Soret and Dufour effects on chemically reacting mixed convection flow in an annulus with Navier slip and convective boundary conditions. (English) Zbl 1524.76135
Summary: This analysis is to study the incompressible mixed convection laminar Newtonian flow through concentric cylindrical annulus associated with slip and convective boundary conditions. This presentation considered the cross diffusions and chemical reaction effects also. The fluid flow in an annulus is due to the rotation of the outer cylinder with constant velocity. The analysis of such kind of fluid flow is governed by nonlinear partial differential equations. The governing system of equations were mapped into dimensionless system with appropriate transformations. The system has been solved using Homotopy Analysis Method (HAM). The influence of Soret, Dufour, slip parameter and the chemical reaction parameter on velocity, temperature and concentration are investigated, and presented through plots. The maximum values of slip leads to increase in velocity and temperature profiles. Further the impact of boundary conditions on velocity, temperature and concentration are also presented.
MSC:
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 76E06 | Convection in hydrodynamic stability |
| 65H20 | Global methods, including homotopy approaches to the numerical solution of nonlinear equations |
| 76V05 | Reaction effects in flows |
| 76R05 | Forced convection |
Keywords:
mixed convection; cross diffusion effects; chemical reaction; convective boundary; Navier slip; HAMReferences:
| [1] | Rogers, B. and Yao, L. S. (1990). The effect of mixed convection instability on heat transfer in a vertical annulus. Int. J. Heat Mass Transfer, 33(1), 79-90. · Zbl 0684.76048 |
| [2] | Tsou, F. K., Win Aung., Moghadam, H. E. and Gau, C. (1992). Wall heating effects in mixed convection in vertical annulus with variable properties. J. Thermophys Heat Transfer, 6(2), 273-276. |
| [3] | Jha, B. K., Daramola, D. and Ajibade, A. O. (2016). Mixed convection in a vertical annulus filled with porous material having time-periodic thermal boundary condition: steady-periodic regime. Meccanica, 51, 1685-1698. · Zbl 1388.76363 |
| [4] | Moderres, M., Abboudi, S., Ihdene, M., Aberkane, S. and Ghezal, A. (2017). Numerical investigation of doublediffusive mixed convection in horizontal annulus partially filled with a porous medium. Int. J. Numer. Methods Heat Fluid Flow, 27(4), 773-794. |
| [5] | Nagaraju, G., Srinivas, J., Murthy, J.V. R. and Rashad, A. (2017). Entropy Generation Analysis of the MHD Flow of Couple Stress Fluid between Two Concentric Rotating Cylinders with Porous Lining. Heat Trans. Asian Res., 46, 316-330. |
| [6] | Abedini, A., Emadoddin, S. and Armaghani, T. (2018). Numerical analysis of mixed convection of different nanofluids in concentric annulus. Int. J. Numer. Methods Heat Fluid Flow, doi:10.1108/HFF-06-2018-0337. · doi:10.1108/HFF-06-2018-0337 |
| [7] | Jamil, M., Fetecau, C. and Imran, M. (2011). Unsteady helical flows of Oldroyd-B fluids. Commun Nonlinear Sci Numer Simul, 16, 1378-1386. · Zbl 1221.76017 |
| [8] | Nik-Ghazali, N., Badruddin, I. A., Badarudin, A., Badarudin, A. and Tabatabaeikia, S. (2014). Dufour and Soret effects on square porous annulus. Adv. in Mech. Eng, 209753, 1-15. |
| [9] | Hayat, T., Muhammad, T., Shehzad, S.A. and Alsaedi, A. (2015). Soret and Dufour effects in three-dimensional flow over an exponentially stretching surface with porous medium, chemical reaction and heat source/sink. Int. J. Numer. Methods Heat Fluid Flow, 25(4), 762-781. · Zbl 1356.76411 |
| [10] | Bilal Ashraf, M., Hayat, T., Alsaedi, A. and Shehzad, S.A. (2016). Soret and Dufour effects on the mixed convection flow of an Oldroyd-B fluid with convective boundary conditions. Results in Physics, 6, 917-924. |
| [11] | Nagaraju, G., Anjanna, M. and Kaladhar, K. (2017). The effects of Soret and Dufour, chemical reaction, Hall and ion currents on magnetized micropolar flow through co-rotating cylinders. AIP Advances, 7(11), 115201-1-16. |
| [12] | Reddy, P.S. and Chamkha, A. (2017). Heat and mass transfer analysis in natural convection flow of nanofluid over a vertical cone with chemical reaction. Int. J. Numer. Methods Heat Fluid Flow, 27(1), 2-22. |
| [13] | Jain, S. and Choudhary, R. (2018). Soret and Dufour Effects on thermophoretic MHD flow and heat transfer over a non-linear stretching sheet with chemical reaction. Int. J. Appl. Comput. Math, 4(1), 50 (1-27). · Zbl 1388.80002 |
| [14] | Matthews, M.T. and Hill, J.M. (2007). Newtonian flow with nonlinear Navier boundary condition. Acta Mech, 191(3- 4), 195-217. · Zbl 1117.76024 |
| [15] | Quarmby, A. (1966). Slip flow in an annulus, Appl. Sci. Res, 16(1), 301-314. |
| [16] | Avci, M. and Aydin, O. (2008). Laminar forced convection slip-flow in a micro-annulus between two concentric cylinders. Int. J. Heat Mass Transfer, 51(13-14), 3460-3467. · Zbl 1148.80304 |
| [17] | Kyritsi-Yiallourou, S. and Georgiou, G. C. (2018). Newtonian Poiseuille flow in ducts of annular-sector cross-sections with Navier slip. Eur. J. Mech. B. Fluids, 72, 87-102. · Zbl 1408.76141 |
| [18] | Malik, R., Khan, M., Munir, A. and Khan, W.A. (2014). Flow and heat transfer in sisko fluid with convective boundary condition. PLoS ONE, 9(10), e107989 (1-11). |
| [19] | Srinivasacharya, D. and Hima Bindu, K. (2016). Entropy generation in a porous annulus due to micropolar fluid flow with slip and convective boundary conditions. Energy, 111, 165-177. |
| [20] | Holman, K. K. and Ashar, S. T. (1971). Mass transfer in concentric rotating cylinders with surface chemical reaction in the presence of Taylor vortexes. Chem. Eng. Sci, 26(11), 1817-1831. |
| [21] | Paul, A. and Deka, R. K. (2013). Chemical reaction effect on transient free convective flow past an infinite moving vertical cylinder. Int. J. Chem. Eng, 531513 (1-9). |
| [22] | Srinivasacharya, D. and Swamy Reddy, G. (2016). Chemical reaction and radiation effects on mixed convection heat and mass transfer over a vertical plate in power-law fluid saturated porous medium. J. Egypt. Math. Soc, 24(1), 108- 115. · Zbl 1332.76004 |
| [23] | Anjanna, M. and Nagaraju, G. (2018). Order of chemical reaction and convective boundary condition effects on micropolar fluid flow over a stretching sheet. AIP Advances, 8(11), 115212 (1-10). |
| [24] | Liao, S. J. (2003). Beyond perturbation. Introduction to homotopy analysis method, Chapman and Hall/CRC Press, and Boca Raton. |
| [25] | Liao, S. J. (2004). On the homotopy analysis method for nonlinear problems. Appl Math Comput, 147(2), 499-513. · Zbl 1086.35005 |
| [26] | Rashidi, M.M., Keimanesh, M. and Rajvanshi, S.C. (2012). Study of pulsatile flow in a porous annulus with the homotopy analysis method. Int. J. Numer. Methods Heat Fluid Flow, 22(8), 971-989. · Zbl 1356.76254 |
| [27] | Gibanov, N. S., Sheremet, M. A., Oztop, H. F. and Al-Salem, K. (2017). Effect of uniform inclined magnetic field on natural convection and entropy generation in an open cavity having a horizontal porous layer saturated with a ferro fluid. Numer. Heat Transfer, Part A, 72(6), 479-494. |
| [28] | Kaladhar, K. and Komuraiah, E. (2018). Influence of cross diffusions on mixed convection chemical reaction flow in a vertical channel with Navier slip: Homotopy approach. J. Appl. Anal.Comput, 8(1), 379-389. · Zbl 1453.76046 |
| [29] | Nagaraju, G., Srinivas, J., Ramana Murthy, J.V., Bég, O.A. and Kadir, A.A. (2018). Second law analysis of flow in a circular pipe with uniform suction and magnetic field effects. ASME. J. Heat Transfer., 141(1): 012004-1-9. |
| [30] | Srinivasacharya, D. and Kaladhar, K. (2012). Analytical solution of mixed convection flow of couple stress fluid between two circular cylinders with hall and ion-slip effects, Turkish J. Eng. Env. Sci., 36, 226 - 235. · Zbl 1335.76061 |
| [31] | Srinivasacharya, D. and Himabindu, K. (2018). Entropy generation due to micropolar fluid flow between concentric cylinders with slip and convective boundary conditions, Ain Shams Engineering Journal, 9, 245-255. · Zbl 1401.76143 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
