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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

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.

Keywords

Unsteady flow Micropolar fluid Newtonian heating Exact solutions 

List of symobls

C

Species concentration (mol m−3)

Cw

Species concentration near the plate (mol m−3)

C

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

Cp

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

hs

Heat transfer coefficient

Gr

Thermal Grashof number

Gm

Modified Grashof number

k

Thermal conductivity (W m−1 K−1)

Pr

Prandtl number

qr

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

Greek symbols

α

Vortex viscosity (kg m−1 s−1)

β

Microrotation parameter

βT

Volumetric coefficient of thermal expansion (K−1)

βC

Volumetric coefficient of mass expansion (K−1)

γ

Conjugate parameter for Newtonian heating

γ0

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

Subscripts

w

Condition at wall

Condition at infinity

Superscript

*

Dimensional variables

Notes

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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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

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