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Study of Different Heating Effects on Two-Phase Flow of Magnetized Couple Stresses Over a Permeable Stretching Cylinder with Velocity Slip and Radiation

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Abstract

The couple stresses of a dusty fluid across a stretching cylinder are investigated using a mathematical model. The governing flow is 2-dimensional in nature and the cylinder is submerged in a porous medium. Effect of radiation, slip velocity, viscous energy dissipation, Newtonian, and Joule heating are incorporated in our mathematical model. The flow system is governed by basic partial differential equations. Our model's governing equations are translated to coupled nonlinear ordinary differential equations using similarity transformations, which are then solved using the Runge–Kutta Fehlberg iterative technique. Variations in velocity and thermal gradient under the influence of relevant parameters are examined numerically and are illustrated graphically. The non-dimensional skin shear stress (coefficient of skin friction) and the rate of heat transfer are calculated for permeable flow over the cylinder for different flow parameters and are displayed through a table. Later, the numerical results obtained are compared to the results available in literature and found to be in reasonable accord. Results indicate that, the rising of coupling parameter values upsurges the fluid velocity but declines the temperature of both phases (fluid and dust). Enhanced thermal profiles are observed with Newtonian heating parameter in two fluid mixtures. The temperature enhances with increasing the radiation parameter where it decreases for increasing the magnetic field parameter and specific heat ratio. Additionally, the rate of heat transfer reduces for higher values of mass concentration and velocity interaction parameter.

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Data availability

The authors declare that the data supporting the findings of this study are available within the article.

Abbreviations

B 0 :

Constant magnetic field

\(B\) :

Slip parameter

\(Ec\) :

Eckert number

K:

Stoke’s resistance constant (\(6\pi r\mu\))

\({K}_{p}\) :

Permeability parameter

k :

Thermal conductivity(Wm−1 K−1)

\({k}^{^{\prime}}\) :

Permeability of the medium (m2)

l :

Characteristic length

\({l}^{*}\) :

Parameter of mass concentration

\(M\) :

Magnetic number

m:

Mass of dust particles

N:

Density number(dust particle)

\(\mathrm{Pr}\) :

Prandtl number

\(\mathrm{Re}\) :

Reynolds number

\(Rd\) :

Radiation parameter

\(s\) :

Couple stresses parameter

\(T,{T}_{p}\) :

Fluid and dust particle temperature

T0 :

Reference temperature

\({T}_{\infty }\) :

Ambient temperature

U0 :

Reference velocity

(u, w), (u p , w p):

Components of velocity in \((r, z)\) directions

\(\beta\) :

Interaction parameter(velocity)

\({\beta }_{T}\) :

Interaction parameter for temperature

\(\gamma\) :

Curvature parameter

\({\gamma }_{1}\) :

Specific heat parameter

\(\lambda\) :

Conjugate parameter of Newtonian heating

µ:

Dynamic viscosity

ρ,\({\rho }_{p}\) :

Fluid and particle phase density(with \({\rho }_{p}=mN\))

\({\tau }_{T}\) :

Thermal equilibrium time

\({\tau }_{\upsilon }\) :

Time relaxation of particle phase

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Authors and Affiliations

  1. University of Technology and Applied Sciences-Shinas, Shinas, Sultanate of Oman

    Mahesh Garvandha & Devendra kumar

  2. Department of BSH, Vaagdevi College of Engineering, Bollikunta, Warangal, Telangana, India

    G. Nagaraju

  3. Faculty of Engineering, Kuwait College of Science and Technology, 35004, Doha, Kuwait

    Ali J. Chamkha

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  1. Mahesh Garvandha
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Garvandha, M., Nagaraju, G., kumar, D. et al. Study of Different Heating Effects on Two-Phase Flow of Magnetized Couple Stresses Over a Permeable Stretching Cylinder with Velocity Slip and Radiation. Int. J. Appl. Comput. Math 8, 249 (2022). https://doi.org/10.1007/s40819-022-01444-9

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