Numerical Solutions on Reiner–Philippoff (RP) Fluid Model with Velocity and Thermal Slip Boundary Condition
DOI:
https://doi.org/10.37934/cfdl.14.12.5265Keywords:
Reiner-Philippoff fluid, heat transfer, velocity slip, non-newtonianAbstract
Non-Newtonian fluid model was created against the Newton’s Law of viscosity where the viscosity is no more constant and dependent on the shear rate. The existing such fluid can be found in many industrial claims especially in food manufacturing, lubrication, biomedical flows and oil and gas. Besides, the used of non-Newtonian fluid occurs in mining industry where the slurries and muds are often handled. There are many models on non-Newtonian fluid available in literature where some of them capture the specific properties. The Reiner–Philippoff (RP) fluid model is considered in this endeavour due to the capabilities of the model which can be acted in three different family of fluid which are viscous, shear thickening and the shear-thinning. Mathematical model is constructed using continuity, momentum and energy equations where in form of partial differential equations (PDEs). The complexity of the proposed model is abridged by deduced the equations into ordinary differential equations (ODEs) by adopting similarity variables before the computation is done by bvp4c function drive in MATLAB software. To ratify the validity of the proposed model as well as numerical outputs, the comparative study is performed and it found to be in very strong agreement under limiting case where the present model is condensed to be identical with the reported model previously. The consequences of pertinent parameters on fluid’s characteristics are analyzed in details through the plotted graphic visuals and tabular form.
References
Abidin, Nurul Hafizah Zainal, Nor Fadzillah Mohd Mokhtar, Izzati Khalidah Khalid, and Siti Nur Aisyah Azeman. "Oscillatory Mode of Darcy-Rayleigh Convection in a Viscoelastic Double Diffusive Binary Fluid Layer Saturated Anisotropic Porous Layer." Journal of Advanced Research in Numerical Heat Transfer 10, no. 1 (2022): 8-19.
Shahrim, Muhammad Nazirul, Ahmad Qushairi Mohamad, Lim Yeou Jiann, Muhamad Najib Zakaria, Sharidan Shafie, Zulkhibri Ismail, and Abdul Rahman Mohd Kasim. "Exact solution of fractional convective Casson fluid through an accelerated plate." CFD Letters 13, no. 6 (2021): 15-25. https://doi.org/10.37934/cfdl.13.6.1525
Mohd Kasim, Abdul Rahman, Nur Syamilah Arifin, Syazwani Mohd Zokri, Mohd Zuki Salleh, Nurul Farahain Mohammad, Dennis Ling Chuan Ching, Sharidan Shafie, and Noor Amalina Nisa Ariffin. "Convective transport of fluid-solid interaction: A study between non-Newtonian Casson model with dust particles." Crystals 10, no. 9 (2020): 814. https://doi.org/10.3390/cryst10090814
Arifin, N. S., S. M. Zokri, N. A. S. Ariffin, A. R. M. Kasim, and M. Z. Salleh. "Modified Magnetic Field Flow of Casson Fluid and Solid Particles with Non-Linear Thermal Radiation Effect." Malaysian Journal of Mathematical Sciences 14 (2020): 171-184.
Zokri, Syazwani Mohd, Nur Syamilah Arifin, Muhammad Khairul Anuar Mohamed, Abdul Rahman Mohd Kasim, Nurul Farahain Mohammad, and Mohd Zuki Salleh. "Mathematical model of mixed convection boundary layer flow over a horizontal circular cylinder filled in a Jeffrey fluid with viscous dissipation effect." Sains Malaysiana 47, no. 7 (2018): 1607-1615. https://doi.org/10.17576/jsm-2018-4707-32
Zokri, Syazwani Mohd, Nur Syamilah Arifin, Abdul Rahman Mohd Kasim, Nurul Farahain Mohammad, and Mohd Zuki Salleh. "Energy dissipation of free convection boundary layer flow in a Jeffrey fluid across a horizontal circular cylinder with suspended nanoparticles." In Proceedings of the Third International Conference on Computing, Mathematics and Statistics (iCMS2017), pp. 93-100. Springer, Singapore, 2019. https://doi.org/10.1007/978-981-13-7279-7_12
Zokri, Syazwani Mohd, Nur Syamilah Arifin, Abdul Rahman Mohd Kasim, and Mohd Zuki Salleh. "Flow of jeffrey fluid over a horizontal circular cylinder with suspended nanoparticles and viscous dissipation effect: Buongiorno model." CFD Letters 12, no. 11 (2020): 1-13. https://doi.org/10.37934/cfdl.12.11.113
Zokri, Syazwani Mohd, Nur Syamilah Arifin, Abdul Rahman Mohd Kasim, Norhaslinda Zullpakkal, and Mohd Zuki Salleh. "Forced Convection of MHD Radiative Jeffrey Nanofluid Over a Moving Plate." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 87, no. 1 (2021): 12-19. https://doi.org/10.37934/arfmts.87.1.1219
Kasim, Abdul Rahman Mohd, Nur Syamilah Arifin, Syazwani Mohd Zokri, and Mohd Zuki Salleh. "Fluid-particle interaction with buoyancy forces on Jeffrey fluid with Newtonian heating." CFD Letters 11, no. 1 (2019): 1-16.
Kasim, Abdul Rahman Mohd, Nur Syamilah Arifin, Syazwani Mohd Zokri, and Mohd Zuki Salleh. "The investigation of a fluid-solid interaction mathematical model under combined convective jeffrey flow and radiation effect embedded newtonian heating as the thermal boundary condition over a vertical stretching sheet." In Defect and Diffusion Forum, vol. 399, pp. 65-75. Trans Tech Publications Ltd, 2020. https://doi.org/10.4028/www.scientific.net/DDF.399.65
Arifin, Nur Syamilah, Abdul Rahman Mohd Kasim, Syazwani Mohd Zokri, and Mohd Zuki Salleh. "Boundary Layer Flow of Dusty Williamson Fluid with Variable Viscosity Effect Over a Stretching Sheet." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 86, no. 1 (2021): 164-175. https://doi.org/10.37934/arfmts.86.1.164175
Arifin, Nur Syamilah, Syazwani Mohd Zokri, Abdul Rahman Mohd Kasim, Mohd Zuki Salleh, and Nurul Farahain Mohammad. "Two-phase mixed convection flow of dusty Williamson fluid with aligned magnetic field over a vertical stretching sheet." In Proceedings of the Third International Conference on Computing, Mathematics and Statistics (iCMS2017), pp. 209-216. Springer, Singapore, 2019. https://doi.org/10.1007/978-981-13-7279-7_26
Aljabali, Ahlam, Abdul Rahman Mohd Kasim, Nur Syamilah Arifin, and Sharena Mohamad Isa. "Mixed convection of non-newtonian erying powell fluid with temperature-dependent viscosity over a vertically stretched surface." Computers, Materials & Continua 66, no. 1 (2020): 421-435. https://doi.org/10.32604/cmc.2020.012322
Aljabali, Ahlam, Abdul Rahman Mohd Kasim, Nur Syamilah Arifin, Sharena Mohamad Isa, and Noor Amalina Nisa Ariffin. "Analysis of convective transport of temperature-dependent viscosity for non-newtonian erying powell fluid: A numerical approach." Computers, Materials and Continua 66, no. 1 (2021): 675-689. https://doi.org/10.32604/cmc.2020.012334
Kapur, J. N., and R. C. Gupta. "Two dimensional flow of Reiner-Philippoff fluids in the inlet length of a straight channel." Applied Scientific Research, Section A 14, no. 1 (1965): 13-24. https://doi.org/10.1007/BF00382227
Na, Tsung-Yen. "Boundary layer flow of Reiner-Philippoff fluids." International Journal of Non-Linear Mechanics 29, no. 6 (1994): 871-877. https://doi.org/10.1016/0020-7462(94)90059-0
Kumar, K. Ganesh, M. Gnaneswara Reddy, M. V. V. N. L. Sudharani, S. A. Shehzad, and Ali J. Chamkha. "Cattaneo-Christov heat diffusion phenomenon in Reiner-Philippoff fluid through a transverse magnetic field." Physica A: Statistical Mechanics and its Applications 541 (2020): 123330. https://doi.org/10.1016/j.physa.2019.123330
Turkyilmazoglu, M. "Flow of a micropolar fluid due to a porous stretching sheet and heat transfer." International Journal of Non-Linear Mechanics 83 (2016): 59-64. https://doi.org/10.1016/j.ijnonlinmec.2016.04.004
Dasman, A., Nur Syamilah Arifin, Abdul Rahman Mohd Kasim, and Nor Azizah Yacob. "Formulation of dusty micropolar fluid mathematical model." In Journal of Physics: Conference Series, vol. 1366, no. 1, p. 012032. IOP Publishing, 2019. https://doi.org/10.1088/1742-6596/1366/1/012032
Dasman, Anisah, Abdul Rahman Mohd Kasim, Iskandar Waini, and Najiyah Safwa Khashi'ie. "Numerical Solution for Boundary Layer Flow of a Dusty Micropolar Fluid Due to a Stretching Sheet with Constant Wall Temperature." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 87, no. 1 (2021): 30-40. https://doi.org/10.37934/arfmts.87.1.3040
Khan, Ansab Azam, Khairy Zaimi, Suliadi Firdaus Sufahani, and Mohammad Ferdows. "MHD Mixed Convection Flow and Heat Transfer of a Dual Stratified Micropolar Fluid Over a Vertical Stretching/Shrinking Sheet With Suction, Chemical Reaction and Heat Source." CFD Letters 12, no. 11 (2020): 106-120. https://doi.org/10.37934/cfdl.12.11.106120
Arifin, N. S., S. M. Zokri, A. R. M. Kasim, M. Z. Salleh, and N. F. Mohammad. "The aligned magnetic field of a dusty fluid flow over a stretching sheet." In AIP Conference Proceedings, vol. 1870, no. 1, p. 040033. AIP Publishing LLC, 2017. https://doi.org/10.1063/1.4995865
Manjunatha, S., and B. J. Gireesha. "Effects of variable viscosity and thermal conductivity on MHD flow and heat transfer of a dusty fluid." Ain Shams Engineering Journal 7, no. 1 (2016): 505-515. https://doi.org/10.1016/j.asej.2015.01.006
Dinesh, P. A., A. S. Vasudevamurthy, and M. Uma. "Effects of Forchheimer, MHD and Radiation Absorption for Chemically Reacting Unsteady Dusty Viscoelastic Fluid Couette Flow in an Irregular Channel." In Advances in Fluid Dynamics, pp. 999-1012. Springer, Singapore, 2021. https://doi.org/10.1007/978-981-15-4308-1_77
Gajjela, Nagaraju, and Raj Nandkeolyar. "Investigating the magnetohydrodynamic flow of a couple stress dusty fluid along a stretching sheet in the presence of viscous dissipation and suction." Heat Transfer 50, no. 3 (2021): 2709-2724. https://doi.org/10.1002/htj.22001
Cortell, Rafael. "A novel analytic solution of MHD flow for two classes of visco-elastic fluid over a sheet stretched with non-linearly (quadratic) velocity." Meccanica 48, no. 9 (2013): 2299-2310. https://doi.org/10.1007/s11012-013-9749-0
Mohd Kasim, Abdul Rahman, Nurul Farahain Mohammad, Sharidan Shafie, and Ioan Pop. "Constant heat flux solution for mixed convection boundary layer viscoelastic fluid." Heat and Mass Transfer 49, no. 2 (2013): 163-171. https://doi.org/10.1007/s00231-012-1075-x
Hayat, T., M. Hussain, M. Awais, and S. Obaidat. "Melting heat transfer in a boundary layer flow of a second grade fluid under Soret and Dufour effects." International Journal of Numerical Methods for Heat & Fluid Flow 23, no. 7 (2013): 1155-1168. https://doi.org/10.1108/HFF-09-2011-0182
Mahat, Rahimah, Noraihan Afiqah Rawi, Abdul Rahman Mohd Kasim, and Sharidan Shafie. "Mixed convection flow of viscoelastic nanofluid past a horizontal circular cylinder with viscous dissipation." Sains Malaysiana 47, no. 7 (2018): 1617-1623. https://doi.org/10.17576/jsm-2018-4707-33
Kanafiah, S. F. H. Mohd, A. R. M. Kasim, S. Mohd Zokri, and S. Shafie. "Numerical solutions of convective transport on Brinkman-viscoelastic fluid over a bluff body saturated in porous region." Case Studies in Thermal Engineering 28 (2021): 101341. https://doi.org/10.1016/j.csite.2021.101341
Kanafiah, Siti Farah Haryatie Mohd, Abdul Rahman Mohd Kasim, Syazwani Mohd Zokri, and Nur Syamilah Arifin. "Numerical Investigation at Lower Stagnation Point Flow Over a Horizontal Circular Cylinder of Brinkman-Viscoelastic Fluid." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 87, no. 2 (2021): 56-65. https://doi.org/10.37934/arfmts.87.2.5665
Ali, Farhad, Madeha Gohar, and Ilyas Khan. "MHD flow of water-based Brinkman type nanofluid over a vertical plate embedded in a porous medium with variable surface velocity, temperature and concentration." Journal of Molecular Liquids 223 (2016): 412-419. https://doi.org/10.1016/j.molliq.2016.08.068
Khan, Zar Ali, Sami Ul Haq, Tahir Saeed Khan, Ilyas Khan, and I. Tlili. "Unsteady MHD flow of a Brinkman type fluid between two side walls perpendicular to an infinite plate." Results in Physics 9 (2018): 1602-1608. https://doi.org/10.1016/j.rinp.2018.04.034
Yasin, Siti Hanani Mat, Muhammad Khairul Anuar Mohamed, Zulkhibri Ismail, Basuki Widodo, and Mohd Zuki Salleh. "Numerical solution on MHD stagnation point flow in ferrofluid with Newtonian heating and thermal radiation effect." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 57, no. 1 (2019): 12-22.
Tan, Jian Hong, Toru Yamada, Yutaka Asako, Lit Ken Tan, and Nor Azwadi Che Sidik. "Study of Self Diffusion of Nanoparticle Using Dissipative Particle Dynamics." Journal of Advanced Research in Numerical Heat Transfer 10, no. 1 (2022): 1-7.
Sharafatmandjoor, Shervin, and C. S. Nor Azwadi. "Effect of Imposition of viscous and thermal forces on Dynamical Features of Swimming of a Microorganism in nanofluids." Journal of Advanced Research in Micro and Nano Engineering 7, no. 1 (2022): 8-13.
Timol, M. G., and N. L. Kalthia. "Similarity solutions of three-dimensional boundary layer equations of non-Newtonian fluids." International Journal of Non-Linear Mechanics 21, no. 6 (1986): 475-481. https://doi.org/10.1016/0020-7462(86)90043-0
Patel, V., and M. G. Timol. "Similarity solutions of the three dimensional boundary layer equations of a class of general non-Newtonian fluids." International Journal of Applied Mathematics and Mechanics 8, no. 2 (2012): 77-88.
Patil, Vishwambhar S., Nalini S. Patil, and M. G. Timol. "A remark on similarity analysis of boundary layer equations of a class of non-Newtonian fluids." International Journal of Non-Linear Mechanics 71 (2015): 127-131. https://doi.org/10.1016/j.ijnonlinmec.2014.10.022
Yam, K. S., S. D. Harris, D. B. Ingham, and I. Pop. "Boundary-layer flow of Reiner-Philippoff fluids past a stretching wedge." International Journal of Non-Linear Mechanics 44, no. 10 (2009): 1056-1062. https://doi.org/10.1016/j.ijnonlinmec.2009.08.006
Ahmad, A., M. Qasim, and S. Ahmed. "Flow of Reiner-Philippoff fluid over a stretching sheet with variable thickness." Journal of the Brazilian Society of Mechanical Sciences and Engineering 39, no. 11 (2017): 4469-4473. https://doi.org/10.1007/s40430-017-0840-7
Reddy, M. Gnaneswara, M. V. V. N. L. Sudharani, K. Ganesh Kumar, Ali Chamkha, and G. Lorenzini. "Physical aspects of Darcy-Forchheimer flow and dissipative heat transfer of Reiner-Philippoff fluid." Journal of Thermal Analysis and Calorimetry 141, no. 2 (2020): 829-838. https://doi.org/10.1007/s10973-019-09072-0
Ahmad, Adeel. "Flow of ReinerPhilippoff based nano-fluid past a stretching sheet." Journal of Molecular Liquids 219 (2016): 643-646. https://doi.org/10.1016/j.molliq.2016.03.068
Reddy, M. Gnaneswara, Sudha Rani, K. Ganesh Kumar, Asiful H. Seikh, Mohammad Rahimi-Gorji, and El-Sayed Mohmed Sherif. "Transverse magnetic flow over a Reiner-Philippoff nanofluid by considering solar radiation." Modern Physics Letters B 33, no. 36 (2019): 1950449. https://doi.org/10.1142/S0217984919504499
Sajid, T., M. Sagheer, and S. Hussain. "Impact of temperature-dependent heat source/sink and variable species diffusivity on radiative Reiner-Philippoff fluid." Mathematical Problems in Engineering 2020 (2020). https://doi.org/10.1155/2020/9701860
Shampine, Lawrence F., Lawrence F. Shampine, Ian Gladwell, and S. Thompson. Solving ODEs with MATLAB. Cambridge University Press, 2003. https://doi.org/10.1017/CBO9780511615542
Shampine, Lawrence F., Jacek Kierzenka, and Mark W. Reichelt. "Solving boundary value problems for ordinary differential equations in MATLAB with bvp4c." Tutorial Notes 2000 (2000): 1-27.
Cortell, Rafael. "Heat and fluid flow due to non-linearly stretching surfaces." Applied Mathematics and Computation 217, no. 19 (2011): 7564-7572. https://doi.org/10.1016/j.amc.2011.02.029
Ferdows, M., Md Jashim Uddin, and A. A. Afify. "Scaling group transformation for MHD boundary layer free convective heat and mass transfer flow past a convectively heated nonlinear radiating stretching sheet." International Journal of Heat and Mass Transfer 56, no. 1-2 (2013): 181-187. https://doi.org/10.1016/j.ijheatmasstransfer.2012.09.020
Waini, Iskandar, Anuar Ishak, and Ioan Pop. "Hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface." International Journal of Numerical Methods for Heat & Fluid Flow (2019). https://doi.org/10.1088/1402-4896/ab0fd5
