Fractional study on heat and mass transfer of MHD Oldroyd-B fluid with ramped velocity and temperature

Iftikhar, Nazish; Saeed, Syed Tauseef; Riaz, Muhammad Bilal

doi:10.22034/cmde.2021.39703.1739

فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری

تعداد نشریات	44
تعداد شماره‌ها	1,323
تعداد مقالات	16,270
تعداد مشاهده مقاله	52,952,902
تعداد دریافت فایل اصل مقاله	15,623,778

	Fractional study on heat and mass transfer of MHD Oldroyd-B fluid with ramped velocity and temperature
Computational Methods for Differential Equations
مقاله 7، دوره 10، شماره 2، تیر 2022، صفحه 372-395 اصل مقاله (634.3 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.39703.1739
نویسندگان
Nazish Iftikhar^* ¹؛ Syed Tauseef Saeed¹؛ Muhammad Bilal Riaz²^{، 3}
¹Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore Campus, Pakistan.
²Department of Mathematics, University of Management and Technology, Pakistan.
³Institute of Grounderwater Studies, University of the Free State, South Africa.
چکیده
‎This study explores the time-dependent flow of MHD Oldroyd-B fluid under the effect of ramped wall velocity and temperature‎. ‎The flow is confined to an infinite vertical plate embedded in a permeable surface with the impact of heat generation and thermal radiation‎. ‎Solutions of velocity‎, ‎temperature‎, ‎and concentration are derived symmetrically by applying non-dimensional parameters along with Laplace transformation $(LT)$ and numerical inversion algorithm‎. Graphical results for different physical constraints are produced for the velocity‎, ‎temperature‎, ‎and concentration profiles‎. ‎Velocity and temperature profile decrease by increasing the effective Prandtl number‎. ‎The existence of an effective Prandtl number may reflect the control of the thickness of momentum and enlargement of thermal conductivity‎. ‎Velocity is decreasing for $\kappa$‎, ‎$M$‎, ‎$Pr_{reff,}$ and $S_{c}$ while increasing for $G_{r}$ and $G_{c}$‎. ‎Temperature is an increasing function of the fractional parameter‎. ‎Additionally‎, ‎Atangana-Baleanu $(ABC)$ model is good to explain the dynamics of fluid with better memory effect as compared to other fractional operators‎.
کلیدواژه‌ها
Oldroyd-B fluid؛ Fractional differential operator؛ Ramped velocity and temperature

مراجع
[1] T. Abdeljawad, M. B. Riaz, S. T. Saeed, and N. Iftikhar, MHD Maxwell Fluid with Heat Transfer Analysis under Ramp Velocity and Ramp Temperature Subject to Non-Integer Differentiable Operators, Comp. Model. Eng. & Sci., (2021), 1-21, DOI: 10.32604/cmes.2021.012529. [2] N. Ahmed and M. Dutta, Transient mass transfer flow past an impulsively started infinite vertical plate with ramped plate velocity and ramped temperature, Int. J. Phys. Sci., 8(7) (2013), 254-263. [3] T. Anwar, I. Khan, P. Kumam, and W. Watthayu, Impacts of Thermal Radiation and Heat Consump- tion/Generation on Unsteady MHD Convection Flow of an OLdroyd-B Fluid with Ramped Velocity and Tem- perature in a Generalized Darcy Medium, Mathematics, 8(1) (2019), 130. [4] A. Atangana and D. Baleanu, New fractional derivative with non local and non-singular kernel: theory and application to heat transfer model, Therm. Sci., 20(2) (2016), 763-769. [5] A. Atangana and I. Koca, New direction in fractional differentiation, Math. in Nat. Sci., 1(1) (2017), 18-25. [6] R. A. Bruce, Evaluation of functional capacity and exercise tolerance of cardiac patients, Mod. Concepts Cardio- vasc. Dis., 25(1) (1956), 321-326. [7] M. Caputo and M. Fabrizio, A new Definition of Fractional Derivative without Singular Kernel, Progr. Fract. Differ. Appl., 1(2) (2015), 1-13. [8] W. Chen, Y. Liang, and X. Hei, Structural derivative based on inverse Mittag-Leffler function for modeling ultraslow diffusion, Fract. Calc. Appl. Anal., 19(5) (2016), 1316-46. [9] A. K. Ghosh and P. Sana, On hydromagnetics flow of an Oldroyd-B fluid near a pulsating plate, Acta Astronaut., 64(2-3) (2009), 272-280. [10] X. M. Gu and S. L. Wu, A parallel-in-time iterative algorithm for Volterra partial integral-differential problems with weakly singular kernel, J. Comp. Phy., (2020), 109576. [11] N. Iftikhar, S. M. Husnine, and M. B. Riaz, Heat and mass transfer in MHD Maxwell Fluid over an infinite vertical plate, J. of Prime Research in Math., 15(1) (2019), 63-80. [12] M. A. Imran, M. Aleem, M.B. Riaz, R. Ali, and I. Khan, A comprehensive report on convective flow of fractional (ABC) and (CF) MHD viscous fluid subject to generalized boundary conditions, Chaos, Solit. Fract., 118 (2018), 274-289. [13] M. A. Imran, M. B. Riaz, N. A. Shah, and A. A. Zafar, Boundary layer flow of MHD generalized Maxwell fluid over an exponentially accelerated infinite vertical surface with slip and Newtonian heating at the boundary, Results in phy., 8(1) (2018), 1061-1067. [14] O. S. Iyiolaa and F. D. Zaman, A fractional diffusion equation model for cancer tumor, AIP Advances, 4(10) (2014), 107121. https://doi.org/10.1063/1.4898331 [15] I. Khan, S. T. Saeed, M. B. Riaz, K. A. Abro, S. M. Husnine, and K. Nisar, Influence in a Darcy’s Medium with Heat Production and Radiation on MHD Convection Flow via Modern Fractional Approach, J. Mater. Research and Tech., 5(9) (2020), 10015-10030. [16] S. Kumara, A. Kumara, B. Samet, J. F. Gómez-Aguilar, and M. S. Osmande, A chaos study of tumor and effector cells in fractional tumor-immune model for cancer treatment, Chaos, Soli. & Fract., 141 (2020), 110321. [17] B. Kundu, Exact analysis for propagation of heat in a biological tissue subject to different surface conditions for therapeutic applications, Appl. Math. and Comput., 285(1) (2016), 204-216. [18] Y. Liang, T. Sandev, and E. K. Lenzi, Reaction and ultraslow diffusion on comb structures, Physical Review E., 101(4) (2020), 042119. [19] Y. Liang, S. Wang, W. Chen, Z. Zhou, and R. L. Magin, A survey of models of ultraslow diffusion in heterogeneous materials, App. Mech. Reviews, 71(4) (2019). [20] C. Liu, Y. Fan, and P. Lin, Numerical investigation of a fractional diffusion model on circular comb-inward structure, App. Math. Letters., 100 (2020), 106053. [21] T. Madeeha, M. A. Imran, N. Raza, M. Abdullah, and A. Maryam, Wall slip and noninteger order derivative effects on the heat transfer flow of Maxwell fluid over an oscillating vertical plate with new definition of fractional Caputo-Fabrizio derivatives, Results in phys., 7 (2017), 1887-1898. [22] J. Myers and D. Bellin, Ramp exercise protocol for clinical and cardiopulmonary exercise testing, Sports Med., 30(1) (2000), 23-29. [23] S. Nadeem, R. Mehmood, and N. S. Akbar, Non-orthogonal stagnation point flow of a nano non-Newtonian fluid towards a stretching surface with heat transfer, J. Heat Mass Trans., 57(2) (2013), 679-689. [24] J. G. Oldroyd, On the formulation of rheological equations of state, Pro. of the Royal Soc. of London. Series A. Math. and Phy. Sci., 200(1063) (1950), 523-541. [25] M. Pan, L. Zheng, F. Liu, C. Liu, and X. Chen, A spatial-fractional thermal transport model for nanofluid in porous media, App. Math. Modelling. 53 (2018), 622-34. [26] M. B. Riaz, A. Atangana, and N. Iftikhar, Heat and mass transfer in Maxwell fluid in view of local and non-local differential operators, J. Therm. Anal. Calorim., (2020), 1-17. [27] M. B. Riaz, A. Atangana, and T. Saeed, MHD free convection flow over a vertical plate with ramped wall temperature and chemical reaction in view of non-singular kernel, Publisher: Wiley, (2020), 253-279. [28] M. B. Riaz and N. Iftikhar, A comparative study of heat transfer analysis of MHD Maxwell fluid in view of local and nonlocal differential operators, Chaos Soli. Frac., 132 (2020), 109556. [29] M. B. Riaz and S. T. Saeed, Comprehensive analysis of integer order, Caputo-Fabrizio and Atangana-Baleanu fractional time derivative for MHD Oldroyd-B fluid with slip effect and time dependent bounday conditions, Discr. Conti. Dynam. Syst., (2020), doi:10.3934/dcdss.2020430. [30] M. B. Riaz, S. T. Saeed, and D. Baleanu, Role of Magnetic field on the Dynamical Analysis of Second Grade Fluid: An Optimal Solution subject to Non-integer Differentiable Operators, J. Appl. Comput. Mech., 7(1) (2021), 54-68. [31] M. B. Riaz, S. T. Saeed, D. Baleanu, and M. M. Ghalib, Computational results with non-singular & non-local kernel flow of viscous fluid in vertical permeable medium with variant temperature, Front. Phys., 8 (2020), 275. [32] M. B. Riaz, I. Siddiqui, S. T. Saeed, and A. Atangana, MHD Oldroyd-B Fluid with Slip Condition in view of Local and Nonlocal Kernels, J. Appl. Comput. Mech., 7(1) (2021), 116–127. [33] S. T. Saeed, I. Khan, M. B. Riaz, and S. M. Husnine, A Study of Heat Transfer under the Impact of Thermal Radiation, Ramped Velocity, and Ramped Temperature on the MHD Oldroyd-B Fluid Subject to non-integer Differentiable Operators, J. Mathe., (2020), 1-14. [34] S. T. Saeed, M. B. Riaz, D. Baleanu, and K. A. Abro, A Mathematical Study of Natural Convection Flow Through a Channel with non-singular Kernels: An Application to Transport Phenomena, Alexandria Engg. J., 59(4) (2020), 2269-2281. [35] G. Seth and S. Sarkar, MHD natural convection heat and mass transfer flow past a time dependent moving vertical plate with ramped temperature in a rotating medium with Hall effects, radiation and chemical reaction, J. Mech., 31(1) (2015), 91-104. [36] G. Seth, R. Sharma, and S. Sarkar, Natural Convection Heat and Mass Transfer Flow with Hall Current, Rotation, Radiation and Heat Absorption Past an Accelerated Moving Vertical Plate with Ramped Temperature, J. Appl. Fluid Mech., 8(1) (2015), 7-20. [37] G. Seth, S. Hussain, and S. Sarkar, Hydromagnetic natural convection flow with heat and mass transfer of a chemically reacting and heat absorbing fluid past an accelerated moving vertical plate with ramped temperature and ramped surface concentration through a porous medium, J. Egypt. Math. Soc., 23(1) (2015), 197-207. [38] K. Sharmilaa and S. Kaleeswari, Dufour effects on unsteady free convection and mass transfer through a porous medium in a slip regime with heat source/sink, Int. J. Sci. Eng. Appl. Sci., 1(6) (2015), 307-320. [39] D. C. Sobral, A new proposal to guide velocity and inclination in the ramp protocol for the Treadmill Ergometer, Arq. Bras. Cardiol., 81(1) (2003), 48-53. [40] H. Stehfest Algorithm, Numerical inversion of Laplace transforms, Commun. ACM., 13(1), (1970), 9-47. [41] M. H. Tiwana, A. B. Mann, M. Rizwan, K. Maqbool, S. Javeed, S. Raza, and M. S. Khan, Unsteady magneto- hydrodynamic convective fluid flow of Oldroyd-B model considering ramped wall temperature and ramped Wall Velocity, Mathematics, 7(8) (2019), 676. [42] D. Y. Tzou, Macro to Microscale Heat Transfer: The Lagging Behaviour, Washington: Taylor and Francis, 1970. [43] Y. Xu, Z. He and O. P. Agrawal, Numerical and analytical solutions of new generalized fractional diffusion equation, Comp. Math. App., 66(10) (2013), 2019-2029. [44] H. Zaman, Z. Ahmad, and M. Ayub, A note on the unsteady incompressible MHD fluid flow with slip conditions and porous walls, ISRN Math. Phy., 1 (2013), 1-10. [45] J. Zhao, L. Zheng, X. Zhang, and F. Liu, Convection heat and mass transfer of fractional MHD Maxwell fluid in a porous medium with Soret and Dufour effects, Int. J. Heat and Mass Trans., 103 (2016), 203-210.
آمار تعداد مشاهده مقاله: 834 تعداد دریافت فایل اصل مقاله: 935

سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب

پیوندهای مفید

آمار

Fractional study on heat and mass transfer of MHD Oldroyd-B fluid with ramped velocity and temperature