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

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## 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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