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

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Abstract

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.

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Abbreviations

C :

Species concentration (mol m−3)

C w :

Species concentration near the plate (mol m−3)

C ∞ :

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

C p :

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

D :

Mass diffusivity (m2 s−1)

g :

Acceleration due to gravity (m s−2)

n :

Scalar constant

i :

Unit vector

h s :

Heat transfer coefficient

Gr :

Thermal Grashof number

Gm :

Modified Grashof number

k :

Thermal conductivity (W m−1 K−1)

Pr:

Prandtl number

q r :

Radiative heat flux (W m−2)

R :

Radiation parameter

Sc :

Schmidt number

T :

Temperature of the fluid (K)

T ∞ :

Ambient temperature (K)

t :

Time (s)

u :

Velocity of the fluid (m s−1)

j :

Microinertia per unit mass (m2)

ωt :

Phase angle

N :

Angular velocity (m s−1)

U :

Amplitude of plate oscillations (m)

H(t):

Unit step function

erfc:

Complementary error function

α :

Vortex viscosity (kg m−1 s−1)

β :

Microrotation parameter

β T :

Volumetric coefficient of thermal expansion (K−1)

β C :

Volumetric coefficient of mass expansion (K−1)

γ :

Conjugate parameter for Newtonian heating

γ 0 :

Spin gradient viscosity (kg m s−1)

η :

Spin gradient viscosity parameter

μ :

Dynamic viscosity (kg m−1 s−1)

ρ :

Fluid density (kg m−3)

σ*:

Stefan–Boltzmann constant (W m−2 K−4)

θ :

Dimensionless temperature

ω :

Frequency of oscillation

w :

Condition at wall

∞ :

Condition at infinity

*:

Dimensional variables

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Acknowledgments

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

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Authors and Affiliations

  1. Applied and Industrial Mathematics Research Group, Faculty of Industrial Science and Technology, Universiti Malaysia Pahang, Lebuhraya Tun Razak, Kuantan, 26300, Pahang, Malaysia

    Abid Hussanan & Mohd Zuki Salleh

  2. Department of Basic Sciences, College of Engineering, Majmaah University, Majmaah, 11952, Saudi Arabia

    Ilyas Khan

  3. Faculty of Industrial Management, Universiti Malaysia Pahang, Lebuhraya Tun Razak, Kuantan, 26300, Pahang, Malaysia

    Razman Mat Tahar

Authors
  1. Abid Hussanan
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  2. Mohd Zuki Salleh
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Correspondence to Mohd Zuki Salleh.

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Hussanan, A., Salleh, M.Z., Khan, I. et al. Heat and mass transfer in a micropolar fluid with Newtonian heating: an exact analysis. Neural Comput & Applic 29, 59–67 (2018). https://doi.org/10.1007/s00521-016-2516-0

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  • DOI: https://doi.org/10.1007/s00521-016-2516-0

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