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A mathematical model to examine the heat transport features in Burgers fluid flow due to stretching cylinder

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Abstract

In this article, a new mathematical modelling is presented for the flow of Burgers fluid induced by a stretching cylinder in the presence of magnetic field. Moreover, the mechanisms of heat and mass transport are also examined by using the law of conservation of energy with Fourier’s and Fick’s laws for thermal and solutal energy, respectively. The ordinary differential equations (ODEs) are attained from partial differential equations by making the use of dimensionless similarity transformations. The homotopic approach is being adopted to solve the developed ODEs. The influences of different physical parameters on velocity, thermal and concentration profiles are pondered through graphs and physical behavior of these parameters is enlightened with the realistic verdicts. The basic physical intimation of pertained results is that the temperature and solutal curves of Burgers liquid show the enhancing trend for larger scales of relaxation time parameter \(\left( \beta _{1}\right)\) and for material parameter of Burgers fluid \(\left( \beta _{2}\right)\) while, opposing behavior is being observed for retardation time parameter \(\left( \beta _{3}\right)\). Moreover, it is assessed that the concentration rate and solutal boundary layer thickness decline with an intensification in Lewis number (Le). Also, it is noted that the temperature distribution enhances/declines with higher values of heat source and sink parameter, respectively.

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Abbreviations

u,  w :

Velocity components

r,  z :

Cylindrical coordinates

\(\lambda _{1}\) :

Fluid relaxation time

\(\lambda _{2}\) :

The material parameter of Burgers fluid

\(\lambda _{3}\) :

Fluid retardation time

\({\mathbf {S}}\) :

Extra stress tensor

\({\mathbf {j}}\) :

Mass flux

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

Heat flux

\(C_\mathrm{w}\) :

Concentration at surface

\(C_{\infty }\) :

Ambient concentration

\(w_\mathrm{z}\) :

Stretching cylinder velocity

k :

Thermal conductivity

p :

Fluid pressure

f :

Dimensionless velocity function

\(\alpha\) :

Thermal diffusivity

\(c_\mathrm{p}\) :

Specific heat at constant pressure

\(c_\mathrm{f}\) :

The specific heat

M :

Magnetic field

\(\beta _{2}\) :

Burgers fluid parameter

\(\delta\) :

Heat source/sink parameter

Pr:

Prandtl number

T :

Fluid temperature

C :

Fluid concentration

\({\mathbf {J}}_{1}\) :

Current density

\(Q_{0}\) :

Heat source/sink

\(A_{1}\) :

First Rivilin–Ericksen tensor

Le:

Lewis number

\(T_\mathrm{w}\) :

Surface temperature

\(T_{\infty }\) :

Ambient temperature

\(D_\mathrm{B}\) :

The diffusion coefficient

\(\rho\) :

Fluid density

\(\eta\) :

Dimensionless similarity variable

\(\mu _{0}\) :

Zero shear viscosity

\(\nu\) :

Kinematic viscosity

\(\theta\) :

Dimensionless temperature

\(\phi\) :

Dimensionless concentration function

\(\rho _\mathrm{f}\) :

The density of liquid

\(\beta _{1}\) :

Fluid relaxation parameter

\(\beta _{3}\) :

Fluid retardation parameter

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Authors and Affiliations

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

    Masood Khan, Zahoor Iqbal & Awais Ahmed

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  1. Masood Khan
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  2. Zahoor Iqbal
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Correspondence to Zahoor Iqbal.

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Khan, M., Iqbal, Z. & Ahmed, A. A mathematical model to examine the heat transport features in Burgers fluid flow due to stretching cylinder. J Therm Anal Calorim 147, 827–841 (2022). https://doi.org/10.1007/s10973-020-10224-w

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