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MHD stagnation point flow and heat transfer in viscoelastic fluid with Cattaneo–Christov heat flux model

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Abstract

This article presents an analysis of stagnation point of coupled flow and heat transfer of an upper-convected Maxwell fluid over a stretching sheet along with magnetic effects and slip condition at the boundary. The recently proposed Cattaneo–Christov model is employed in the energy equation to investigate the effects of thermal relaxation time. Similarity transformations are adopted to convert the governing partial differential equations into ordinary differential equations. Numerical solution of the system of ODEs is achieved by shooting method together with Runge–Kutta method of order four. The effects of stretching ratio parameter (0 ≤ e ≤ 0.5), elasticity number (0 ≤ β ≤ 1.5), heat flux relaxation time (0 ≤ γ ≤ 1.5), magnetic parameter (0 ≤ M ≤ 1.5), slip coefficient (1 ≤ b ≤ 4) and Prandtl number (0 ≤ Pr ≤ 1.5) on velocity and temperature are investigated graphically and numerically. It is observed that temperature boosts up with an increase in thermal relaxation time.

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Abbreviations

a, c :

Constants (1/time)

b :

Slip coefficient

e :

Stretching ratio parameter \( \left( {\tfrac{c}{a}} \right) \)

T w :

Wall temperature (K)

f′:

Dimensionless velocity \( \left( {\tfrac{\text{m}}{\text{s}}} \right) \)

M :

Magnetic parameter

\( {\mathbf{V}} \) :

Velocity vector \( \left( {\tfrac{\text{m}}{\text{s}}} \right) \)

Pr:

Prandtl number \( \left( {\tfrac{\nu }{\alpha }} \right) \)

α :

Thermal diffusivity \( \left( {\tfrac{{{\text{m}}^{ 2} }}{\text{s}}} \right) \)

η :

Similarity variable (m)

σ :

Electrical conductivity \( \left( {\tfrac{\text{S}}{\text{m}}} \right) \)

λ 1 :

Relaxation time of the fluid (s)

σ v :

Tangential momentum accommodation

θ :

Dimensionless temperature (K)

B 0 :

Magnetic field strength (T)

c p :

Specific heat \( \left( {\tfrac{\text{J}}{\text{kgK}}} \right) \)

T :

Temperature of fluid (K)

T ∞ :

Ambient temperature (K)

(x, y):

Coordinate axis (m)

k :

Thermal conductivity \( \left( {\tfrac{\text{W}}{\text{mK}}} \right) \)

\( {\mathbf{q}} \) :

Heat flux \( \left( {\tfrac{\text{J}}{\text{s}}} \right) \)

(u, v):

Velocity components \( \left( {\tfrac{\text{m}}{\text{s}}} \right) \)

β :

Elasticity number

ρ :

Density of fluid \( \left( {\tfrac{\text{kg}}{{{\text{m}}^{ 3} }}} \right) \)

λ 0 :

Free path of molecular mean

λ 2 :

Relaxation time of heat flux (s)

ν :

Kinematic viscosity \( \left( {\tfrac{{{\text{m}}^{ 2} }}{\text{s}}} \right) \)

γ :

Thermal relaxation time (s)

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Computing, Capital University of Science and Technology, Islamabad, Pakistan

    Y. Mehmood, M. Sagheer, S. Hussain & M. Bilal

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  1. Y. Mehmood
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  2. M. Sagheer
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  3. S. Hussain
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  4. M. Bilal
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Mehmood, Y., Sagheer, M., Hussain, S. et al. MHD stagnation point flow and heat transfer in viscoelastic fluid with Cattaneo–Christov heat flux model. Neural Comput & Applic 30, 2979–2986 (2018). https://doi.org/10.1007/s00521-017-2902-2

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