Modeling unsteady mixed convection in stagnation point flow of Oldroyd-B nanofluid along a convective heated stretched sheet

Technical Paper
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Abstract

The current contribution aims to address an unsteady mixed convection in stagnation point flow of an Oldroyd-B nanofluid induced due to a stretched sheet with Biot number impact. Implementation of convenient similarity transformation changes the highly nonlinear-coupled governing equations to nonlinear ordinary differential equations. Obtaining governing system has been solved for the convergent series solutions. Several experimental correlations describe nanofluid effective viscosity and nanofluid thermal conductivity has been utilized. Behaviors of the velocity, temperature distributions and local Nusselt number against number of sundry variables have been scrutinized. Computed results illustrate that the nanoparticle volume fraction and the fluid constants of relaxation and retardation time have an opposite behavior on the velocity and temperature distributions. Larger values of relaxation time parameter make temperature distribution increases. Impact of different parameters that described the flow and heat transfer behavior is depicted and examined.

Keywords

Unsteady Oldroyd-B nanofluid Stagnation point Biot number Mixed 

List of symbols

Bi

Biot number

cp

Specific heat at constant pressure (J Kg−1 K−1)

g

Gravitational acceleration (m s−2)

Gr

Local Grashof number

j1

Dimensionless relaxation time constant

j2

Dimensionless retardation time constant

k

Thermal conductivity (W m−1 K−1)

Nu

Nusselt number

Pr

Prandtl number

S

Unsteadiness parameter

t

Time (s)

T

Temperature (K)

(u, v)

Dimensional velocity components (m s−1)

(x, y)

Dimensional coordinate axes (m)

Greek symbols

θ

Dimensionless temperature

φ

Nanoparticle volume fraction

\(\gamma^{{ \star }}\)

Mixed convection parameter

β

Thermal expansion coefficient (K−1)

ψ

Stream function (m2 s−1)

μ

Dynamic viscosity (kg m−1 s−1)

ρ

Density (kg m−3)

η

Similarity parameter

δ

Relaxation time constant (s−1)

\(\tilde{\delta }\)

Retardation time constant (s−1)

Subscripts

f

Fluid

nf

Nanofluid particle

s

Solid material

Conditions in the free stream

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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.Mathematics Department, Faculty of ScienceSouth Valley UniversityQenaEgypt

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