Transient Heat and Mass Transfer of Micropolar Fluid between Porous Vertical Channel with Boundary Conditions of Third Kind
-
D. H. Doh
and
D. Prakash
Abstract
An investigation of heat and mass transfer characteristics of unsteady free convective flow of viscous incompressible micropolar fluid between the vertical porous plates in the presence of thermal radiation is carried out in the present work. The fluid is considered to be grey, absorbing–emitting but non scattering medium and the Cogley–Vincent–Gilles formulation is adopted to simulate the radiation component of heat transfer. The resulting system of equations is solved numerically with Crank–Nicolson implicit finite difference method. The effects of various physical parameters such as transient, micropolar parameter, radiation parameter, Reynolds number, Schmidt number, heat and mass transfer Biot numbers on the velocity, temperature and concentration field are discussed graphically.
Funding source: National Research Foundation of Korea
Award Identifier / Grant number: No. 2014R1A1A4A01005191
Award Identifier / Grant number: No. 2015H1C1A1035890
Funding statement: This work was supported by the National Foundation of Korea (NRF) grant funded by the Human Resource Training Program for Regional Innovation and Creativity through the Ministry of Education (NRF-2015H1C1A1035890).
Acknowledgement
The authors wish to express their sincere thanks to the honourable referees for their valuable comments to improve the quality of the paper.
Nomenclature
micropolar material constants
species concentration
specific heat (
acceleration due to gravity (
micro inertia density (
external convection/mass diffusion coefficients at the left wall (
external convection/mass diffusion coefficients at the right wall (
thermal conductivity (
rotational viscosity coefficient (
thickness of the channel (m)
dimensionless angular velocity
angular velocity, rad s−1
Prandtl number
radiative heat flux
cross flow Reynolds number
temperature (K)
temperature and concentration in hydrostatic state (K)
reference temperature and concentration (K)
suction/injection velocity (
velocities in x,y-directions (
axial and perpendicular coordinates (m)
dimensionless coordinate
- Greek Symbols
volumetric coefficient of thermal expansion (
micro rotational coupling coefficient (
kinematic viscosity (
density
dimensionless time
dimensionless temperature
micropolar parameter
micropolar material constant
- Subscripts
- i, j
nodes along
end boundary node along Y direction
condition at the wall
References
[1] D. A. Nield and A. Bejan, Convection in Porous Media, 4th edition, Springer Verlag, New York, 2013.10.1007/978-1-4614-5541-7Search in Google Scholar
[2] D. B. Ingham and I. Pop, Transport Phenomena in Porous Medium-III, Pergamon, Oxford, 2005.Search in Google Scholar
[3] A. C. Eringen, Theory of micropolar fluids, J. Math. Mech. 16 (1966), 1–16.10.21236/AD0469176Search in Google Scholar
[4] A. C. Eringen, Theory of thermo micro fluids, J. Math. Anal. Appl. 38 (1972), 480–496.10.1016/0022-247X(72)90106-0Search in Google Scholar
[5] T. Ariman, M. A. Turk, and N. D. Sylvester, Micro continuum fluid mechanics: A review, Int. J. Eng. Sci. 11 (1973), 905–930.10.1016/0020-7225(73)90038-4Search in Google Scholar
[6] P. Subhadra Ramachandran, M. N. Mathur, and S. K. Ojha, Heat transfer in boundary layer flow of a micropolar fluid past a curved surface with suction and injection, Int. J. Eng. Sci. 17 (1979), 625–639.10.1016/0020-7225(79)90131-9Search in Google Scholar
[7] M. Ashraf, M. Anwar Kamala, and K. S. Syeda, Numerical study of asymmetric laminar flow of micropolar fluids in a porous channel, Comput. Fluids 38 (2009), 1895–1902.10.1016/j.compfluid.2009.04.009Search in Google Scholar
[8] M. M. Rashidi, S. A. Mohimanian Pour, and N. Laraqi, A semi-analytical solution of micropolar flow in a porous channel with mass injection by using differential transform method, Nonlinear Anal. – Model 15 (2010), 341–350.10.15388/NA.15.3.14329Search in Google Scholar
[9] N. A. Kelson and T. W. Farrell, Micropolar fluid flow over a porous stretching sheet with strong suction or injection, Int. Commun. Heat Mass Transfer 28 (2001), 479–488.10.1016/S0735-1933(01)00252-4Search in Google Scholar
[10] Z. Ziabakhsh and D. Domairry, Homotopy analysis solution of micro-polar flow in a porous channel with high mass transfer, Adv. Theor. Appl. Mech. 1 (2008), 79–94.Search in Google Scholar
[11] A. A. Joneidi, D. D. Ganji, and M. Babaelahi, Micropolar flow in a porous channel with high mass transfer, Int. Commun. Heat Mass Transf. 36 (2009), 1082–1088.10.1016/j.icheatmasstransfer.2009.06.021Search in Google Scholar
[12] X. H. Si, L. C. Zheng, X. X. Zhang, and Y. Chao, The flow of micropolar flow through a porous channel with expanding or contracting walls, Cent. Eur. J. Phys. 9 (2011), 825–834.10.2478/s11534-010-0100-2Search in Google Scholar
[13] X. H. Si, L. C. Zheng, P. Lin, X. X. Zhang, and Y. Zhang, Flow and heat transfer of a micropolar fluid in a porous channel with expanding or contracting walls, Int. J. Heat Mass Transf. 67 (2013), 885–895.10.1016/j.ijheatmasstransfer.2013.08.012Search in Google Scholar
[14] A. Tetbirt, M. N. Bouaziz, and M. Tahar Abbes, Numerical study of magnetic effect on the velocity distribution field in a macro/micro-scale of a micropolar and viscous fluid in vertical channel, J. Mol. Liquids 216 (2016), 103–110.10.1016/j.molliq.2015.12.088Search in Google Scholar
[15] P. V. S. N. Murthy, S. Mukherjee, D. Srinivasacharya, and P. V. S. S. S. R. Krishna, Combined radiation and mixed convection from a vertical wall with suction/injection in a non-darcy porous medium, Acta Mech. 168 (2004), 145–156.10.1007/s00707-004-0084-3Search in Google Scholar
[16] T. Grosan and I. Pop, Thermal radiation effect on fully developed mixed convection flow in a vertical channel, Tech. Mech. 27 (2007), 37–47.Search in Google Scholar
[17] F. S. Ibrahim, A. M. Elaiw, and A. A. Bakr, Effect of the chemical reaction and radiation absorption on the unsteady MHD free convection flow past a semi infinite vertical permeable moving plate with heat source and suction, Commun. Nonlinear Sci. Numer. Simul. 13 (2008), 1056–1066.10.1016/j.cnsns.2006.09.007Search in Google Scholar
[18] S. M. Mahfooz and M. A. Hossain, Conduction-radiation effect on transient natural convection with thermophoresis, Appl. Math. Mech. 33 (2012), 271–288.10.1007/s10483-012-1549-6Search in Google Scholar
[19] E. M. Abo-Eldahab and A. F. Ghonaim, Radiation effect on heat transfer of a micropolar fluid through a porous medium, Appl. Math. Comput. 169 (2005), 500–510.10.1016/j.amc.2004.09.059Search in Google Scholar
[20] A. M. Rahman and T. Sultan, Radiative heat transfer flow of micropolar fluid with variable heat flux in a porous medium, Nonlinear Anal.: Model Contr. 13 (2008), 71–87.10.15388/NA.2008.13.1.14590Search in Google Scholar
[21] K. Das, Effect of chemical reaction and thermal radiation on heat and mass transfer flow of MHD micropolar fluid in a rotating frame of reference, Int. J. Heat Mass Transfer 54 (2011), 3505–3513.10.1016/j.ijheatmasstransfer.2011.03.035Search in Google Scholar
[22] D. Prakash and M. Muthtamilselvan, Effect of radiation on transient MHD flow of micropolar fluid between porous vertical channel with boundary conditions of the third kind, Ain. Shams Eng. J. 5 (2014), 1277–1286.10.1016/j.asej.2014.05.004Search in Google Scholar
[23] A. C. Cogley, W. G. Vincent, and S. E. Gilles, Differential approximation for radiative transfer in a non-gray gas near equilibrium, AIAA J. 6 (1968), 551–553.10.2514/3.4538Search in Google Scholar
[24] J. Zueco, P. Eguia, L. M. Lopez-Ochoa, J. Collazo, and D. Patino, Unsteady MHD free convection of a micropolar fluid between two parallel porous vertical walls with convection from the ambient, Int. Commun. Heat Mass Transfer 36 (2009), 203–209.10.1016/j.icheatmasstransfer.2008.11.008Search in Google Scholar
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- Multiple Soliton Solutions, Soliton-Type Solutions and Hyperbolic Solutions for the Benjamin–Bona–Mahony Equation with Variable Coefficients in Rotating Fluids and One-Dimensional Transmitted Waves
- Nonhomogeneous Porosity and Thermal Diffusivity Effects on a Double-Diffusive Convection in Anisotropic Porous Media
- Unsteady Convective Boundary Layer Flow of Maxwell Fluid with Nonlinear Thermal Radiation: A Numerical Study
- Transient Heat and Mass Transfer of Micropolar Fluid between Porous Vertical Channel with Boundary Conditions of Third Kind
- Traveling Waves of DDEs with Rational Nonlinearity
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Articles in the same Issue
- Frontmatter
- Dynamics of Two-Phase Dusty Fluid Flow Along a Wavy Surface
- Multiple Soliton Solutions, Soliton-Type Solutions and Hyperbolic Solutions for the Benjamin–Bona–Mahony Equation with Variable Coefficients in Rotating Fluids and One-Dimensional Transmitted Waves
- Nonhomogeneous Porosity and Thermal Diffusivity Effects on a Double-Diffusive Convection in Anisotropic Porous Media
- Unsteady Convective Boundary Layer Flow of Maxwell Fluid with Nonlinear Thermal Radiation: A Numerical Study
- Transient Heat and Mass Transfer of Micropolar Fluid between Porous Vertical Channel with Boundary Conditions of Third Kind
- Traveling Waves of DDEs with Rational Nonlinearity
- Numerical Investigation of Hydromagnetic Hybrid Cu – Al2O3/Water Nanofluid Flow over a Permeable Stretching Sheet with Suction
