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
  • 21 Downloads

Abstract

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.

Keywords

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

List of symbols

A

Half angle of the cone

B0

Externally imposed radial magnetic field

C

Concentration

Cf

Skin-friction coefficient

cp

Specific heat

Dm

Mass (species) diffusivity

F

Radiation parameter

f

Dimensionless stream function

Grx

Local Grashof number

g

Acceleration due to gravity

K

Thermal diffusivity

k

Thermal conductivity of the fluid

M

Magnetic parameter

N

Buoyancy ratio parameter

Nu

Local Nusselt number

Pr

Prandtl number

qr

Radiative heat flux

r

Local radius of the truncated cone

Sc

Schmidt number

Sh

Local Sherwood number

T

Fluid temperature

u, v

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

V

Velocity vector

x

Stream wise coordinate

y

Transverse coordinate

Greek symbols

α

Thermal diffusivity

β

Coefficient of thermal expansion

β*

Coefficient of concentration expansion

ε1

First viscoelastic material fluid parameter

ε2

Second viscoelastic material fluid parameter

β3

Third-grade material parameter

ν

Kinematic viscosity

ρ

Fluid density

μ

Newtonian dynamic viscosity

η

Dimensionless radial coordinate

θ

Dimensionless temperature

ϕ

Dimensionless concentration

Δ

Heat generation/absorption parameter

φ

Third-grade dimensionless viscoelastic fluid parameter

σ*

Stefan–Boltzmann constant

ξ

Dimensionless tangential coordinate

ψ

Dimensionless stream function

Subscripts

w

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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