MHD Hybrid Nanofluid Flow over a Stretching/Shrinking Sheet with Skin Friction: Effects of Radiation and Mass Transpiration
Abstract
:1. Introduction
2. Mathematical Analysis
SR. No. | Thermophysical Properties | Liquid Phase (Water) | Copper | Alumina |
---|---|---|---|---|
1 | ${C}_{P}$ (J/kgK) | 4179 | 385 | 765 |
2 | $\rho $ (kg/m^{3}) | 997.1 | 8933 | 3970 |
3 | $\kappa $ (W/mK) | 0.613 | 400 | 40 |
4 | $\sigma $ (Sm^{−1}) | 0.05 | 5.97 × 10^{7} | 35 × 10^{6} |
3. Results and Discussion
4. Concluding Remarks
- ${f}_{Y}\left(Y\right)$ is more for more $R{a}_{s}$ values for both ${V}_{C}>0$ and ${V}_{C}<0$.
- $f\left(Y\right)$ is more for more values of $R{a}_{s}$, and ${\varphi}_{1}$ for both ${V}_{C}>0$ and ${V}_{C}<0$.
- $\mathrm{Pr}$ value increases with increases of $\lambda $.
- $R{a}_{s}$ value decreases with increases of $\lambda $.
- Dual nature is observed.
- The present study helps to motivate the future researchers to conduct the investigations on stretching sheet problems with the help of mixed convective flow with hybrid nanofluid.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
Symbol | Description | S.I. Unit |
$d$ | Coefficient of stretching/shrinking parameter | $\left(-\right)$ |
$f\left(Y\right)$ | Dimensionless transverse velocity | $\left(-\right)$ |
${f}_{Y}\left(Y\right)$ | Dimensionless tangential velocity | $\left(-\right)$ |
$\overrightarrow{g}$ | Gravity | (N) |
${k}^{*}$ | Coefficient of mean absorption | $\left(-\right)$ |
$K$ | Permeability parameter | (m^{2}) |
$T$ | Temperature | (K) |
${V}_{C}$ | Mass transpiration | $\left(-\right)$ |
Greek symbols | ||
$\alpha $ | Dimensional stretching/shrinking parameter | $\left(-\right)$ |
$\beta $ | Thermal expansion coefficient | (K^{−1}) |
$\chi $ | Thermal diffusivity | (m^{2}s^{−1}) |
$\lambda $ | Dimensional stretching/shrinking parameter | $\left(-\right)$ |
$\theta $ | Temperature profile | $\left(-\right)$ |
$\nu $ | Kinematic viscosity | (m^{2}s^{−1}) |
$\rho $ | Density | (kgm^{−3}) |
$\mu $ | Dynamic viscosity of nanofluid | (kgm^{−1}s^{−1}) |
${\sigma}^{*}$ | Stefan–Boltzmann constant | (Wm^{−2}s^{−4}) |
Subscripts | ||
$w$ | Quantities at wall | $\left(-\right)$ |
$\infty $ | Quantities at for stream | $\left(-\right)$ |
$f$ | Fluid | $\left(-\right)$ |
$hnf$ | Hybrid nanofluid | $\left(-\right)$ |
Abbreviations | ||
B. Cs | Boundary conditions | $\left(-\right)$ |
MHD | Magnetohydrodynamics | $\left(-\right)$ |
ODE | Ordinary differential equations | $\left(-\right)$ |
PDE | Partial differential equations | $\left(-\right)$ |
References
- Baranovskii, E.S. Flows of a polymer fluid in domain with impermeable boundaries. Comput. Math. Math. Phys. 2014, 54, 1589–1596. [Google Scholar] [CrossRef]
- Sakiadis, B.C. Boundary-layer behaviour on continuous solid surface. AICHE J. 1961, 7, 26–28. [Google Scholar] [CrossRef]
- Sakiadis, B.C. Boundary-layer behavior on continuous solid surfaces. II. The boundary layer on a continuous flat surface. AIChE J. 1961, 7, 221–225. [Google Scholar] [CrossRef]
- Crane, L.J. Flow past a stretching plate. Z. Angew. Math. Phys. 1970, 21, 645–647. [Google Scholar] [CrossRef]
- Kumaran, G.; Sandeep, N.; Ali, M.E. Computational analysis of magnetohydrodynamic Casson and Maxwell flows over a stretching sheet with cross diffusion. Results Phys. 2017, 7, 147–155. [Google Scholar] [CrossRef]
- Andersson, H.I.; Bech, K.H.; Dandapat, B.S. Magnetohydrodynamic flow of a power-law fluid over a stretching sheet. Int. J. Non-Linear Mech. 1992, 27, 929–936. [Google Scholar] [CrossRef]
- Andersson, H.I. MHD flow of a viscoelastic fluid past a stretching surface. Acta Mech. 1992, 95, 227–230. [Google Scholar] [CrossRef]
- Aly, E.H. Existence of the multiple exact solutions for nanofluids flow over a stretching/shrinking sheet embedded in a porous medium at the presence of magnetic field with electrical conductivity and thermal radiation effects. Powder Tech. 2016, 301, 760–781. [Google Scholar] [CrossRef]
- Aly, E.H.; Hassan, M.A. suction and injection analysis of MHD nano boundary-layer over a stretching surface through a porous medium with partial slip boundary condition. J. Comput. Theor. Nanosci. 2014, 11, 827–839. [Google Scholar] [CrossRef]
- Anusha, T.; Huang, H.-N.; Mahabaleshwar, U.S. Two dimensional unsteady stagnation point flow of Casson hybrid nanofluid over a permeable flat surface and heat transfer analysis with radiation. J. Taiwan Inst. Chem. Eng. 2021, 127, 79–91. [Google Scholar] [CrossRef]
- Anusha, T.; Mahabaleshwar, U.S.; Sheikhnejad, Y. An MHD of nanofluid flow over a porous stretching/shrinking plate with mass transpiration and Brinkman ratio. Trans. Porous Media 2021, 142, 333–352. [Google Scholar] [CrossRef]
- Sarkar, J.; Ghosh, P.; Adil, A. A review on hybrid nanofluids: Recent research, development and applications. Renew. Sust. Energ. Rev. 2015, 43, 164–177. [Google Scholar] [CrossRef]
- Devi, S.S.; Devi, S.P. Heat transfer enhancement of Cu-Al_{2}O_{3}/water hybrid nanofluid flow over a stretching sheet. J. Niegerian Math. Soc. 2017, 36, 419–433. [Google Scholar]
- Mishra, N.K.; Sharma, M.; Sharma, B.K.; Khanduri, U. Soret and Dufour effects on MHD nanofluid flow of blood through a stenosed artery with variable viscosity. Int. J. Mod. Phys. B 2023, 2350266. [Google Scholar] [CrossRef]
- Sharma, B.K.; Kumar, A.; Gandhi, R.; Bhatti, M.M.; Mishra, N.K. Entropy generation and thermal radiation analysis of EMHD Jeffrey nanofluid flow: Applications in solar energy. Nanomaterials 2023, 13, 544. [Google Scholar] [CrossRef]
- Gandhi, R.; Sharma, B.K.; Mishra, N.K.; Al-Mdallal, Q.M. Computer simulations of EMHD Casson nanofluid flow of blood through an irregular Stenotic Permeable Artery: Applications of Koo-Kleinstreuer-Li Correlations. Nanomaterials 2023, 13, 652. [Google Scholar] [CrossRef]
- Jana, S.; Salehi-Khojin, A.; Zhong, W.H. Enhancement of fluid thermal conductivity by the addition of single and hybrid nano-additives. Thermochim. Acta 2007, 462, 45–55. [Google Scholar] [CrossRef]
- Mahabaleshwar, U.S.; Sarris, I.E.; Hill, A.A.; Lorenzini, G.; Pop, I. An MHD couple stress fluid due to a perforated sheet undergoing linear stretching with heat transfer. Int. J. Heat Mass Transf. 2017, 105, 157–167. [Google Scholar] [CrossRef]
- Xenos, M.; Petropoulou, E.; Siokis, A.; Mahabaleshwar, U.S. Solving the Nonlinear Boundary Layer Flow Equations with Pressure Gradient and Radiation. Symmetry 2020, 12, 710. [Google Scholar] [CrossRef]
- Reddy, G.B.; Goud, B.S.; Shekar, M.N.R. Numerical solution of MHD mixed convective boundary layer flow of a nanofluid through a porous medium due to an exponentially stretching sheet with Magnetic effect. Int. J. Appl. Eng. Res. 2019, 14, 2074–2083. [Google Scholar]
- Jia, Q.; Muhammad, M.B.; Munawwar, A.A.; Mohammad, M.R.; El-Sayed Ali, M. Entropy Generation on MHD Casson Nanofluid Flow over a Porous Stretching/Shrinking Surface. Entropy 2016, 4, 123. [Google Scholar]
- Umair, K.; Aurang, Z.; Sakhinah, A.B.; Ishak, A. Stagnatiom-point flow of a hybrid nanoliquid over a non-isothermal stretching/shrinking sheet with charecteristics of inertial and microstructure. Case Stud. Therm. Eng. 2021, 26, 101150. [Google Scholar]
- Nandy, S.K.; Pop, I. Effects of magnetic field and thermal radiation on stagnation flow and heat transfer of nanofluid over a shrinking surface, Int. Commun. Heat Mass Tranf. 2014, 53, 50–55. [Google Scholar] [CrossRef]
- Cortell, R. Radiation effects for the Blasius and sakiadis flows with a convective surface boundary condition. Appl. Math. Comput. 2008, 206, 832–840. [Google Scholar]
- Nayak, M.K.; Akbar, N.S.; Pandey, V.S.; Khan, Z.H.; Tripathi, D. 3D free convective MHD flow of nanofluid over permeable linear stretching sheet with thermal radiation. Powder Tech. 2017, 315, 205–215. [Google Scholar] [CrossRef]
- Sreedevi, P.; Reddy, P.S.; Chamkha, A.J. Heat and Mass transfer analysis of nanofluid over linear and non-linear stretching surfaces with thermal radiation and chemical reaction. Powder Tech. 2017, 315, 194–204. [Google Scholar] [CrossRef]
- Umair, K.; Aurang, Z.; Ishak, A. Magnetic field effect on sisko fluid flow containing gold nanoparticles through a porous covered surface in the presence of radiation and partial slip. Mathematics 2021, 9, 921. [Google Scholar]
- Ashraf, M.B.; Hayat, T.; Alsaedi, A. Mixed convection flow of Casson fluid over a stretching sheet with convective boundary conditions and Hall effect. Bound. Value Probl. 2017, 137, 1–17. [Google Scholar]
- Patil, P.M.; Roy, S.; Chamkha, A.J. Mixed convection flow over a vertical power-law stretching sheet. Int. J. Num. Meth. Heat Fluid Flow. 2010, 20, 445–458. [Google Scholar] [CrossRef]
- Sharma, B.K.; Khanduri, U.; Mishra, N.K.; Mekheimer, K.S. Combined effect of thermophoresis and Brownian motion on MHD mixed convective flow over an inclined stretching surface with radiation and chemical reaction. Res. Pap. 2023, 37, 2350095. [Google Scholar] [CrossRef]
- Aly, E.H.; Pop, I. MHD flow and heat transfer near stagnation point over a stretching/shrinking surface with partial slip and viscous dissipation: Hybrid nanofluid versus nanofluid. Powder Technol. 2020, 367, 192–205. [Google Scholar] [CrossRef]
- Taherialekouhi, R.; Rasouli, S.; Khosravi, A. An experimental study on stability and thermal conductivity of water-graphene oxide/aluminium oxide nanoparticles as a cooling hybrid nanofluid. Int. J. Heat Mass Transf. 2019, 145, 118751. [Google Scholar] [CrossRef]
- KSneha, N.; Mahabaleshwar, U.S.; Bennacer, R.; Ganaoui, E.L. Darcy Brinkman equations for hybrid dusty nanofluid flow with heat transfer and mass transpiration. Computation 2021, 9, 118. [Google Scholar]
- Fang, T.; Shanshan, Y.; Pop, I. Flow and heat transfer over a generalized stretching/shrinking wall problem-Exact solutions of the Navier-Stokes equations. Int. J. Non-Linear Mech. 2011, 46, 1116–1127. [Google Scholar] [CrossRef]
- Iskandar, W.; Ishak, A.; Pop, I. Mixed convection flow over an exponentially stretching/shrinking vertical surface in a hybrid nanofluid. Alex. Eng. J. 2020, 59, 1881–1891. [Google Scholar]
- Sharma, B.K.; Kumar, A.; Gandhi, R.; Bhatti, M.M. Exponential space and thermal-dependent heat source effects on electro-magneto-hydrodynamic Jeffrey fluid flow over a vertical stretching surface. Int. J. Mod. Phys. B 2022, 30, 2250220. [Google Scholar] [CrossRef]
- Khanduri, U.; Sharma, B.K. Entropy analysis for MHD flow subject to temperature-dependent viscosity and thermal conductivity. In Nonlinear Dynamics and Applications; Springer: Cham, Switzerland, 2022; pp. 457–471. [Google Scholar] [CrossRef]
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Vishalakshi, A.B.; Mahesh, R.; Mahabaleshwar, U.S.; Rao, A.K.; Pérez, L.M.; Laroze, D. MHD Hybrid Nanofluid Flow over a Stretching/Shrinking Sheet with Skin Friction: Effects of Radiation and Mass Transpiration. Magnetochemistry 2023, 9, 118. https://doi.org/10.3390/magnetochemistry9050118
Vishalakshi AB, Mahesh R, Mahabaleshwar US, Rao AK, Pérez LM, Laroze D. MHD Hybrid Nanofluid Flow over a Stretching/Shrinking Sheet with Skin Friction: Effects of Radiation and Mass Transpiration. Magnetochemistry. 2023; 9(5):118. https://doi.org/10.3390/magnetochemistry9050118
Chicago/Turabian StyleVishalakshi, Angadi Basettappa, Rudraiah Mahesh, Ulavathi Shettar Mahabaleshwar, Alaka Krishna Rao, Laura M. Pérez, and David Laroze. 2023. "MHD Hybrid Nanofluid Flow over a Stretching/Shrinking Sheet with Skin Friction: Effects of Radiation and Mass Transpiration" Magnetochemistry 9, no. 5: 118. https://doi.org/10.3390/magnetochemistry9050118