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Transient flow and heat transfer mechanism for Williamson-nanomaterials caused by a stretching cylinder with variable thermal conductivity

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Abstract

The utilization of nanometre-sized solid particles in working fluids has been seriously recommended due to their enhanced thermal characteristics. This suspension of solid particles in base fluids can significantly enhance the physical properties, such as, viscosity and thermal conductivity. They are widely used in several engineering processes, like, heat exchangers, cooling of electronic equipment, etc. In this exploration, we attempt to deliver a numerical study to simulate the nanofluids flow past a circular cylinder with convective heat transfer in the framework of Buongiorno’s model. A non-Newtonian Williamson rheological model is used to describe the behavior of nanofluid with variable properties (i.e., temperature dependent thermal conductivity). The leading flow equations for nanofluid transport are mathematical modelled with the assistance of Boussinesq approximation. Numerical simulation for the system of leading non-linear differential equations has been performed by employing versatile, extensively validated, Runge–Kutta Fehlberg scheme with Cash–Karp coefficients. Impacts of active physical parameters on fluid velocity, temperature and nanoparticle concentration is studied and displayed graphically. It is worth to mention that the temperature of non-Newtonian nanofluids is significantly enhanced by higher variable thermal conductivity parameter. One major outcome of this study is that the nanoparticle concentration is raised considerably by an increasing values of thermophoresis parameter.

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Abbreviations

a, β :

Positive constants

t :

Time

ρ :

Density of the fluid

B 0 :

Strength of magnetic field

μ ∞ :

Viscosity at infinite shear rate

μ 0 :

Viscosity at zero shear rate

β * :

Viscosities ratio

x, r :

Cylindrical polar coordinates

u, v :

Velocity components

U w :

Stretching cylinder velocity

Γ :

Relaxation time

ν :

Kinematic viscosity

σ :

Electrical conductivity

T f :

Temperature of hot fluid

h f :

Heat transfer coefficient

T :

Temperature of the fluid

C :

Concentration of nanoparticles

T ∞ :

Free stream temperature

C ∞ :

Free stream nanoparticles concentration

D B :

Brownian diffusion coefficient

D T :

Thermophoretic diffusion coefficient

c p :

Specific thermal capacity

k(T):

Variable thermal conductivity

τ :

Ratio of effective heat capacities

ψ :

Stream function

f :

Dimensionless velocity

θ :

Dimensionless temperature

φ :

Dimensionless concentration

η :

Dimensionless variable

γ :

Curvature parameter

We :

Weissenberg number

A :

Unsteadiness parameter

Pr:

Prandtl number

Sc :

Schmidt number

Nt :

Thermophoretic parameter

Nb :

Brownian motion parameter

Re :

Local Reynolds number

(ρc)f :

Heat capacity of the fluid

(ρc)p :

Heat capacity of nanoparticles

τ w :

Surface shear stress

C f :

Skin friction coefficient

Nu :

Nusselt number

Sh :

Sherwood number

q w :

Surface heat flux

q m :

Surface mass flux

γ 1 :

Thermal Biot number

γ 2 :

Concentration Biot number

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Authors and Affiliations

  1. Department of Mathematics & Statistics, Riphah International University, Islamabad, Pakistan

    Hashim

  2. Department of Mathematics, Quaid-i-Azam University, Islamabad, 44000, Pakistan

    Aamir Hamid & Masood Khan

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  1. Hashim
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  2. Aamir Hamid
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  3. Masood Khan
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Hashim, Hamid, A. & Khan, M. Transient flow and heat transfer mechanism for Williamson-nanomaterials caused by a stretching cylinder with variable thermal conductivity. Microsyst Technol 25, 3287–3297 (2019). https://doi.org/10.1007/s00542-019-04364-9

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  • DOI: https://doi.org/10.1007/s00542-019-04364-9

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