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Analysis of Dual Solutions in MHD Fluid Flow with Heat and Mass Transfer Past an Exponentially Shrinking/Stretching Surface in a Porous Medium

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Abstract

The present study examines the nature of dual solutions in hydromagnetic boundary layer flow a conducting fluid past an exponentially shrinking/stretching sheet with simultaneous thermal and concentration distributions in a porous medium. Due to the non-linearity of the model boundary value problem, both similarity transformation and the “MATLAB built-in bvp4c numerical scheme” are utilized to solve this problem. For shrinking surface flow, the model exhibits non-unique dual solutions and a linear stability analysis is executed in order to identify the stable and physically achievable solution. Influences of various emerging parameters on the flow with heat and mass transfer are discussed through graphs and in tabular form. A comparison has been made with existing results and excellent agreement is achieved.

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Data Availability

Software application (MATLAB).

Abbreviations

\(C_{0}\) :

Concentration

\(a,c\) :

Constants

\(L\) :

Characteristics length,

\(T_{0}\) :

Characteristic temperature

\(C\) :

Concentration of the fluid

\(Kr*\) :

Chemical reaction rate on the species concentration

\(f^{\prime}(\eta )\) :

Dimensionless velocity

\(Kr\) :

Local chemical reaction parameter

\(M\) :

Magnetic field parameter

\(D\) :

Mass diffusivity

\(Nu\) :

Nusselt number

\(K\) :

Permeability of the porous medium,

\(\Pr\) :

Prandtl number

\({\text{Re}}\) :

Reynolds number

\(Sc\) :

Schmidt number

\(s\) :

Suction/injection parameter

\(C_{f}\) :

Skin friction coefficient

\(Sh\) :

Sherwood number

\(C_{p}\) :

Specific heat at constant pressure

\(B_{0}\) :

Strength of magnetic field

\(\psi\) :

Stream function

\(T\) :

Temperature of the fluid

\(k\) :

Thermal conductivity

\(t\) :

Time

\(u,v\) :

Velocity components along x,y – directions

\(\mu\) :

Dynamic viscosity

\(\rho\) :

Density of the fluid

\(\theta (\eta )\) :

Dimensionless temperature

\(\phi (\eta )\) :

Dimensionless concentration

\(\omega\) :

Eigen-value parameter.

\(\sigma\) :

Electrical conductivity

\(\upsilon\) :

Kinematic viscosity

\(\psi\) :

Stream function

\(\eta\) :

Similarity variable

\(\lambda\) :

Stretching/shrinking parameter

\(\tau\) :

Time variable

\(w\) :

At wall

\(\infty\) :

At infinity

\(^{\prime}\) :

Differentiation with respect to the dimensionless similarity variable \(\eta\)

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Authors and Affiliations

  1. Department of Mathematics, Dibrugarh University, Dibrugarh, 786004, India

    Debasish Dey & Rupjyoti Borah

  2. Faculty of Military Science, Stellenbosch University, Stellenbosch, South Africa

    O. D. Makinde

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  1. Debasish Dey
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Correspondence to Rupjyoti Borah.

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Dey, D., Makinde, O.D. & Borah, R. Analysis of Dual Solutions in MHD Fluid Flow with Heat and Mass Transfer Past an Exponentially Shrinking/Stretching Surface in a Porous Medium. Int. J. Appl. Comput. Math 8, 66 (2022). https://doi.org/10.1007/s40819-022-01268-7

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