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Darcy flow of polymer from an inclined plane with convective heat transfer analysis: a numerical study

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Abstract

An analytical model is developed to study the Darcy flows in viscoelastic convection from an inclined plate as a simulation of electro-conductive polymer materials processing with Biot number effects. The Jeffery’s viscoelastic model describes the non-Newtonian characteristics of the fluid and provides a good approximation for polymers, which constitutes a novelty of the present work. The normalized nonlinear boundary value problem is solved computationally with the Keller Box implicit finite difference technique. Extensive solutions for velocity, surface temperature, skin friction and heat transfer rate are visualized numerically and graphically for various thermophysical parameters. Validation is conducted with earlier published work for the case of a vertical plate in the absence of non-Newtonian effects. The boundary layer flow is accelerated with increase in Deborah number, whereas temperatures are decelerated slightly. Temperatures are boosted with increase in inclination parameter, whereas velocity is lowered. A reverse trend is seen for increasing mixed convection parameter. Increase in Biot number enhances both velocity and temperature. Increasing Darcy number is found to enhance velocity, whereas it suppresses temperature. This particle study finds applications in different industries like reliable equipment design, nuclear plants, gas turbines and different propulsion devices.

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Abbreviations

Cf :

Skin friction coefficient

cp :

Specific heat (J K−1 kg−1)

Da:

Darcy parameter

De:

Local Deborah number (–)

F:

Dimensionless stream function (–)

G:

Gravitational acceleration (m s− 2)

Gr:

Thermal Grashof number (–)

hw :

Convective heat transfer coefficient

K:

Thermal conductivity of the fluid (W m−1k−1)

L:

Characteristic length (m)

Nu:

Heat transfer coefficient (–)

Pr:

Prandtl number

P:

Pressure

R:

Mixed convection parameter

Re:

Reynolds number

Rex :

Local Reynolds number

S :

Cauchy stress tensor

T:

Fluid temperature (K)

T :

Cauchy stress tensor

V :

Velocity vector (m s− 1)

u, v :

Dimensionless velocity components in X and Y direction, respectively (m s− 2)

x :

Stream wise coordinate

y :

Transverse coordinate

α:

Thermal diffusivity (m2 s− 1)

β:

Coefficient of thermal expansion (ppm/°F)

λ:

Ratio of relaxation to retardation times

λ1 :

Retardation time (s)

σ:

Electric conductivity of the fluid (kg−1 m−3 s3 A2)

Ω:

Angle of inclination

μ:

Dynamic viscosity (Ns m−2)

ξ:

Non-dimensional tangential coordinate

ν:

Kinematic viscosity (Ns m−2)

θ:

Dimensionless temperature

ρ:

Fluid density (kg m−3)

ψ:

Non-dimensional stream function

γ:

Thermal Biot number

η:

Dimensionless radial coordinate

w:

Conditions on the wall

∞:

Free stream condition

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Acknowledgements

The authors are thankful to DST-WOS-A [Ref: N0. SR/WOS-A/MS-09/2014(G)], New Delhi, for financial support and the management of Madanapalle Institute of Technology and Science, Madanapalle for providing research facilities in the campus.

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Authors and Affiliations

  1. Department of Mathematics, MITS, Madanapalle, 517325, India

    K. Madhavi

  2. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, 632014, India

    V. Ramachandra Prasad

  3. Department of Information Technology, Mathematics Section, Salalah College of Technology, Salalah, Oman

    S. Abdul Gaffar

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  1. K. Madhavi
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  2. V. Ramachandra Prasad
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  3. S. Abdul Gaffar
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Correspondence to S. Abdul Gaffar.

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Madhavi, K., Prasad, V.R. & Gaffar, S.A. Darcy flow of polymer from an inclined plane with convective heat transfer analysis: a numerical study. J Therm Anal Calorim 146, 117–129 (2021). https://doi.org/10.1007/s10973-020-09942-y

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