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Cattaneo–Christov heat flux theory on transverse MHD Oldroyd-B liquid over nonlinear stretched flow

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Abstract

A hydromagnetic transverse flow of an Oldroyd-B-type liquid with a heat flux of the Cattaneo–Christov model with variable thickness has been analyzed. Consider additional impacts of thermal conductivity as well as heat generation. Governing equations were transmitted into a set of nonlinear ordinary differential equations using similarity conversion, and then, numerical solution was evaluated using the procedure Runge–Kutta–Fehlberg. The physical response related to velocity and temperature is investigated computationally. The outcomes also show that the momentum boundary-layer thickness increases the values of magnetic field strength, but the reverse trend is observed for the thermal boundary layer. Impacts of retardation and relaxation time effects are quite the opposite of the temperature field. The obtained computations are useful in transport phenomena which are involving hydromagnetic rheological fluids.

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Abbreviations

B 0 :

Magnetic field strength (N m−1 A−1)

B :

Applied magnetic field (N m−1 A−1)

b :

Positive constant (s−1)

U w :

Stretching velocity (ms−1)

T w :

Temperature of fluid at the wall (K)

T ∞ :

Ambient fluid temperature (K)

x 1, x 2 :

Coordinate axis (m)

T :

Temperature (K)

n :

Power law index

G :

Dimensionless velocity

M :

Magnetic parameter

C p :

Heat capacity (J kg−1 K)

U 0 :

Reference velocity (s−1)

k ∞ :

Ambient fluid thermal conductivity

Q :

Heat generation/absorption coefficient (J kg−3 K−1 s−1)

k :

Thermal conductivity (Wm−1 K−1)

Pr:

Prandtl number

q w :

Wall heat flux (Wm−2)

\( Cf_{{{\rm x}_{1} }} \) :

Skin friction coefficient

\( {\text{Nu}}_{{{\rm x}_{1} }} \) :

Local Nusselt number

\( {\text{Re}}_{{{\rm x}_{1} }} \) :

Local Reynolds number

ξ 1, ξ 2 :

Velocity components (ms−1)

ν :

Kinematic viscosity (m2 s−1)

λ 1 :

Relaxation time (s)

λ 2 :

Retardation time (s)

η :

Similarity variable

τ w :

Wall shear stress

β 1, β 2 :

Deborah numbers

δ :

Heat generation/absorption parameter

\( {{\Theta }} \) :

Dimensionless temperature

\( \gamma \) :

Thermal relaxation parameter

ρ :

Density of the fluid (kg m−3)

σ :

Electrical conductivity (Sm−1)

∞:

Condition at the free stream

w :

Condition at the wall/surface

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Authors and Affiliations

  1. Department of Mathematics, Vignan’s Lara Institute of Technology and Science, Vadlamudi, Guntur, Andhra Pradesh, 522213, India

    K. Venkata Ramana

  2. Department of Mathematics, Acharya Nagarjuna University, Ongole, Andhra Pradesh, 523001, India

    K. Gangadhar

  3. Department of Mathematics, School of Humanities and Sciences, SASTRA Deemed University, Thanjavur, TN, India

    T. Kannan

  4. Institute of Research and Development, Duy Tan University, Da Nang, 550000, Vietnam

    Ali J. Chamkha

  5. Institute of Theoretical and Applied Research (ITAR), Duy Tan University, Hanoi, 100000, Vietnam

    Ali J. Chamkha

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  1. K. Venkata Ramana
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  2. K. Gangadhar
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  4. Ali J. Chamkha
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Correspondence to Ali J. Chamkha.

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Venkata Ramana, K., Gangadhar, K., Kannan, T. et al. Cattaneo–Christov heat flux theory on transverse MHD Oldroyd-B liquid over nonlinear stretched flow. J Therm Anal Calorim 147, 2749–2759 (2022). https://doi.org/10.1007/s10973-021-10568-x

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