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Stability analysis and modeling for the three-dimensional Darcy-Forchheimer stagnation point nanofluid flow towards a moving surface

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Abstract

In this research, the three-dimensional (3D) steady and incompressible laminar Homann stagnation point nanofluid flow over a porous moving surface is addressed. The disturbance in the porous medium has been characterized by the Darcy-Forchheimer relation. The slip for viscous fluid is considered. The energy equation is organized in view of radiative heat flux which plays an important role in the heat transfer rate. The governing flow expressions are first altered into first-order ordinary ones and then solved numerically by the shooting method. Dual solutions are obtained for the velocity, skin friction coefficient, temperature, and Nusselt number subject to sundry flow parameters, magnetic parameter, Darcy-Forchheimer number, thermal radiation parameter, suction parameter, and dimensionless slip parameter. In this research, the main consideration is given to the engineering interest like skin friction coefficient (velocity gradient or surface drag force) and Nusselt number (temperature gradient or heat transfer rate) and discussed numerically through tables. In conclusion, it is noticed from the stability results that the upper branch solution (UBS) is more reliable and physically stable than the lower branch solution (LBS).

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Abbreviations

ξU, ξV :

velocities in x- and y-directions, respectively

α :

momentum accommodation coefficient

K*:

permeability of porous space

Kn :

Knudsen number

Λ:

mean free path

M 1, M 2 :

slip coefficients in x- and y-directions

x, y, z :

Cartesian coordinates

u, v, w :

velocity vectors

T ∞ :

ambient temperature

k*:

mean absorption coefficient

Q*:

heat generation/absorption coefficient

β*:

porosity parameter

Re :

Reynold number

C f1, C f2 :

skin frictions

Nu :

Nusselt number

ν nf :

kinematic viscosity

\(F\left(\frac{C_b}{xK^{* \frac{1}{2}}}\right)\) :

coefficient of non-uniform inertia

T :

temperatures

c p :

specific heat

k nf :

thermal conductivity

σ*:

Stefan-Boltzmann constant

u w(x):

stretching velocity

C b :

drag coefficient

μ f :

dynamic viscosity

w 0 :

suction/injection

Tw:

wall temperature

s :

suction/injection variable

Pr :

Prandtl number

R :

radiation number

A, B :

slip parameters in x- and y-directions

λ, λ 1 :

dimensionless constant parameters

Q*:

heat generation parameter

F x, F y :

coefficients of inertia in x- and y-directions

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Author information

Authors and Affiliations

  1. Department of Mathematics, Huzhou University, Huzhou, 313000, Zhejiang Province, China

    Yuming Chu

  2. Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha, 410114, China

    Yuming Chu

  3. Department of Mathematics, Riphah International University, Faisalabad Campus, Faisalabad, 38000, Pakistan

    M. I. Khan

  4. Department of Mathematics, Quaid-i-Azam University, Islamabad, 44000, Pakistan

    M. I. U. Rehman & S. Qayyum

  5. Department of Mathematics and Computer Science, Beirut Arab University, Beirut, 11072809, Lebanon

    S. Kadry

  6. NUTECH School of Applied Sciences and Humanities, National University of Technology, Islamabad, 44000, Pakistan

    M. Waqas

Authors
  1. Yuming Chu
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  2. M. I. Khan
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  3. M. I. U. Rehman
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  4. S. Kadry
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  5. S. Qayyum
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  6. M. Waqas
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Corresponding author

Correspondence to M. I. Khan.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11971142, 11871202, 61673169, 11701176, 11626101, and 11601485)

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Chu, Y., Khan, M.I., Rehman, M.I.U. et al. Stability analysis and modeling for the three-dimensional Darcy-Forchheimer stagnation point nanofluid flow towards a moving surface. Appl. Math. Mech.-Engl. Ed. 42, 357–370 (2021). https://doi.org/10.1007/s10483-021-2700-7

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  • DOI: https://doi.org/10.1007/s10483-021-2700-7

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