Dufour and Soret effects on unsteady MHD mixed convective flow across a stretching curved surface with thermal and velocity slip: A numerical study

Year 2024, Volume: 10 Issue: 3, 572 - 584, 21.05.2024

Temjennaro Jamir Hemanta Konwar

Abstract

The current research relates to numerical analysis of the unsteady MHD mixed convective flow over a curved stretching surface. The Dufour and Soret effects, chemical reaction and joule heating are accounted into the flow together with the thermal and velocity slip effects. The governing partial differential equations of the flow which are in curvilinear coordinates are transformed into ordinary differential equations by using suitable similarity transformations. The numerical results are obtained using the MATLAB built-in solver bvp4c. The stability of the numerical technique has been verified and compared with the available literatures. The resultant boundary layer flow field parameters and the parameters of engineering interest have been presented graphically along with tabular data. The results thus obtained show that the surface drag significantly drops by about 9.4% and 23.4% respectively upon enlargement of the curvature parameter (0.5 ≤ K ≤ 0.7) and velocity slip parameter (0.4 ≤ λ ≤ 0.6) at the stretching surface. The thermal boundary layer thickness and heat transfer rate also tend to be drastically depleted as lesser heat gets transferred from the curve surface to the fluid. Incrementing the unsteadiness parameter (0.5 ≤ δ ≤ 1) significantly improves the heat and mass transfer rates by about 13.5% and 13% respectively. It is also found that the rates of heat and mass transfer can be increased by enhancing the Dufour and Soret effects respectively.

Keywords

Curved Surface, Dufour Effect, Soret Effect, Thermal Slip, Unsteady, Velocity Slip

References

• [1] Crane LJ. Flow past a stretching plate. Z Angew Math Phys 1970;21:645–647. [CrossRef]
• [2] Mabood F, Das K. Melting heat transfer on hydromagnetic flow of a nanofluid over a stretching sheet with radiation and second-order slip. Eur Phys J Plus 2016;131:1–12. [CrossRef]
• [3] Sajid M, Ali N, Javed T, Abbas Z. Stretching a curved surface in a viscous fluid. Chin Phys Lett 2010;27: 024703. [CrossRef]
• [4] Abbas Z, Naveed M, Sajid M. Heat transfer analysis for stretching flow over a curved surface with magnetic field. J Eng Thermophys 2013;22:337–345. [CrossRef]
• [5] Okechi NF, Jalil M, Asghar S. Flow of viscous fluid along an exponentially stretching curved surface. Results Phys 2017;7:2851–2854. [CrossRef]
• [6] Ijaz Khan M, Khan SA, Hayat T, Qayyum S, Alsaedi A. Entropy generation analysis in MHD flow of viscous fluid by a curved stretching surface with cubic autocatalysis chemical reaction. Eur Phys J Plus 2020;135:249. [CrossRef]
• [7] Raza R, Mabood F, Naz R, Abdelsalam SI. Thermal transport of radiative Williamson fluid over stretchable curved surface. Therm Sci Eng Prog 2021;23:100887. [CrossRef]
• [8] Roşca NC, Pop I. Unsteady boundary layer flow over a permeable curved stretching/shrinking surface. Eur J Mech B Fluids 2015;51:61–67. [CrossRef]
• [9] Naveed M, Abbas Z, Sajid M. Hydromagnetic flow over an unsteady curved stretching surface. Eng Sci Technol Int J 2016;19:841–845. [CrossRef]
• [10] Imtiaz M, Hayat T, Alsaedi A, Hobiny A. Homogeneous-heterogeneous reactions in MHD flow due to an unsteady curved stretching surface. J Mol Liq 2016;221:245–253. [CrossRef]
• [11] Yasmin A, Ali K, Ashraf M. Study of heat and mass transfer in MHD flow of micropolar fluid over a curved stretching sheet. Sci Rep 2020;10:1–11. [CrossRef]
• [12] Abbas N, Nadeem S, Khan MN. Numerical analysis of unsteady magnetized micropolar fluid flow over a curved surface. J Therm Anal Calorim 2022;147:6449–6459. [CrossRef]
• [13] Abbas N, Shatanawi W. Theoretical survey of time-dependent micropolar nanofluid flow over a linear curved stretching surface. Symmetry (Basel) 2022;14:1629. [CrossRef]
• [14] Yasir M, Ahmed A, Khan M, Alzahrani AK, Malik ZU, Alshehri AM. Mathematical modelling of unsteady Oldroyd-B fluid flow due to stretchable cylindrical surface with energy transport. Ain Shams Eng J 2022;14:101825. [CrossRef]
• [15] Chandel S, Sood S. Unsteady flow of Williamson fluid under the impact of prescribed surface temperature (PST) and prescribed heat flux (PHF) heating conditions over a stretching surface in a porous enclosure. ZAMM Z Angew Math Mech 2022;102:1–25. [CrossRef]
• [16] Saranya S, Ragupathi P, Al-Mdallal Q. Analysis of bio-convective heat transfer over an unsteady curved stretching sheet using the shifted Legendre collocation method. Case Stud Therm Eng 2022;39:102433. [CrossRef]
• [17] Hussein AK. Mixed convection in cylinders-a comprehensive overview and understanding. J Basic Appl Sci Res 2013;3:328–338.
• [18] Sivasankaran S, Sivakumar V, Hussein AK, Prakash P. Mixed convection in a lid-driven two-dimensional square cavity with corner heating and internal heat generation. Numer Heat Transf Part A Appl 2014;65:269–286. [CrossRef]
• [19] Hussein AK, Hussain SH. Characteristics of magnetohydrodynamic mixed convection in a parallel motion two-sided lid-driven differentially heated parallelogrammic cavity with various skew angles. J Therm Engineer 2015;1:221–235. [CrossRef]
• [20] Mallikarjuna B, Rashad AM, Hussein AK, Hariprasad Raju S. Transpiration and thermophoresis effects on non-darcy convective flow past a rotating cone with thermal radiation. Arab J Sci Eng 2016;41:4691–4700. [CrossRef]
• [21] Bhuvaneswari M, Eswaramoorthi S, Sivasankaran S, Hussein AK. Cross-diffusion effects on MHD mixed convection over a stretching surface in a porous medium with chemical reaction and convective condition. Eng Trans 2019;67:3–19.
• [22] Laouira H, Mebarek-Oudina F, Hussein AK, Kolsi L, Merah A, Younis O. Heat transfer inside a horizontal channel with an open trapezoidal enclosure subjected to a heat source of different lengths. Heat Transf - Asian Res 2019;49:406–423. [CrossRef]
• [23] Waini I, Ishak A, Pop I. Mixed convection flow over an exponentially stretching/shrinking vertical surface in a hybrid nanofluid. Alexandria Eng J 2020;59:1881–1891. [CrossRef]
• [24] Ahmad L, Alshomrani AS, Khan M. Radiation and mixed convection effects on chemically reactive sisko fluid flow over a curved stretching surface. Iran J Chem Chem Eng 2020;39:339–354.
• [25] Ramzan M, Rafiq A, Chung JD, Kadry S, Chu YM. Nanofluid flow with autocatalytic chemical reaction over a curved surface with nonlinear thermal radiation and slip condition. Sci Rep 2020;10:1–13. [CrossRef]
• [26] Ramzan M, Dawar A, Saeed A, Kumam P, Watthayu W, Kumam W. Heat transfer analysis of the mixed convective flow of magnetohydrodynamic hybrid nanofluid past a stretching sheet with velocity and thermal slip conditions. PLoS One 2021;16:1–31. [CrossRef]
• [27] Khan WA, Waqas M, Ali M, Sultan F, Shahzad M, Irfan M. Mathematical analysis of thermally radiative time-dependent Sisko nanofluid flow for curved surface. Int J Numer Methods Heat Fluid Flow 2019;29:3498–3514. [CrossRef]
• [28] Imtiaz M, Nazar H, Hayat T, Alsaedi A. Soret and Dufour effects in the flow of viscous fluid by a curved stretching surface. Pramana - J Phys 2020;94:48. [CrossRef]
• [29] Ali B, Hussain S, Nie Y, Hussein AK, Habib D. Finite element investigation of Dufour and Soret impacts on MHD rotating flow of Oldroyd-B nanofluid over a stretching sheet with double diffusion Cattaneo Christov heat flux model. Powder Technol 2021;377:439–452. [CrossRef]
• [30] Jamir T, Konwar H. Effects of radiation absorption, soret and dufour on unsteady MHD mixed convective flow past a vertical permeable plate with slip condition and viscous dissipation. J Heat Mass Transf Res 2023;9:155–168.
• [31] Shatanawi W, Abbas N, Shatnawi TAM, Hasan F. Heat and mass transfer of generalized fourier and Fick’s law for second-grade fluid flow at slendering vertical Riga sheet. Heliyon 2023;9:e14250. [CrossRef]
• [32] Jamir T, Konwar H. Unsteady magnetohydrodynamic slip flow, heat and mass transfer over a permeable stretching cylinder with Soret and Dufour effects in porous medium. Defect Diffus Forum 2023;424:143–154. [CrossRef]
• [33] Shampine L, Kierzenka J, Reichelt M. Solving boundary value problems for ordinary differential equations in MATLAB with bvp4c. Tutor Notes 2000;75275:1–27.