Neural Computing and Applications

, Volume 29, Issue 6, pp 59–67 | Cite as

Heat and mass transfer in a micropolar fluid with Newtonian heating: an exact analysis

  • Abid Hussanan
  • Mohd Zuki SallehEmail author
  • Ilyas Khan
  • Razman Mat Tahar
Original Article


Heat and mass transfer phenomenon in a micropolar fluid is analyzed. The fluid occupies the space over an infinite oscillating vertical plate with Newtonian heating. The plate executes cosine type of oscillations. Exact solutions are obtained using the Laplace transform technique. Expressions for velocity, microrotation, temperature and concentration are obtained. Graphs for velocity and microrotation are plotted for various embedded parameters and discussed.


Unsteady flow Micropolar fluid Newtonian heating Exact solutions 

List of symobls


Species concentration (mol m−3)


Species concentration near the plate (mol m−3)


Species concentration far away from the plate (mol m−3)


Heat capacity at a constant pressure (J kg−1 K−1)


Mass diffusivity (m2 s−1)


Acceleration due to gravity (m s−2)


Scalar constant


Unit vector


Heat transfer coefficient


Thermal Grashof number


Modified Grashof number


Thermal conductivity (W m−1 K−1)


Prandtl number


Radiative heat flux (W m−2)


Radiation parameter


Schmidt number


Temperature of the fluid (K)


Ambient temperature (K)


Time (s)


Velocity of the fluid (m s−1)


Microinertia per unit mass (m2)


Phase angle


Angular velocity (m s−1)


Amplitude of plate oscillations (m)


Unit step function


Complementary error function

Greek symbols


Vortex viscosity (kg m−1 s−1)


Microrotation parameter


Volumetric coefficient of thermal expansion (K−1)


Volumetric coefficient of mass expansion (K−1)


Conjugate parameter for Newtonian heating


Spin gradient viscosity (kg m s−1)


Spin gradient viscosity parameter


Dynamic viscosity (kg m−1 s−1)


Fluid density (kg m−3)


Stefan–Boltzmann constant (W m−2 K−4)


Dimensionless temperature


Frequency of oscillation



Condition at wall

Condition at infinity



Dimensional variables



The authors would like to acknowledge Universiti Malaysia Pahang, Malaysia for the financial support through Vote Numbers RDU140111 (FRGS) and RDU150101 (FRGS).


  1. 1.
    Eringen AC (1966) Theory of micropolar fluids. J Appl Math Mech 16:1–18MathSciNetGoogle Scholar
  2. 2.
    Hsu PT, Chen CK, Wang CC (2000) Mixed convection of micropolar fluids along a vertical wavy surface. Acta Mech 144:231–247CrossRefzbMATHGoogle Scholar
  3. 3.
    Hassanien IA (1999) Flow and heat transfer in the boundary layer of a micropolar fluid on a continuous moving. Int J Numer Meth Heat Fluid Flow 9:643–659CrossRefzbMATHGoogle Scholar
  4. 4.
    Kim YJ (1999) Thermal boundary layer flow of a micropolar fluid past a wedge with constant wall temperature. Acta Mech 138:113–121CrossRefzbMATHGoogle Scholar
  5. 5.
    Damseh RA, Azab TAA, Shannak BA, Husein MA (2007) Unsteady natural convection heat transfer of micropolar fluid over a vertical surface with constant heat flux. Turk J Eng Environ Sci 31:225–233Google Scholar
  6. 6.
    Rahman MM, Sultana Y (2008) Radiative heat transfer flow of micropolar fluid with variable heat flux in a porous medium. Nonlinear Anal Model Control 13:71–87zbMATHGoogle Scholar
  7. 7.
    Reddy MG (2012) Magnetohydrodynamics and radiation effects on unsteady convection flow of micropolar fluid past a vertical porous plate with variable wall heat flux. ISRN Thermodyn 2012:1–8Google Scholar
  8. 8.
    Mahmoud MAA, Waheed SE (2012) MHD flow and heat transfer of a micropolar fluid over a stretching surface with heat generation (absorption) and slip velocity. J Egypt Math Soc 20:20–27MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Si X, Zheng L, Lin P, Zhang X, Zhang Y (2013) Flow and heat transfer of a micropolar fluid in a porous channel with expanding or contracting walls. Int J Heat Mass Transf 67:885–895CrossRefGoogle Scholar
  10. 10.
    Sheikholeslami M, Ashorynejad HR, Ganji DD, Rashidi MM (2014) Heat and mass transfer of a micropolar fluid in a porous channel. Commun Numer Anal 2014:1–20MathSciNetCrossRefGoogle Scholar
  11. 11.
    Hakiem MAE (2014) Heat transfer from moving surfaces in a micropolar fluid with internal heat generation. J Eng Appl Sci 1:30–36Google Scholar
  12. 12.
    Sherief HH, Faltas MS, Ashmawy EA (2011) Exact solution for the unsteady flow of a semi-infinite micropolar fluid. Acta Mech Sin 27:354–359MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Qasim M, Hayat T (2010) Effects of thermal radiation on unsteady magnetohydrodynamic flow of a micropolar fluid with heat and mass transfer. Zeitschrift für Naturforschung A 64:950–960Google Scholar
  14. 14.
    Qasim M, Khan I, Sharidan S (2013) Heat transfer in a micropolar fluid over a stretching sheet with Newtonian heating. PLoS One 8:e59393CrossRefGoogle Scholar
  15. 15.
    Bakier AY (2011) Natural convection heat and mass transfer in a micropolar fluid-saturated non-darcy porous regime with radiation and thermophoresis effects. Therm Sci 15:317–326CrossRefGoogle Scholar
  16. 16.
    Aurangzaib, Kasim ARM, Mohammad NF, Sharidan S (2013) Unsteady MHD mixed convection flow with heat and mass transfer over a vertical plate in a micropolar fluid-saturated porous medium. J Appl Sci Eng 16:141–150Google Scholar
  17. 17.
    Khan I, Qasim M, Sharidan S (2015) Flow of an Erying–Powell fluid over a stretching sheet in presence of chemical reaction. Therm Sci. doi: 10.2298/TSCI131129111K Google Scholar
  18. 18.
    Fetecau C, Vieru D, Fetecau C, Pop I (2015) Slip effects on the unsteady radiative MHD free convection flow over a moving plate with mass diffusion and heat source. Eur Phys J Plus 130:1–13CrossRefGoogle Scholar
  19. 19.
    Srinivasacharya D, Upendar M (2013) Effect of double stratification on MHD free convection in a micropolar fluid. J Egypt Math Soc 21:370–378MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Srinivasacharya D, Upendar M (2014) Thermal radiation and chemical reaction effects on magnetohydrodynamic free convection heat and mass transfer in a micropolar fluid. Turk J Eng Environ Sci. doi: 10.3906/muh-1209-3 zbMATHGoogle Scholar
  21. 21.
    Fakour M, Vahabzadeh A, Ganjib DD, Hatami M (2015) Analytical study of micropolar fluid flow and heat transfer in a channel with permeable walls. J Mol Liq 204:198–204CrossRefGoogle Scholar
  22. 22.
    Merkin JH (1994) Natural convection boundary layer flow on a vertical surface with Newtonian heating. Int J Heat Fluid Flow 15:392–398CrossRefGoogle Scholar
  23. 23.
    Mohamed KAM, Salleh MZ, Nazar R, Ishak A (2012) Stagnation point flow over a stretching sheet with Newtonian heating. Sains Malays 41:1467–1473Google Scholar
  24. 24.
    Merkin JH, Nazar R, Pop I (2012) The development of forced convection heat transfer near a forward stagnation point with Newtonian heating. J Eng Math 76:53–60MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Salleh MZ, Nazar R, Pop I (2012) Numerical solutions of free convection boundary layer flow on a solid sphere with Newtonian heating in a micropolar fluid. Meccanica 47:1261–1269MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Alkasasbeh HT, Salleh MZ (2014) Numerical solutions of radiation effect on MHD free convection boundary layer flow about a solid sphere with Newtonian heating. Appl Math Sci 8:6989–7000Google Scholar
  27. 27.
    Mebine P, Adigio EM (2009) Unsteady free convection flow with thermal radiation past a vertical porous plate with Newtonian heating. Turk J Phys 33:109–119Google Scholar
  28. 28.
    Narahari M, Nayan MY (2011) Free convection flow past an impulsively started infinite vertical plate with Newtonian heating in the presence of thermal radiation and mass diffusion. Turk J Eng Environ Sci 35:187–198Google Scholar
  29. 29.
    Hussanan A, Khan I, Sharidan S (2013) An exact analysis of heat and mass transfer past a vertical plate with Newtonian heating. J Appl Math 2013:1–9MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Hussanan A, Zakaria MN (2013) Samiulhaq, Khan, I., Sharidan, S., Radiation effect on unsteady magnetohydrodynamic free convection flow in a porous medium with Newtonian heating. Int J Appl Math Stat 42:474–480Google Scholar
  31. 31.
    Hussanan A, Khan I, Salleh MZ, Sharidan S (2015) Slip effects on unsteady free convective heat and mass transfer flow with Newtonian heating. Therm Sci. doi: 10.2298/TSCI131119142A Google Scholar
  32. 32.
    Vieru D, Fetecau C, Fetecau C, Nigar N (2014) Magnetohydrodynamic natural convection flow with Newtonian heating and mass diffusion over an infinite plate that applies shear stress to a viscous fluid. Zeitschrift für Naturforschung A 69:714–724CrossRefGoogle Scholar

Copyright information

© The Natural Computing Applications Forum 2016

Authors and Affiliations

  • Abid Hussanan
    • 1
  • Mohd Zuki Salleh
    • 1
    Email author
  • Ilyas Khan
    • 2
  • Razman Mat Tahar
    • 3
  1. 1.Applied and Industrial Mathematics Research Group, Faculty of Industrial Science and TechnologyUniversiti Malaysia PahangKuantanMalaysia
  2. 2.Department of Basic Sciences, College of EngineeringMajmaah UniversityMajmaahSaudi Arabia
  3. 3.Faculty of Industrial ManagementUniversiti Malaysia PahangKuantanMalaysia

Personalised recommendations