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Free convection in the boundary layer flow of a micropolar fluid along a vertical wavy surface

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Summary

A cubic spline collocation numerical method and a simple transposition theorem have been used to study the free convection in the flow of a micropolar fluid along irregular vertical surfaces. A sinusoidal surface is used to elucidate the amplitude wavelength ratio effects on the free convection in a micropolar boundary layer. The effects of micropolar parameterR and geometries on the velocity and temperature fields have been graphically studied. The skin friction stress on the wall has also been studied and discussed. It is observed that the frequency of the local heat transfer rate is twice that of the wavy surface, irrespective of whether the fluid is a Newtonian fluid or micropolar fluid; the same result is also obtained for the skin friction on the wall.

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Abbreviations

\(\bar a\) :

amplitude

B :

dimensionless material parameter, Eq. (8)

C p :

specific heat of the fluid at constant pressure

C f :

skin-friction coefficient

g :

gravitational acceleration

Gr:

Grashof number

h :

heat transfer coefficient

j :

micro-inertia density

K f :

thermal conductivity

L :

wave length

N :

microrotation

Nu:

local Nusselt number defined in Eq. (20)

\(\overline {Nu} \) :

total Nusselt number defined in Eq. (21)

p :

pressure

Pr:

Prandtl number

R :

micropolar parameter, ϰ/μ

s :

distance measured along the surface from the leading edge

T :

temperature

u, v :

velocity components

x, y :

coordinates

α:

amplitude-wavelength ratio\((\bar a/L)\)

β:

thermal expansion coefficient

γ:

spin-gradient viscosity

η:

dimensionless parameter

σ:

surface geometry function

θ:

dimensionless temperature,(T−T ∞)/(T w −T ∞)

ϰ:

vortex viscosity

λ:

dimensionless material parameter

μ:

absolute viscosity

ν3 :

microrotation component

ξ:

dimensionless parameter

ϱ:

density of fluid

−:

dimensional quantity

∧:

nondimensional quantity

′:

derivative with respect tox

w :

surface conditions

∞:

conditions far away from the surface

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  1. C. -P. Chiu &  H. -M. Chou

    Present address: Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan, Republic of China

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    1. C. -P. Chiu
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    Chiu, C.P., Chou, H.M. Free convection in the boundary layer flow of a micropolar fluid along a vertical wavy surface. Acta Mechanica 101, 161–174 (1993). https://doi.org/10.1007/BF01175604

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