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Characteristic of heat transfer in flow of Cross nanofluid during melting process

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Abstract

This struggle is part of a responsible method for the development of nanoscience and nanotechnology inspect closely of nanofluid. The conformist melting phenomena for steady Falkner–Skan flow of Cross nanofluid is considered. The Buongiorno model is used to discuss the thermal efficacies of the fluid flows in the presence of nanoparticles. MATLAB’s scheme of bvp4c is adopted to solve these non-linear ODEs and graphical results are presented in the form of graphs and tables. The main findings of the study are velocity boost up for melting heat and velocity ratio parameter. Concentration goes down for the Brownian motion of molecules and arises for thermophoresis diffusion.

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Abbreviations

u,v :

Velocity components

x,y :

Space coordinate

a,b,c,m :

Positive constants

β:

Wedge angle parameter

\(U_{w} (x,t)\) :

Stretching velocity

\(U_{e} (x,t)\) :

Free stream velocity

\(T_{0}\) :

Initial temperature

\(T_{\infty }\) :

Ambient temperature of fluid

\(T_{m}\) :

Melting temperature

\(\tau\) :

Cauchy stress tensor

\(k\) :

Thermal conductivity

\(Pr\) :

Prandtl number

s :

Velocity ratio parameter

Nu :

Nusselt number

Re :

Reynold number

t :

Time

\(\mu_{0}\) :

Zero shear rate viscosity

A 1 :

First Rivlin–Erickson tensor

μ ∞ :

Infinite shear rate viscosity

p :

Pressure

I :

Identity tensor

\(\Gamma\) :

Relaxation time constant

\(\psi_{{\left( {x,\,y,t} \right)}}\) :

Stokes stream function

Sc:

Schmidt number

μ :

Viscosity

A :

Unsteadiness parameter

q w :

Wall shear stress

\(c_s\) :

Surface heat capacity

M :

Melting parameter

c f :

Skin friction

n :

Power law index

\(\dot{\gamma }\) :

Shear strain

\(\eta\) :

Dimensionless variable

c p :

Specific heat

R r :

Chemical reaction parameter

σ :

Reaction rate parameter

ρ :

Density

C :

Fluid Concentration

T :

Fluid Temperature

\(\theta_{w}\) :

Temperature ratio parameter

We:

Weissenberg Number

\(\alpha_{m}\) :

Thermal diffusivity

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Authors and Affiliations

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

    Mehboob Ali, Faisal Sultan & Syed Zahir Hussain Shah

  2. Department of Mathematics, University of Haripur, Haripur, 22620, Pakistan

    Muhammad Shahzad

  3. Department of Mathematics, Mohi-ud-Din Islamic University, Nerian Sharif, Azad Jammu & Kashmir, 12010, Pakistan

    Waqar Azeem Khan

Authors
  1. Mehboob Ali
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  2. Muhammad Shahzad
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  3. Faisal Sultan
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  4. Waqar Azeem Khan
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  5. Syed Zahir Hussain Shah
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Correspondence to Mehboob Ali.

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Ali, M., Shahzad, M., Sultan, F. et al. Characteristic of heat transfer in flow of Cross nanofluid during melting process. Appl Nanosci 10, 5201–5210 (2020). https://doi.org/10.1007/s13204-020-01532-6

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