Peristaltic Transport of a Casson Fluid in a Non-uniform Inclined Tube with Rosseland Approximation and Wall Properties
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RESEARCH ARTICLE-MECHANICAL ENGINEERING
Peristaltic Transport of a Casson Fluid in a Non-uniform Inclined Tube with Rosseland Approximation and Wall Properties Z. Abbas1 · M. Y. Rafiq1 · J. Hasnain2
· T. Javed3
Received: 19 June 2020 / Accepted: 17 September 2020 © King Fahd University of Petroleum & Minerals 2020
Abstract In this article, the peristaltic transport (PT) of Casson fluid (CF) in the presence of mass and heat transfer under the impacts of slip conditions and wall properties in a non-uniform inclined tube has been analyzed. Furthermore, the effects of Dufour and Soret numbers are also considered. The governing two-dimensional equations for the flow of non-Newtonian CF along with the mass and heat transfer are reformulated by the supposition of a long wavelength and a low Reynolds number. Analytic solutions are computed and outcomes are exhibited graphically to analyze the impact of the parameters emerging in the problem. It is shown that the velocity profile is enhanced with a rise in the Casson parameter. The fluid temperature enhances for enhanced values of thermal slip and source/sink parameter. A validity of closed-form results for the velocity of the fluid is made by comparing it with numerical outcomes computed by MATLAB through bvp4c and finite element method. Keywords Casson fluid · Peristaltic flow · Slip conditions · Thermal radiation · Wall properties · Non-uniform inclined tube
List of symbols r, z U ∗, W ∗ T∗ C∗ P∗ qr w C T0 C0 R B GT Pr
B 1
Radial and axial directions in wave frame Components of velocity along radial and axial directions Temperature Concentration Pressure Thermal radiation Dimensionless velocity Coefficient of viscous damping Constant wall temperature Constant wall concentration Radiation parameter Heat source/sink parameter Grashof number Prandtl number
J. Hasnain [email protected] Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan
2
Department of Computer Sciences, Bahria University Islamabad Campus, Islamabad 44000, Pakistan
3
Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan
Gc Concentration buoyancy parameter E 1 , E 2 , E 3 Rigidity, stiffness, viscous damping force parameters Velocity slip parameter L∗ m Mass per unit area Shear stress τr z Fluid velocity near the wall Ww∗ p Dimensionless pressure ei j (i, j)th components of the deformation rate Yield stress of the fluid py Non-uniform wave H∗ c Uniform velocity Re Reynolds number b Radius of the non-uniform tube Schmidt number Sc Soret number Sr Du Dufour number
Greek Symbols σ∗ k ε θ cp
Stefan–Boltzmann constant Non-uniform parameter Amplitude ratio Dimensionless fluid temperature Specific heat capacity
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Arabian Journal for Science and Engineering
γ1∗ ψ σ γ2∗ ζ k∗ ρ K θ μ μB π η λ
Thermal slip parameter Dimensionless concentration Elastic tension in the membrane Mass slip parameter Casson parameter Mean absorption coefficient Density Thermal conductivity Dimensionless temperature Dynamic vi
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