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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.

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Abbreviations

\(A^{*}\) :

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

\(\beta\) :

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

\('\) :

Differentiate with respect to \(\xi\)

\(p\) :

Dust phase

\(\infty\) :

Fluid property at ambient condition

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Authors and Affiliations

  1. Department of Mathematics, Acharya Nagarjuna University Ongole Campus, Ongole, 523 001, India

    M. Gnaneswara Reddy & M. V. V. N. L. Sudha Rani

  2. Department of Studies and Research in Mathematics, Kuvempu University, Shankaraghatta, 577 451, India

    K. Ganesh Kumar

  3. Department of Mathematics, Government First Grade College, Koppa, 577126, India

    B. C. Prasannakumara

Authors
  1. M. Gnaneswara Reddy
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  2. M. V. V. N. L. Sudha Rani
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  3. K. Ganesh Kumar
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  4. B. C. Prasannakumara
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Correspondence to M. Gnaneswara Reddy.

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Technical Editor: Cezar Negrao.

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Reddy, M.G., Rani, M.V.V.N.L.S., Kumar, K.G. et al. Cattaneo–Christov heat flux and non-uniform heat-source/sink impacts on radiative Oldroyd-B two-phase flow across a cone/wedge. J Braz. Soc. Mech. Sci. Eng. 40, 95 (2018). https://doi.org/10.1007/s40430-018-1033-8

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