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Impacts of Viscous Dissipation and Thermal Radiation on Rabinowitsch Fluid Model Obeying Peristaltic Mechanism with Wall Properties

  • Research Article-Mechanical Engineering
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Abstract

This exploration intends to focus on the impacts of viscous dissipation and thermal radiation on the peristaltic transport of the Rabinowitsch fluid model through a non-uniform inclined tube. Velocity and convective slip impacts are imposed at the walls of the tube. The lubrication approach is utilized to simplify the normalized constitutive equations. The exact outcomes are estimated for the velocity, temperature, and stream function. The impacts of diverse parameters on flow quantities are deliberated and featured through graphs. It is established that the Brickman number communicates to the viscous dissipation impacts; therefore, it helps to raise the liquid temperature in all situations. The higher values of rigidity and stiffness parameters enhanced the number of streamlines because of the liquid circulation for shear thickening case, but it has an opposite trend for the viscous damping force parameter.

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Abbreviations

\(\bar{r},\bar{z}\) :

Radial and axial direction in the wave frame

\(\bar{u},\bar{v}\) :

Fluid velocity along \(\bar{r}\) and \(\bar{z}\) directions

\(\bar{p}\) :

Pressure in the wave motion

P :

Pressure in laboratory motion

c :

Wave speed

\(\bar{p}\) :

Time

\(C^{\prime }\) :

Coefficient of viscous damping force

\(\bar{T}\) :

Temperature

\(\bar{T}_{0}\) :

Constant wall temperature

w :

Dimensionless fluid velocity

α*:

Velocity slip parameter

\(l\left( {\bar{z}} \right)\) :

Radius of the non-uniform tube

m :

Mass per unit area

b :

Wave amplitude

Rd :

Radiation parameter

E 3 :

Viscous damping force parameter

E 2 :

Stifness parameter

k :

Non-uniform tube

\(\tau _{{\bar{r}\,\bar{z}}} ,\tau _{{\bar{z}\,\bar{z}}} ,\tau _{{\bar{r}\,\bar{r}}}\) :

Shear stress

Re:

Reynold’s number

Br :

Brickman number

E 1 :

Rigidity parameter

λ:

Wavelength

σ * :

Stephen Boltzmann constant

k * :

Mean absorption coefficient

c p :

Specific heat capacity

η d :

Heat transfer coefficient

k 1 :

Thermal conductivity

θ:

Dimensionless fluid temperature

ε :

Amplitude ratio

η :

Inclined angle

β :

Biot number

α :

Velocity slip parameter

γ :

Rabinwitsch fluid parameter

δ :

Dimensional less wave number

ρ :

Density

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Authors and Affiliations

  1. Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, 63100, Pakistan

    M. Y. Rafiq & Z. Abbas

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  1. M. Y. Rafiq
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  2. Z. Abbas
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Correspondence to Z. Abbas.

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Rafiq, M.Y., Abbas, Z. Impacts of Viscous Dissipation and Thermal Radiation on Rabinowitsch Fluid Model Obeying Peristaltic Mechanism with Wall Properties. Arab J Sci Eng 46, 12155–12163 (2021). https://doi.org/10.1007/s13369-021-05870-7

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