Analysis of chemically reactive species with mixed convection and Darcy–Forchheimer flow under activation energy: a novel application for geothermal reservoirs

  • Aaqib MajeedEmail author
  • Ahmad Zeeshan
  • Farzan Majeed Noori


In the present article, an analysis has been performed to discuss the impact of steady mixed convection with Darcy–Forchheimer flow towards linear surface. Investigation has been achieved in the presence of Arrhenius activation energy and radiative heat flux which are associated with the heat and mass transport analysis which has not been performed so far. Porous media features are elaborated by utilizing Darcy–Forchheimer relation. Boundary-layer idea is employed for the simplification of governing expressions. The resulting set of mathematical expression is now solved with the help of bvp4c MATLAB package which applies a three-stage Lobatto IIIa finite-difference collocation scheme. Diagrams are drawn against pertinent parameters such as buoyancy forces ratio parameter, mixed convection parameter, porosity parameter, local inertia coefficient, activation energy, chemical reaction rate constant, Schmidt number, temperature difference ratio, exponentially fitted constant, magnetic parameter, radiation parameter, first-order and second-order slip parameter, suction or injection parameter and Prandtl number. It is observed that both mixed convection and activation energy parameters have an opposite impact on species profile. Also the present results are compared with those available in the literature for some cases, and an excellent agreement is found between them.


Mixed convection Activation energy Darcy–Forchheimer Chemical reaction Magnetic field 

List of symbols

\(\bar{A}\), \(\bar{B}\)



Magnetic field


Wall concentration


Reference concentration


Wall velocity


Reference velocity


Temperature (K)


Wall temperature


Reference temperature

\(T_{\infty }\)

Free-stream temperature


Specific heat \(({\text{J}}\,{\text{kg}}^{ - 1} \,{\text{K}}^{ - 1} )\)


Skin friction


Dimensionless stream function


Local inertial coefficient


Thermal conductivity \(({\text{W}}\,{\text{m}}^{ - 1} \,{\text{K}}^{ - 1} )\)


Knudsen number


Porosity parameter


Characteristic length


Ratio of thermal and solutal expansions


Local Nusselt number


Prandtl number


Radiation parameter


Magnetic field \(({\text{A/m}})\)


Local Reynolds number


Initial strength of suction


Activation energy


Schmidt number

(u, v)

Components of velocity \(({\text{m}}\,{\text{s}}^{ - 1} )\)

(x, y)

Coordinate axes normal to sheet (m)


Dynamic viscosity \(({\text{N}}\,{\text{s}}\,{\text{m}}^{ - 1} )\)


Dimensionless temperature


Suction/injection parameter

Greek symbols


First-order slip


Second-order slip


Mean free molecular path


Momentum accommodation


Temperature difference ratio


Density \(({\text{k}}\,{\text{g}}\,{\text{m}}^{ - 3} )\)

\(k^{ * }\)

Mean absorption coefficient


Chemical reaction rate constant


Stefan–Boltzmann constant


Stream function \(({\text{m}}^{ 2} \,{\text{s}}^{ - 1} )\)


Mixed convection parameter



The corresponding author is profoundly grateful to the Higher Education Commission (HEC) for their financial support under Start-Up Research Grant Program (SRGP) with Project No. 2495.


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsBacha Khan UniversityCharsaddaPakistan
  2. 2.Department of Mathematics and StatisticsFBAS, IIUIIslamabadPakistan
  3. 3.Department of Informatics, Faculty of Mathematics and Natural SciencesUniversity of OsloOsloNorway

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