Peristaltic transport of diethylene glycol-based magnesium aluminate nanofluid under the effects of viscous dissipation and Hall current

ABSTRACT

The fundamental importance of peristaltic phenomena in numerous biological systems, including dialysis, heart-lung machines, urine transportation, invertebrate locomotion, and the passage of gallbladder bile into the intestines, persuaded scientists to investigate the different aspects of it over the past few years. In addition, peristaltic pumping is an important consideration in industrial processes including, roller pumps used for the transport of sanitary materials, finger pumps, cell separation, and endoscopes. Keeping such inspirational applications in mind, the present investigation is dedicated to exploring the peristaltic transport of a Cross-magneto nanofluid through a curved geometry in the presence of heat transfer. The inspection of the heat transfer is conducted by utilizing variable viscosity and ohmic heating aspects. This study also retains the characteristics of viscous dissipation, heat generation/absorption, and thermal conductivity of nanofluids. Modeling of the 2D, incompressible Cross nanofluid with peristaltic movement is carried out using a curvilinear coordinate system. The basic equations of the problem are mPodeled in the light of physical laws and then simplified by adopting the lubrication theory. The solutions of the resulting nonlinear system are computed numerically. The outcomes of the related flow parameters on the nanofluid’s temperature, pressure gradient, velocity distribution, heat transfer, streamlines pattern, and stresses at the wall are discussed through graphs. The graphical results depict that the rates of heat transfer are augmented by increasing the curvature parameter, Hartmann number, and nanoparticles’ volume fraction while decreasing the Hall parameter and temperature-dependent viscosity parameter. Moreover, the nanofluid’s temperature increases by improving the values of the heat generation parameter, whereas it decreases for the Hall parameter. Furthermore, a reduction in the axial velocity occurs near the center of the channel, when Hartmann number attains higher values.

KEYWORDS:

• Peristalsis
• diethylene glycol
• heat transfer
• hall current
• temperature-dependent viscosity

Supplementary Material

Supplemental data for this article can be accessed online at https://doi.org/10.1080/02286203.2024.2345250

Disclosure statement

No potential conflict of interest was reported by the author(s).

Nomenclature

$K_{\mathit{nf}}$	=	Nanofluid thermal conductivity $\left(\mathit{W}{m}^{-1}{K}^{-1}\right)$. $$
${\rho }_{\mathit{nf}}$	=	Nanofluid density$\left(\mathit{kg}/m^3\right)$.
$\mathit{\varphi }$	=	Nanoparticles’ volume fraction of $\left(\mathit{MgA}{l}_2{O}_4\right)$.
$\mathit{c}$	=	Wave speed$\left(\mathit{m}.s^{-1}\right)$.
${\mu }_{\mathit{nf}}$	=	Hybrid nanofluid viscosity$\left(\mathit{pa}.\mathit{\hspace{0.17em}}\mathit{s}\right)$.
$K_f$	=	Thermal conductivity of $\left(C_4{H}_{10}{O}_3\right)$ $\left(\mathit{W}{m}^{-1}{K}^{-1}\right).$
$\mathrm{\Phi }$	=	Heat sink/source.
$\tilde{p}$	=	Pressure in moving frame.
$\tilde{P}$	=	Pressure in laboratory frame$\left(\mathit{pa}\right)$.
$C_p$	=	Specific heat$\left(\mathit{J}.\mathit{k}{g}^{-1}{K}^{-1}\right)$.
$\tilde{H}$	=	Peristaltic wall.
$\mathit{\lambda }$	=	Wavelength.
$Re$	=	Reynolds number
${\rho }_f$	=	Base liquid density$\left(\mathit{kg}/m^3\right)$.
$\left(\tilde{r},\tilde{x}\right)$	=	Curvilinear coordinates in wave frame.
${\chi }_2$	=	Wave amplitude.
$\mathit{k}$	=	Characteristic time.
${\eta }_{\mathrm{\infty }}$	=	Dynamic viscosity at infinite-shear rate.
${\alpha }_1$	=	Variable viscosity parameter.
$\left(\tilde{u},\tilde{v}\right)$	=	Velocity components in wave frame.
${\chi }_1$	=	Half uniform width of the channel ($\mathit{m}$).
$\mathit{\psi }$	=	Stream function.
${\eta }_0$	=	Dynamic viscosity at zero-shear rate.
$\mathit{m}$	=	Hall parameter.
$\bar{R}$	=	Radius of the channel
$\mathit{Br}$	=	Brinkman number.
$\left(\tilde{U},\tilde{V}\right)$	=	Velocity component in fixed frame
${\tilde{T}}_0$	=	Wall temperature.
$\mathit{\delta }$	=	Wave number.
$Pr$	=	Prandtl number.
$k_r$	=	Curvature parameter.
$\left(\tilde{R},\mathit{\hspace{0.17em}}\tilde{X}\right)$	=	Curvilinear coordinates in fixed frame.

Data availability statement

No data are associated with the manuscript.

Additional information

Notes on contributors

J. Iqbal

J. Iqbal has received a Bachelor’s and Master’s Degree in Mathematics from COMSATS University Islamabad, Islamabad, Pakistan. He currently serves as a Ph.D. research scholar specializing in the intricate domain of Fluid Dynamics. His research pursuits span a wide spectrum, including Fluid Mechanics, Magnetohydrodynamics (MHD), Peristalsis, Curved Channels, and Newtonian and non- Newtonian flows. Demonstrating robust analytical expertise, he stands as a young and promising researcher in his field.

F. M. Abbasi

Dr. F. M. Abbasi did his Ph.D. in Fluid Mechanics at Quaid- I-Azam University in Islamabad, Pakistan, in 2014. Presently, he is working as a Professor at the Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan. His work mainly addresses the peristaltic flows of viscous and non- Newtonian fluids. Over the past couple of years, his work in the field of Newtonian and non-Newtonian fluid mechanics has been published extensively in the International Journal of Good Repute. He is among the most promising young researchers in Pakistan.

R. Nawaz

Dr. R. Nawaz is a promising researcher working in the broader area of Mechanics and Applied Mathematics, with a distinguished academic career spanning fifteen years, widely recognized within the scientific community. He has contributed significantly to various esteemed organizations as both a researcher and educator, and is currently affiliated with the Gulf University of Science and Technology, Kuwait.