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Nonlinear Mixed Convection Impact on Radiated Flow of Nanomaterials Subject to Convective Conditions

  • Research Article-Mechanical Engineering
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Abstract

The heat transportation features of current liquids are improved via suspension of nano-sized solid elements having diameter (< 100 nm), regarded as potential working liquids to utilize in automobile radiators, electronic chilling systems, solar collectors, heat pipes and nuclear reactors. The present investigation explores the simultaneous impacts of convective conditions, and stratifications in thermally radiated flow of magneto-Jeffrey nanomaterials, nonlinear convection, heat source and Joule heating are taken into account. Implementation of boundary layer theory leads to rheological model of considered problem. The relevant variables have been used to convert PDEs into ODEs. Convergent solutions are achieved through homotopic algorithm, while significance of sundry factors are provided via graphical and tabular data. We have examined reduction in liquid temperature along with concentration subject to higher thermal/concentration stratification factors.

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Abbreviations

\((u,v)\;(x,y)\) :

Velocity components and space coordinates

\(T\) :

Temperature

\(T_{\text{w}}\) :

Wall temperature

\(T_{\infty }\) :

Ambient fluid temperature

\(C\) :

Concentration

\(C_{\text{w}}\) :

Wall concentration

\(C_{\infty }\) :

Ambient fluid concentration

\(C_{0}\) :

Reference concentration

\(T_{0}\) :

Reference temperature

\(Q_{0}\) :

Coefficient for absorption/generation

\(g\) :

Gravitational acceleration

\(h_{\text{f}}\) :

Heat transfer coefficient

\(h_{\text{g}}\) :

Mass transfer coefficient

\(B_{0}\) :

Magnetic field strength

\(D_{\text{B}}\) :

Coefficient of Brownian diffusion

\(D_{\text{T}}\) :

Coefficient of thermophoresis diffusion

\(c\) :

Stretching rate

\((\gamma_{1} ,\gamma_{2} )\) :

Thermal and concentration Biot numbers

\(S_{1}\) :

Thermal stratification variable

\(N\) :

Ratio of concentration to thermal buoyancy

\(\varLambda_{1}\) :

Linear thermal expansion coefficient

\(\varLambda_{2}\) :

Nonlinear thermal expansion coefficient

\((d_{1} ,d_{2} )\) :

Dimensional constants

\(\beta_{\text{t}}\) :

Nonlinear thermal convection variables

\(c_{\text{p}}\) :

Specific heat

\({\text{Ha}}\) :

Hartmann number

\(\Pr\) :

Prandtl number

\(\varLambda_{4}\) :

Nonlinear concentration expansion coefficient

\(\varLambda_{3}\) :

Linear concentration expansion coefficient

\(N_{\text{t}}\) :

Thermophoresis parameter

\({\text{Sc}}\) :

Schmidt number

\(S\) :

Heat generation variable

\(q_{\text{w}}\) :

Surface heat flux

\(q_{\text{m}}\) :

Surface mass flux

\(G_{\text{r}}\) :

Grashof number for thermal buoyancy

\(G^{*}_{\text{r}}\) :

Grashof number for concentration buoyancy

\(N_{\text{b}}\) :

Brownian motion parameter

\({\text{Nu}}_{x}\) :

Local Nusselt number

\(\lambda_{1}\) :

Ratio of relaxation to retardation time

\(\lambda_{2}\) :

Retardation time

\((\rho c)_{\text{f}}\) :

Liquid heat capacity

\((\rho c)_{\text{p}}\) :

Nanoparticles effective heat capacity

\(u_{\text{w}}\) :

Stretching velocity

\(k^{*}\) :

Coefficient of mean absorption

\({\text{Sh}}_{x}\) :

Local Sherwood number

\(\text{Re}_{x}\) :

Local Reynolds number

\(\beta_{\text{t}} ,\beta_{\text{c}}\) :

Nonlinear concentration convection variables

\(S_{2}\) :

Concentration stratification variable

\(k\) :

Thermal conductivity

\(\sigma\) :

Electrical conductivity

\(\beta\) :

Deborah number

\(\nu\) :

Kinematic viscosity

\(\rho\) :

Liquid density

\(\alpha\) :

Thermal diffusivity

\(\tau\) :

Ratio of heat capacity

\(\lambda\) :

Mixed convection variable

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Correspondence to Ikram Ullah.

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Waqas, M., Ullah, I., Hayat, T. et al. Nonlinear Mixed Convection Impact on Radiated Flow of Nanomaterials Subject to Convective Conditions. Arab J Sci Eng 46, 2349–2359 (2021). https://doi.org/10.1007/s13369-020-04978-6

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  • DOI: https://doi.org/10.1007/s13369-020-04978-6

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