Physical aspects of Darcy–Forchheimer flow and dissipative heat transfer of Reiner–Philippoff fluid


The main focus of the present research work is to elaborate the Reiner–Philippoff fluid flow over a stretching sheet along with thermal radiation effect. A Darcy–Forchheimer medium was imposed and a linear stretching surface was used to generate the flow. Application of appropriate transformation yields nonlinear ordinary differential equation through nonlinear Navier–Stokes equations and solved by Runge–Kutta–Fehlberg shooting technique. Importance of influential variables such as velocity and temperature was elaborated graphically. It is envisaging that the boost up values of γ declines the both velocity and temperature profiles.

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a :


\(u_{\text{w}} \left( x \right) = ax^{1/3}\) :

Stretched velocity

\(K^{*}\) :

Permeability of porous medium

\(F = \frac{{C_{\text{b}} }}{{K^{*1/2} }}\) :

Non-uniform inertia coefficient of porous medium

C b :

Drag coefficient


Forchheimer number

K p :

Porosity parameter

T :

Fluid temperature

T w :

Wall temperature

T :

Temperature outside the surface


Prandtl number

q w :

Heat flux from the sheet

k :

Thermal conductivity

Nu x :

Nusselt number

\(Re_{\text{x}} = \frac{{u_{\text{w}} x}}{\nu }\) :

Reynolds number

λ :

Reiner–Philippoff fluid parameter

γ :

Bingham number

σ :

Electrical conductivity,

ρ :

Fluid density

α :

Thermal diffusivity

τ w :

Wall shear stress


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Correspondence to K. Ganesh Kumar.

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Gnaneswara Reddy, M., Sudharani, M.V.V.N.L., Ganesh Kumar, K. et al. Physical aspects of Darcy–Forchheimer flow and dissipative heat transfer of Reiner–Philippoff fluid. J Therm Anal Calorim 141, 829–838 (2020).

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  • Reiner–Philippoff fluid
  • Darcy–Forchheimer
  • Thermal radiation
  • Stretching sheet