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Numerical solution to natural convection over an inclined wavy surface embedded in a porous medium saturated with a nanofluid

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Abstract

This article presents the study of natural convection in a nanofluid along an inclined wavy surface embedded in a porous medium. A coordinate transformation is employed to transform the complex wavy surface to a smooth surface. The governing equations are transformed into a set of ordinary differential equations using the similarity transformation. These nonlinear ordinary differential equations are reduced to a system of linear differential equations using the successive linearization method. The Chebyshev pseudo spectral method is then used to solve the linearized differential equations. The present results are compared with previously published work and are found to be in very good agreement. The effects of Brownian motion parameter, thermophoresis parameter, amplitude of the wavy surface, angle of inclination of the wavy surface on the non-dimensional velocity, temperature, nanoparticle volume fraction, heat and nanoparticle mass transfer rates are studied and presented graphically.

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Abbreviations

a :

Amplitude of the wavy surface.

D B :

Brownian diffusion coefficient.

D T :

Thermophoretic diffusion coefficient.

f :

Dimensionless stream function.

g :

Acceleration due to gravity.

k :

Thermal conductivity.

K :

Permeability.

l :

Characteristic length of the wavy surface.

Le:

Lewis number.

N b :

Brownian motion parameter.

N r :

Buoyancy ratio.

N t :

Thermophoresis parameter.

NSh x :

Local nanoparticle Sherwood number.

Nu x :

Local Nusselt number.

P :

Pressure.

q w :

Heat flux.

q np :

Nanoparticle Mass flux.

Ra:

Rayleigh number.

s :

Rescaled nanoparticle volume fraction.

T :

Temperature of the fluid.

u, v :

Velocity components in the x and y directions, respectively.

x, y :

Cartesian coordinates.

α :

Thermal diffusivity of porous medium.

β :

Volumetric coefficient of thermal expansion of fluid.

γ :

The ratio between the effective heat capacity of the nanoparticle material and heat capacity of the fluid.

η :

Similarity variable.

θ :

Dimensionless temperature.

μ :

Dynamic viscocity.

ξ :

Nonsimilar variable.

ρ f :

Density of the fluid.

ρ p :

Nanoparticle mass density.

(ρ c ) f :

Heat capacity of the fluid.

(ρ c ) p :

Effective heat capacity of the nanoparticle material.

ϕ :

Nanoparticle volume fraction.

ψ :

Stream function.

w :

Conditions at the wall.

∞:

Conditions in the free stream.

′:

Differentiation with respect to η.

.:

Differentiation with respect to ξ.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology, Warangal, Telangana, 506004, India

    D. Srinivasacharya & P. Vijay Kumar

  2. School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsville, 3209, Pietermaritzburg, South Africa

    P. Sibanda

Authors
  1. D. Srinivasacharya
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  2. P. Vijay Kumar
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  3. P. Sibanda
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Correspondence to D. Srinivasacharya.

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Srinivasacharya, D., Vijay Kumar, P. & Sibanda, P. Numerical solution to natural convection over an inclined wavy surface embedded in a porous medium saturated with a nanofluid. Meccanica 51, 1723–1737 (2016). https://doi.org/10.1007/s11012-015-0331-9

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