Radiative and magnetohydrodynamics flow of third-grade viscoelastic fluid past an isothermal inverted cone in the presence of heat generation/absorption

  • S. Abdul Gaffar
  • V. Ramachandra Prasad
  • O. Anwar Bég
  • Md. H. Hidayathullah Khan
  • K. Venkatadri
Technical Paper


A mathematical analysis to investigate the non-linear, isothermal, steady state, free convection boundary layer flows of an incompressible third-grade viscoelastic fluid past an isothermal inverted cone in the presence of magnetohydrodynamic, thermal radiation, and heat generation/absorption. The transformed conservation equations for linear momentum, heat, and mass are solved numerically subject to the realistic boundary conditions using the second-order accurate implicit finite-difference Keller-box method. The numerical code is validated with the previous studies. Detailed interpretation of the computations is included. The present simulations are of interest in chemical engineering systems and solvent and low-density polymer material processing.


Viscoelastic fluid Third-grade fluid parameter Solvent processing Skin friction Magnetohydrodynamics Thermal radiation 

List of symbols


Half angle of the cone


Externally imposed radial magnetic field




Skin-friction coefficient


Specific heat


Mass (species) diffusivity


Radiation parameter


Dimensionless stream function


Local Grashof number


Acceleration due to gravity


Thermal diffusivity


Thermal conductivity of the fluid


Magnetic parameter


Buoyancy ratio parameter


Local Nusselt number


Prandtl number


Radiative heat flux


Local radius of the truncated cone


Schmidt number


Local Sherwood number


Fluid temperature

u, v

Dimensionless velocity components along the x- and y-directions, respectively


Velocity vector


Stream wise coordinate


Transverse coordinate

Greek symbols


Thermal diffusivity


Coefficient of thermal expansion


Coefficient of concentration expansion


First viscoelastic material fluid parameter


Second viscoelastic material fluid parameter


Third-grade material parameter


Kinematic viscosity


Fluid density


Newtonian dynamic viscosity


Dimensionless radial coordinate


Dimensionless temperature


Dimensionless concentration


Heat generation/absorption parameter


Third-grade dimensionless viscoelastic fluid parameter


Stefan–Boltzmann constant


Dimensionless tangential coordinate


Dimensionless stream function



Surface conditions on cone (wall)

Free stream conditions


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.Department of MathematicsSalalah College of TechnologySalalahOman
  2. 2.Department of Mathematics, School of Advanced SciencesVIT UniversityVelloreIndia
  3. 3.Fluid Mechanics, Aeronautical and Mechanical Engineering DepartmentUniversity of SalfordManchesterUK
  4. 4.Department of MathematicsMadanapalle Institute of Technology and ScienceMadanapalleIndia

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