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A rheological analysis of nanofluid subjected to melting heat transport characteristics

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Abstract

This work focuses on the characteristics of heat sink–source and melting phenomena for time-dependent Falkner–Skan flow of Cross nanofluid. Additionally, stagnation point flow features are accounted. Modeling is based on thermophoresis diffusion and Brownian moment slip mechanisms. Zero mass flux condition is used at stretchable surface. Compact form of cross fluid equations are converted to component form by employing boundary layer concept. Appropriate transformations are engaged to give rise ODEs. Moreover, system of ODEs is tackled numerically. Detailed discussion for velocity, temperature, concentration, local Nusselt and Sherwood numbers is presented through graphs. Obtained statistical data reveals that velocity of cross nanoliquid boosts for larger melting and velocity ratio parameters. Intensification in Schmidt number corresponds to rise in concentration distribution.

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Abbreviations

\(u,v\) :

Velocity components

\(x,y\) :

Space coordinates

\(U_{\text{w}} \left( {x,t} \right)\) :

Stretching velocity

\(U_{\text{e}} \left( {x,t} \right)\) :

Free stream velocity

\(a, \, b, \, m, \, c\) :

Positive constants

\(\nu\) :

Kinematics viscosity

\(n\) :

Power law index

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

Fluid density

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

Thermophoresis diffusion coefficient

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

Heat capacity of fluid

\(T\) :

Fluid temperature

\(T_{0}\) :

Solid temperature

\(T_{\infty }\) :

Ambient fluid temperature

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

Melting temperature

t :

Time

\(C\) :

Fluid concentration

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

Concentration at the surface

\(C_{\infty }\) :

Ambient concentration

\(\varGamma\) :

Cross time constant

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

Thermophoresis diffusion coefficient

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

Brownian diffusion coefficient

\(Q_{0}\) :

Heat generation/absorption co-efficient

\(\tau\) :

Effective heat capacity ratio

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

Effective thermal diffusivity

\(s\) :

Velocity ratio parameter

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

Specific heat

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

Surface heat capacity

\(\lambda\) :

Fluid latent heat

\(k\) :

Thermal conductivity

\(\eta\) :

Dimensionless variable

\(\varPsi (x,y,t)\) :

Stokes stream function

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

Thermophoresis parameter

\(A\) :

Unsteadiness parameter

\(Pr\) :

Prandtl number

\(\beta\) :

Wedge angle parameter

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

Brownian motion parameter

\(We\) :

Local Weissenberg number

\(Q\) :

Heat generation/absorption

\(M\) :

Melting parameter

\(Sc\) :

Schmidt number

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

Wall shear stress

\(f\) :

Dimensionless velocity

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

Wall mass flux

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

Wall heat flux

\(\theta\) :

Dimensionless temperature

\(Sh\) :

Local Sherwood number

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

Skin fraction

\(Nu\) :

Local Nusselt number

\(\phi\) :

Dimensionless concentration

\(Re_{x}\) :

Local Reynolds number

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Authors and Affiliations

  1. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China

    W. A. Khan

  2. Department of Mathematics, Mohi-ud-Din Islamic University, Nerian Sharif, Islamabad, 12010, Azad Jammu and Kashmir, Pakistan

    W. A. Khan

  3. Department of Mathematics and Statistics, Hazara University, Mansehra, 21300, Pakistan

    M. Ali, M. Shahzad & F. Sultan

  4. Department of Mathematics, Quaid-I-Azam University, Islamabad, 44000, Pakistan

    M. Irfan & M. Khan

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  1. W. A. Khan
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  2. M. Ali
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  3. M. Irfan
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  4. M. Khan
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  6. F. Sultan
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Correspondence to F. Sultan.

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Khan, W.A., Ali, M., Irfan, M. et al. A rheological analysis of nanofluid subjected to melting heat transport characteristics. Appl Nanosci 10, 3161–3170 (2020). https://doi.org/10.1007/s13204-019-01067-5

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