary layer flow in the region of the stagnation point on a stretching sheet." International journal of engineering science 42, no. 11-12 (2004): 1241-1253. https://doi.org/10.1016/j.ijengsci.2003.12.002
Cai, Chunpei. "Near continuum boundary layer flows at a flat plate." Theoretical and Applied Mechanics Letters 5, no. 3 (2015): 134-139. https://doi.org/10.1016/j.taml.2015.03.005
Afify, Ahmed A., and Nasser S. Elgazery. "Effect of a chemical reaction on magnetohydrodynamic boundary layer flow of a Maxwell fluid over a stretching sheet with nanoparticles." Particuology 29 (2016): 154-161. https://doi.org/10.1016/j.partic.2016.05.003
Khan, Masood, and Muhammad Azam. "Unsteady boundary layer flow of Carreau fluid over a permeable stretching surface." Results in Physics 6 (2016): 1168-1174. https://doi.org/10.1016/j.rinp.2016.11.035
Rahimi, J., D. D. Ganji, M. Khaki, and Kh Hosseinzadeh. "Solution of the boundary layer flow of an Eyring-Powell non-Newtonian fluid over a linear stretching sheet by collocation method." Alexandria Engineering Journal 56, no. 4 (2017): 621-627. https://doi.org/10.1016/j.aej.2016.11.006
Liu, Lin, and Fawang Liu. "Boundary layer flow of fractional Maxwell fluid over a stretching sheet with variable thickness." Applied Mathematics Letters 79 (2018): 92-99. https://doi.org/10.1016/j.aml.2017.10.008
Khan, Ansab Azam, Khairy Zaimi, Suliadi Firdaus Sufahani, and Mohammad Ferdows. "MHD flow and heat transfer of double stratified micropolar fluid over a vertical permeable shrinking/stretching sheet with chemical reaction and heat source." Journal of Advanced Research in Applied Sciences and Engineering Technology 21, no. 1 (2020): 1-14. https://doi.org/10.37934/araset.21.1.114
Hamrelaine, Salim, Fateh Mebarek-Oudina, and Mohamed Rafik Sari. "Analysis of MHD Jeffery Hamel flow with suction/injection by homotopy analysis method." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 58, no. 2 (2019): 173-186.
Mahat, Rahimah, Muhammad Saqib, Imran Ulah, Sharidan Shafie, and Sharena Mohamad Isa. "MHD Mixed Convection of Viscoelastic Nanofluid Flow due to Constant Heat Flux." Journal of Advanced Research in Numerical Heat Transfer 9, no. 1 (2022): 19-25.
Shafique, Ahmad, Muhammad Ramzan, Zaib Un Nisa, Mudassar Nazar, and Hafeez Ahmad. "Unsteady magnetohydrodynamic flow of second grade Nanofluid (Ag-Cu) with CPC fractional derivative: Nanofluid." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 97, no. 2 (2022): 103-114. https://doi.org/10.37934/arfmts.97.2.103114
Bakar, Fairul Naim Abu, and Siti Khuzaimah Soid. "MHD Stagnation-Point Flow and Heat Transfer Over an Exponentially Stretching/Shrinking Vertical Sheet in a Micropolar Fluid with a Buoyancy Effect." Journal of Advanced Research in Numerical Heat Transfer 8, no. 1 (2022): 50-55.
Yoshimura, Ann, and Robert K. Prud'homme. "Wall slip corrections for Couette and parallel disk viscometers." Journal of Rheology 32, no. 1 (1988): 53-67. https://doi.org/10.1122/1.549963
Sparrow, E. M., and S. H. Lin. "Laminar heat transfer in tubes under slip-flow conditions." (1962): 363-369. https://doi.org/10.1115/1.3684399
Inman, Robert M. Heat transfer for laminar slip flow of a rarefied gas between parallel plates with unsymmetrical wall heat flux. National Aeronautics and Space Administration, 1964.
Larrodé, Francisco Ezquerra, Christos Housiadas, and Yannis Drossinos. "Slip-flow heat transfer in circular tubes." International Journal of Heat and Mass Transfer 43, no. 15 (2000): 2669-2680. https://doi.org/10.1016/S0017-9310(99)00324-5
Spillane, Sandra B. "A Study of Boundary Layer fFlow with No-slip and Slip Boundary Conditions." (2008). https://doi.org/10.21427/D7CG6Q
Yu, Shiping, and Timothy A. Ameel. "Slip flow convection in isoflux rectangular microchannels." J. Heat Transfer 124, no. 2 (2002): 346-355. https://doi.org/10.1115/1.1447932
Crane, L. J., and A. G. McVeigh. "Slip flow on a microcylinder." Zeitschrift für angewandte Mathematik und Physik 61, no. 3 (2010): 579-582. https://doi.org/10.1007/s00033-009-0019-x
Wuest, W. "Boundary layers in rarefied gas flow." Progress in Aerospace Sciences 8 (1967): 295-352. https://doi.org/10.1016/0376-0421(67)90006-1
Akbar, Noreen Sher, S. Nadeem, R. Ul Haq, and Z. H. Khan. "Numerical solutions of magnetohydrodynamic boundary layer flow of tangent hyperbolic fluid towards a stretching sheet." Indian journal of Physics 87 (2013): 1121-1124. https://doi.org/10.1007/s12648-013-0339-8
Gaffar, S. Abdul, V. Ramachandra Prasad, and O. Anwar Bég. "Computational analysis of magnetohydrodynamic free convection flow and heat transfer of non-Newtonian tangent hyperbolic fluid from a horizontal circular cylinder with partial slip." International Journal of Applied and Computational Mathematics 1 (2015): 651-675. https://doi.org/10.1007/s40819-015-0042-x
Amanulla, C. H., S. Saleem, Abderrahim Wakif, and M. M. AlQarni. "MHD Prandtl fluid flow past an isothermal permeable sphere with slip effects." Case Studies in Thermal Engineering 14 (2019): 100447. https://doi.org/10.1016/j.csite.2019.100447
Amanulla, C. H., Abderrahim Wakif, Zoubair Boulahia, M. Suryanarayana Reddy, and N. Nagendra. "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): 1-15. https://doi.org/10.1007/s40430-018-1385-0
Amanulla, C. H., Abderrahim Wakif, Zoubair Boulahia, Syed Fazuruddin, and S. Noor Mohammed. "A study on non-Newtonian transport phenomena in MHD fluid flow from a vertical cone with Navier slip and convective heating." Nonlinear Engineering 8, no. 1 (2019): 534-545. https://doi.org/10.1515/nleng-2018-0065
Amanulla, C. H., N. Nagendra, and M. Suryanarayana Reddy. "Numerical simulations on magnetohydrodynamic non-Newtonian nanofluid flow over a semi-infinite vertical surface with slipeffects." Journal of Nanofluids 7, no. 4 (2018): 718-730. https://doi.org/10.1166/jon.2018.1499
Amanulla, C. H., N. Nagendra, and M. Suryanarayana Reddy. "MHD flow and heat transfer in a williamson fluid from a vertical permeable cone with thermal and momentum slip effects: a mathematical study." Frontiers in Heat and Mass Transfer (FHMT) 8 (2017). http://dx.doi.org/10.5098/hmt.8.40
Atif, S. M., S. Hussain, and M. Sagheer. "Effect of viscous dissipation and Joule heating on MHD radiative tangent hyperbolic nanofluid with convective and slip conditions." Journal of the Brazilian Society of Mechanical Sciences and Engineering 41 (2019): 1-17. https://doi.org/10.1007/s40430-019-1688-9
Shahzad, U., M. Mushtaq, S. Farid, K. Jabeen, and R. M. A. Muntazir. "A Numerical Approach for an unsteady tangent hyperbolic nanofluid flow past a wedge in the presence of suction/injection." Mathematical Problems in Engineering 2021 (2021): 1-15. https://doi.org/10.1155/2021/8653091
Ismael, Hajar F. "Carreau-Casson fluids flow and heat transfer over stretching plate with internal heat source/sink and radiation." Int. J. Adv. Appl. Sci. J 6, no. 2 (2017): 81-86. https://doi.org/10.21833/ijaas.2017.07.003
Ismael, Hajar F., and N. M. Arifin. "Flow and heat transfer in a maxwell liquid sheet over a stretching surface with thermal radiation and viscous dissipation." JP J Heat Mass Transf 15 (2018): 847-66. http://dx.doi.org/10.17654/HM015040847
Ng, K. S., and J. P. Hartnett. "Effects of mechanical degradation on pressure drop and heat transfer performance of polyacrylamide solutions in turbulent pipe flow." Studies in Heat Transfer 297 (1979): 307.
Kwack, E. Y., and Cho Yi. "Turbulent heat transfer in circular tube flows of viscoelastic fluids." (1982). https://doi.org/10.1007/BF01322804
Kwack, E. Y., and J. P. Hartnett. "Effect of diameter on critical Weissenberg numbers for polyacrylamide solutions in turbulent pipe flow." International Journal of Heat and Mass Transfer 25, no. 6 (1982): 797-805. https://doi.org/10.1016/0017-9310(82)90092-8
Kwack, E. Y., and J. P. Hartnett. "Effect of solvent chemistry on critical Weissenberg numbers." International Journal of Heat and Mass Transfer 25, no. 9 (1982): 1445-1450. https://doi.org/10.1016/0017-9310(82)90138-7
Downloads
Published
How to Cite
Issue
Section
