# Non-coaxial rotating flow of viscous fluid with heat and mass transfer

- 257 Downloads
- 1 Citations

## Abstract

Heat and mass transfer in unsteady non-coaxial rotating flow of viscous fluid over an infinite vertical disk is investigated. The motion in the fluid is induced due to two sources. Firstly, due to the buoyancy force which is caused because of temperature and concentration gradients. Secondly, because of non-coaxial rotation of a disk such that the disk executes cosine or since oscillation in its plane and the fluid is at infinity. The problem is modeled in terms of coupled partial differential equations with some physical boundary and initial conditions. The dimensionless form of the problem is solved via Laplace transform method for exact solutions. Expressions for velocity field, temperature and concentration distributions are obtained, satisfying all the initial and boundary conditions. Skin friction, Nusselt number and Sherwood number are also evaluated. The physical significance of the mathematical results is shown in various plots and is discussed for several embedded parameters. It is found that magnitude of primary velocity is less than secondary velocity. In limiting sense, the present solutions are found identical with published results.

## Keywords

Buoyancy convection Non-coaxial rotation Heat and mass transfer Exact solution## Notes

### Acknowledgements

The authors would like to acknowledge Ministry of Higher Education (MOHE), Research Management Centre of Universiti Teknologi Malaysia (UTM) and Universiti Malaysia Pahang (UMP) for the financial support through vote numbers 4F713, 13H74, 15H80 and RDU131405 for this research.

### Compliance with ethical standards

### Conflict of interest

Authors confirm that there is no conflict of interest.

## References

- 1.Takhar HS, Roy S, Nath G (2003) Unsteady free convection flow over an infinite vertical porous plate due to the combined effects of thermal and mass diffusion, magnetic field and hall currents. Heat Mass Transf 39(10):825–834CrossRefGoogle Scholar
- 2.Ellahi R, Hassan M, Zeeshan A (2016) Aggregation effects on water base nano fluid over permeable wedge in mixed convection. Asia Pac J Chem Eng 11(2):179–186CrossRefGoogle Scholar
- 3.Hussanan A, Salleh MZ, Tahar RM, Khan I (2015) Thermal-diffusion effects on mixed convection flow in a heat absorbing fluid with newtonian heating and chemical reaction. AIP Conf Proc 1643:587–593CrossRefGoogle Scholar
- 4.Srinivasacharya D, Reddy GS (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):108–115MathSciNetCrossRefGoogle Scholar
- 5.Bhukta D, Dasha GC, Mishra SR, Baag S (2015) Dissipation effect on MHD mixed convection flow over a stretching sheet through porous medium with non-uniform heat source/sink. Ain Shams Eng J 1–9. doi: 10.1016/j.asej.2015.08.017 CrossRefGoogle Scholar
- 6.Raju MC, Veeresh C, Varma SVK, Rushi KB, Vijaya KAG (2015) Heat and mass transfer in MHD mixed convection flow on a moving inclined porous plate. J Appl Comput Math 4(5):1–7Google Scholar
- 7.Hayat T, Ashraf MB, Alsulami HH, Alhuthali MS (2014) Three-dimensional mixed convection flow of viscoelastic fluid with thermal radiation and convective conditions. PLoS ONE 9(3):1–11CrossRefGoogle Scholar
- 8.Ellahi R, Hassan M, Zeeshan A, Khan AA (2016) The shape effects of nanoparticles suspended in HFE-7100 over wedge with entropy generation and mixed convection. Appl Nanosci 6(5):641–651CrossRefGoogle Scholar
- 9.Mamourian M, Shirvan KM, Ellahi R, Rahimi AB (2016) Optimization of mixed convection heat transfer with entropy generation in a wavy surface square lid-driven cavity by means of Taguchi approach. Int J Heat Mass Transf 120:544–554CrossRefGoogle Scholar
- 10.Pal D, Talukdar B (2011) Combined effects of Joule heating and chemical reaction on unsteady magnetohydrodynamic mixed convection of a viscous dissipating fluid over a vertical plate in porous media with thermal radiation. Math Comput Model 54(11–12):3016–3036MathSciNetCrossRefGoogle Scholar
- 11.Khan I, Ali F, Shafie S, Mustapha N (2011) Effects of hall current and mass transfer on the unsteady magnetohydrodynamic flow in a porous channel. J Phys Soc Jpn 80:1–6Google Scholar
- 12.Samiulhaq Khan I, Ali F, Shafie S (2012) MHD free convection flow in a porous medium with thermal diffusion and ramped wall temperature. J Phys Soc Jpn 81:1–9Google Scholar
- 13.Ali F, Khan I, Shafie S, Musthapa N (2013) Heat and mass transfer with free convection MHD flow past a vertical plate embedded in a porous medium. Math Probl Eng 2013:1–13MathSciNetzbMATHGoogle Scholar
- 14.Nadeem S, Riaz A, Ellahi R, Akbar NS (2014) Effects of heat and mass transfer on peristaltic flow of a nanofluid between eccentric cylinders. Appl Nanosci 4(4):393–404CrossRefGoogle Scholar
- 15.Nadeem S, Riaz A, Ellahi R, Akbar NS, Zeeshan A (2014) Heat and mass transfer analysis of peristaltic flow of nanofuid in a vertical rectangular duct by using the optimized series solution and genetic algorithm. J Comput Theor Nanosci 11(4):1133–1149CrossRefGoogle Scholar
- 16.Ellahi R, Rahman SU, Nadeem S, Akbar NS (2014) Influence of heat and mass transfer on micropolar fluid of blood flow through a tapered stenosed arteries with permeable walls. J Comput Theor Nanosci 11(4):1156–1163CrossRefGoogle Scholar
- 17.Adnan AM, Khan U, Ahmed N, Mohyud-Din ST (2016) Analytical and numerical investigation of thermal radiation effects on flow of viscous incompressible fluid with stretchable convergent/divergent channels. J Mol Liq 224:768–775CrossRefGoogle Scholar
- 18.Khan U, Ahmed N, Mohyud-Din ST (2016) Analysis of magnetohydrodynamic flow and heat transfer of Cu-Water nanofluid between parallel plates for different shapes of nanoparticles. Neural Comput Appl. doi: 10.1007/s00521-016-2596-x CrossRefGoogle Scholar
- 19.Khan U, Mohyud-Din ST, Bin-Mohsin B (2016) Convective heat transfer and thermo-diffusion effects on flow of nanofluid towards a permeable stretching sheet saturated by a porous medium. Aerosp Sci Technol 50:196–203CrossRefGoogle Scholar
- 20.Khan U, Ahmed N, Mohyud-Din ST, Bin-Mohsin B (2016) Nonlinear radiation effects on MHD flow of nanofluid over a nonlinearly stretching/shrinking wedge. Neural Comput Appl. doi: 10.1007/s00521-016-2187-x CrossRefGoogle Scholar
- 21.Khan U, Ahmed N, Mohyud-Din ST (2017) Numerical investigation for three dimensional squeezing flow of nanofluid in a rotating channel with lower stretching wall suspended by carbon nanotube. Appl Therm Eng 113:1107–1117CrossRefGoogle Scholar
- 22.Ismail Z, Khan I, Shafie S (2014) Rotation and heat absorption effects on unsteady MHD free convection flow in a porous medium past an infinite inclined plate with ramped wall temperature. Recent Adv Math 7:161–167Google Scholar
- 23.Ismail Z, Khan I, Nasir NM, Jusoh R, Salleh MZ, Shafie S (2014) Rotation effects on coupled heat and mass transfer by unsteady MHD free convection flow in a porous medium past an infinite inclined plate. AIP Conf Proc 1605:410–415CrossRefGoogle Scholar
- 24.Islam N, Alam MM (2007) Dufour and soret effects on steady MHD free convection mass transfer fluid flow through a porous medium in a rotating system. J Nav Archit Mar Eng 4:43–55Google Scholar
- 25.Muthucumaraswamy R, Lal T, Ranganayakulu D (2010) Effects of rotation on MHD flow past accelerated isothermal vertical plate with heat and mass diffusion. Theor Appl Mech 37(3):189–202MathSciNetCrossRefGoogle Scholar
- 26.Muthucumaraswamy R, Lal T, Ranganayakulu D (2011) Rotation effects on flow past an accelerated vertical plate with variable temperature and uniform mass diffusion. Int J Eng 9:229–234zbMATHGoogle Scholar
- 27.Mohyud-Din ST, Zaidi ZA, Khan U, Ahmed N (2015) On heat and mass transfer analysis for the flow of a nanofluid between rotating parallel plates. Aerosp Sci Technol 46:514–522CrossRefGoogle Scholar
- 28.Erdogan ME (1997) Unsteady flow of a viscous fluid due to non-coaxial rotations of a disk and a fluid at infinity. Int J Nonlinear Mech 32(2):285–290CrossRefGoogle Scholar
- 29.Hayat T, Asghar S, Siddiqui AM, Haroon T (2001) Unsteady MHD flow due to non-coaxial rotations of a porous disk and a fluid at infinity. Acta Mech 151:127–134CrossRefGoogle Scholar
- 30.Asghar S, Hanif K, Hayat T, Khalique CM (2007) MHD non-newtonian flow due to non-coaxial rotations of an accelerated disk and a fluid at infinity. Commun Nonlinear Sci Numer Simul 12:465–485MathSciNetCrossRefGoogle Scholar
- 31.Guria M, Das S, Jana RN (2007) Hall effects on unsteady flow of a viscous fluid due to non-coaxial rotation of a porous disk and a fluid at infinity. Int J Nonlinear Mech 42:1204–1209CrossRefGoogle Scholar
- 32.Maji SL, Ghara N, Jana RN, Das S (2009) Unsteady MHD flow between two eccentric rotating disks. J Phys Sci 13:87–96Google Scholar
- 33.Guria M, Kanch AK, Das S, Jana RN (2010) Effects of hall current and slip condition on unsteady flow of a viscous fluid due to non-coaxial rotation of a porous disk and a fluid at infinity. Meccanica 45:23–32MathSciNetCrossRefGoogle Scholar
- 34.Ahmad I (2012) Flow induced by non-coaxial rotations of porous disk and a fluid in a porous medium. Afr J Math Comput Sci Res 5(2):23–27CrossRefGoogle Scholar
- 35.Das S, Maji SL, Ghara N, Jana RN (2012) Combined effects of hall currents and slip condition on steady flow of a viscous fluid due to non-coaxial rotation of a porous disk and a fluid at infinity. J Mech Eng Res 4(5):175–184Google Scholar
- 36.Das S, Jana RN (2014) Hall effects on unsteady hydromagnetic flow induced by an eccentricconcentric rotation of a disk and a fluid at infinity. Ain Shams Eng J 5:1325–1335CrossRefGoogle Scholar
- 37.Das S, Jana M, Jana RN (2013) Unsteady hydromagnetic flow due to concentric rotation of eccentric disks. J Mech 29(1):169–176CrossRefGoogle Scholar
- 38.Lakshmi R, Muthuselvi M (2014) Investigation of viscous fluid in a rotating disk. IOSR J Math 10(5):42–47CrossRefGoogle Scholar
- 39.Ersoy HV (2003) Unsteady viscous flow induced by eccentric–concentric rotation of a disk and the fluid at infinity. Turk J Eng Env Sci 27:115–123Google Scholar
- 40.Ersoy HV (2010) MHD flow of a second order/grade fluid due to noncoaxial rotation of a porous disk and the fluid at infinity. Math Comput Appl 15(3):354–363MathSciNetzbMATHGoogle Scholar
- 41.Ersoy HV (2014) Flow of a maxwell fluid between two porous disks rotating about noncoincident axes. Adv Mech Eng 2014:1–7Google Scholar
- 42.Mohamad AQ, Khan I, Ismail Z, Shafie S (2016) Exact solutions for unsteady free convection flow over an oscillating plate due to non-coaxial rotation. SpringerPlus 5(2090):1–22Google Scholar