Characteristic of heat transfer in flow of Cross nanofluid during melting process
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ORIGINAL ARTICLE
Characteristic of heat transfer in flow of Cross nanofluid during melting process Mehboob Ali1 · Muhammad Shahzad2 · Faisal Sultan1 · Waqar Azeem Khan3 · Syed Zahir Hussain Shah1 Received: 13 January 2020 / Accepted: 5 August 2020 © King Abdulaziz City for Science and Technology 2020
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. Keywords 2D Cross fluid · Melting transport of heat · Infinite shear rate viscosity · Brownian motion · Thermophoresis diffusion Abbreviations u,v Velocity components x,y Space coordinate a,b,c,m Positive constants β Wedge angle parameter Uw (x, t) Stretching velocity Ue (x, t) Free stream velocity T0 Initial temperature T∞ Ambient temperature of fluid Tm Melting temperature 𝜏 Cauchy stress tensor k Thermal conductivity Pr Prandtl number s Velocity ratio parameter Nu Nusselt number Re Reynold number * Mehboob Ali [email protected] Faisal Sultan [email protected] 1
Department of Mathematics and Statistics, Hazara University Mansehra, Mansehra 21300, Pakistan
2
Department of Mathematics, University of Haripur, Haripur 22620, Pakistan
3
Department of Mathematics, Mohi-ud-Din Islamic University, Nerian Sharif, Azad Jammu & Kashmir 12010, Pakistan
t Time 𝜇0 Zero shear rate viscosity A1 First Rivlin–Erickson tensor μ∞ Infinite shear rate viscosity p Pressure I Identity tensor Γ Relaxation time constant 𝜓(x, y,t) Stokes stream function Sc Schmidt number μ Viscosity A Unsteadiness parameter qw Wall shear stress cs Surface heat capacity M Melting parameter cf Skin friction n Power law index 𝛾̇ Shear strain 𝜂 Dimensionless variable cp Specific heat Rr Chemical reaction parameter σ Reaction rate parameter ρ Density C Fluid Concentration T Fluid Temperature 𝜃w Temperature ratio parameter We Weissenberg Number 𝛼m Thermal diffusivity
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Applied Nanoscience
Introduction Now, in recent days, the concept of nanoscience has been broadly developed to solve many problems by raising the conventional heat transfer to increase the feature of heat transfer in many fluids. The low thermal conductivity of many fluids is the main difficulty to raise the heat transport in the engineering framework. Therefore, it needs to have liquids that can hold high thermal conductivity. Nanoliquids are imperative for this purpose. These are stable and selfpossessed having nanometer-size
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