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Melting heat transfer effects on stagnation point flow of micropolar fluid saturated in porous medium with internal heat generation (absorption)

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Abstract

The effect of melting heat transfer on the two dimensional boundary layer flow of a micropolar fluid near a stagnation point embedded in a porous medium in the presence of internal heat generation/absorption is investigated. The governing non-linear partial differential equations describing the problem are reduced to a system of nonlinear ordinary differential equations using similarity transformations solved numerically using the Chebyshev spectral method. Numerical results for velocity, angular velocity and temperature profiles are shown graphically and discussed for different values of the inverse Darcy number, the heat generation/absorption parameter, and the melting parameter. The effects of the pertinent parameters on the local skin-friction coefficient, the wall couple stress, and the local Nusselt number are tabulated and discussed. The results show that the inverse Darcy number has the effect of enhancing both velocity and temperature and suppressing angular velocity. It is also found that the local skin-friction coefficient decreases, while the local Nusselt number increases as the melting parameter increases.

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Abbreviations

c p :

specific heat at constant pressure

c s :

heat capacity of solid surface

C fx :

local skin-friction coefficient

D −1 a :

permeability parameter

f′:

dimensionless velocity

G :

micro-rotation parameter

G 1 :

micro-rotation constant

h :

dimensionless microrotation

k :

gyro-viscosity

K :

material parameter

k 1 :

permeability

M :

melting parameter

M x :

dimensionless wall couple stress

m 0 :

boundary parameter

m w :

wall couple stress

N :

dimensional component of microrotation vector normal to x−y plane

Nu x :

local Nusselt number

Pr :

Prandtl number

Q 0 :

heat generation or absorption constant

q w :

heat transfer from plate

Re x :

local Reynolds number

T :

fluid temperature

T 0 :

solid temperature

u, v :

dimensional components of velocities along and perpendicular to plate, respectively

T m :

temperature of melting surface

T ∞ :

free stream condition

x, y :

dimensional distances along and perpendicular to plate, respectively

α :

thermal diffusivity

γ :

heat generation or absorption parameter

θ :

dimensionless temperature

κ :

thermal conductivity

λ :

latent heat fluid

µ:

dynamic viscosity

ρ :

fluid density

τ w :

surface shear stress

′:

differentiation with respect to η

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Benha University, 13518, Benha, Egypt

    M. A. A. Mahmoud & S. E. Waheed

  2. Department of Mathematics and Statistic, Faculty of Science, Taif University, 21974, Taif, Kingdom of Saudi Arabia

    S. E. Waheed

Authors
  1. M. A. A. Mahmoud
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  2. S. E. Waheed
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Correspondence to S. E. Waheed.

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Mahmoud, M.A.A., Waheed, S.E. Melting heat transfer effects on stagnation point flow of micropolar fluid saturated in porous medium with internal heat generation (absorption). Appl. Math. Mech.-Engl. Ed. 35, 979–992 (2014). https://doi.org/10.1007/s10483-014-1840-7

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  • DOI: https://doi.org/10.1007/s10483-014-1840-7

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