Cattaneo–Christov heat flux and non-uniform heat-source/sink impacts on radiative Oldroyd-B two-phase flow across a cone/wedge

  • M. Gnaneswara Reddy
  • M. V. V. N. L. Sudha Rani
  • K. Ganesh Kumar
  • B. C. Prasannakumara
Technical Paper
  • 27 Downloads

Abstract

Impact of Cattaneo–Christov heat flux on radiative Oldroyd-B two-phase flow across a cone/wedge is addressed. RKF-45 method with shooting technique is used to obtain solution of the problem. The obtained results are presented through graphs and tables. We examined the results under non-linear variation of thermal radiation. Our simulations established that influence of physical parameter highly effective for cone when compare to wedge.

Keywords

Cattaneo–Christov heat flux Thermal radiation Oldroyd-B fluid Fluid–particle suspension 

Nomenclature

\(A^{*}\)

Heat-source parameter

\(B^{*}\)

Heat-sink parameter

\(B_{0}\)

Uniform magnetic field

\(Ec\)

Eckert number

\(Gr\)

Grashoff number

\(g\)

Gravitational acceleration

\(K\)

Stokes drag coefficient

\(K*\)

Mean absorption coefficient

\(l\)

Dust particle concentration parameter

\(M\)

Magnetic parameter

\(m\)

Mass of dust particle

\(N\)

Number of dust particles

\(Pr\)

Prandtl number

\(q'''\)

Temperature-dependent on heat-source/sink parameters

\(R\)

Radiation parameter

\(Re\)

Reynolds number

\(T\)

Fluid-phase temperature

\(T_{\text{p}}\)

Dust-phase temperature

\(u\)

Fluid-phase velocity components along \(x\)

\(u_{\text{p}}\)

Dust-phase velocity components along \(x\)

\(v\)

Fluid-phase velocity components along \(y\)

\(v_{\text{p}}\)

Dust-phase velocity components along \(y\)

\(x\)

Direction of both fluid and particle phases

\(y\)

Direction of both fluid and particle phases

Greek symbols

\(\beta\)

Thermal relaxation parameter

\(\beta_{1}\)

Deborah number with respect to relaxation of time

\(\beta_{2}\)

Deborah number with respect to retardation of time

\(\beta_{\upsilon }\)

Fluid–particle interaction parameter for velocity

\(\beta_{t}\)

Fluid–particle interaction parameter for temperature

\(\gamma\)

Specific heat ratio

\(\gamma_{1}\)

Non-linear convection parameter

\(\lambda\)

Mixed convection parameter

\(\lambda_{1}\)

Relaxation of time

\(\lambda_{2}\)

Retardation of time

\(\rho\)

Densities of the fluid

\(\rho_{\text{p}}\)

Densities of the particle phase

\(\nu\)

Viscosity of the fluid

\(\rho\)

Electrical conductivity

\(\delta\)

Relaxation time of heat flux

\(\sigma^{*}\)

Stefan–Boltzman coefficient

\(\tau_{\text{T}}\)

Relaxation time for temperature

\(\tau_{\text{v}}\)

Relaxation time for velocity

Superscript

\('\)

Differentiate with respect to \(\xi\)

Subscripts

\(p\)

Dust phase

\(\infty\)

Fluid property at ambient condition

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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.Department of MathematicsAcharya Nagarjuna University Ongole CampusOngoleIndia
  2. 2.Department of Studies and Research in MathematicsKuvempu UniversityShankaraghattaIndia
  3. 3.Department of MathematicsGovernment First Grade CollegeKoppaIndia

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