Capturing the Transient Features of Double Diffusive Thin Film Flow of a Second Grade Fluid Through a Porous Medium

  • Mehari Fentahun Endalew
  • Subharthi SarkarEmail author
Original Paper


The transient features of double-diffusive natural convection thin film flow of a second grade fluid past an inclined plate embedded in a porous medium has been captured. Laplace transform technique combined with INVLAP subroutine of MATLAB is employed to solve the governing equations. The numerical values of all fluid flow characteristics are demonstrated graphically for different values of pertinent flow parameters. Furthermore, the time bound effects of the flow parameters influencing unsteady heat and mass transfer thin film flow of a fluid of second grade are revealed and supported with physical interpretations. We have found that the influence of thermal and solutal buoyancy forces grow with respect to time while the effects of thermal and solutal diffusion diminish with time. Also, the effect of second grade parameter becomes more pronounced with the passage of time. Researchers are welcome to validate the novel results presented in this paper through experiments which may find use in the upgraded design of mechanical systems involving second grade thin film flow in a way that supports better heat and mass transfer.


Unsteady flow Thin film Second grade fluid Porous medium Heat and mass transfer 

List of Symbols

\( A_{1} \), \( A_{2} \)

Rivlin–Ericksen tensors

\( P \)

Fluid pressure

\( I \)

Identity tensor

\( C_{p} \)

Specific heat capacity

\( G_{r} \)

Thermal Grashof number

\( G_{c} \)

Solutal Grashof number

\( g \)

Gravitational accleration

\( K \)

Permeability of medium

\( P_{r} \)

Prandtl number

\( S_{c} \)

Schmidt number


Chemical molecular diffusivity

\( T^{\prime} \)

Dimensional temperature

\( T \)

Dimensionless temperature

\( T_{w}^{'} \)

Constant plate temperature

\( T_{\infty }^{'} \)

Temperature of free stream

\( \bar{T} \)

Transformed temperature


Dimensionless solutal concentration

\( C^{\prime} \)

Dimensional solutal concentration

\( C_{w}^{'} \)

Solutal concentration at the plate

\( C_{\infty }^{'} \)

Solutal concentration at free stream

\( \bar{C} \)

Transformed concentration

\( Sh_{0} \)

Sherwood number at \( y = 0 \)

\( Sh_{1} \)

Sherwood number at \( y = 1 \)

\( Nu_{0} \)

Nusselt number at \( y = 0 \)

\( Nu_{1} \)

Nusselt number at \( y = 1 \)

\( u' \)

Dimensional fluid velocity

\( u \)

Dimensionless fluid velocity

\( \bar{u} \)

Transformed velocity

\( t' \)

Dimensional time

\( t \)

Dimensionless time

Greek Symbols

\( \beta^{*} \)

Expansion coefficient for mass transfer

\( \beta \)

Expansion coefficient for heat transfer

\( \kappa \)

Thermal conductivity of the fluid

\( \nu \)

Kinematic viscosity

\( \rho \)

Density of the fluid

\( \theta \)

Inclination angle of the plate

\( \phi ' \)

Dimensional porosity parameter

\( \phi \)

Dimensionless porosity parameter

\( \mu \)

Dynamic viscosity

\( \alpha \)

Second grade parameter

\( \delta \)

Thin film thickness

\( \alpha_{1} ,\;\alpha_{2} \)

Material constants of second grade

\( \tau_{0} \)

Skin friction at \( y = 0 \)

\( \tau \)

Cauchy stress tensor



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Copyright information

© Springer Nature India Private Limited 2019

Authors and Affiliations

  1. 1.Department of MathematicsKalinga Institute of Industrial Technology Deemed to be University (KIIT)BhubaneswarIndia

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