Two dimensional MHD nanofluid flow analysis of fractional dual-phase-lag heat conduction between inclined cylinders with variable thickness

Abstract

Purpose

This study aims to investigate the two-dimensional magnetohydrodynamic flow and heat transfer of a fractional Maxwell nanofluid between inclined cylinders with variable thickness. Considering the cylindrical coordinate system, the constitutive relation of the fractional viscoelastic fluid and the fractional dual-phase-lag (DPL) heat conduction model, the boundary layer governing equations are first formulated and derived.

Design/methodology/approach

The newly developed finite difference scheme combined with the L1 algorithm is used to numerically solve nonlinear fractional differential equations. Furthermore, the effectiveness of the algorithm is verified by a numerical example.

Findings

Based on numerical analysis, the effects of parameters on velocity and temperature are revealed. Specifically, the velocity decreases with the increase of the fractional derivative parameter α owing to memory characteristics. The temperature increase with the increase of fractional derivative parameter ß due to a decrease in thermal resistance. From a physical perspective, the phase lag of the heat flux vector and temperature gradients τ_q and τ_T exhibit opposite trends to the temperature. The ratio τ_T/τ_q plays an important role in controlling different heat conduction behaviors. Increasing the inclination angle θ, the types and volume fractions of nanoparticles Φ can increase velocity and temperature, respectively.

Originality/value

Fractional Maxwell nanofluid flows from a fixed-thickness pipe to an inclined variable-thickness pipe, and the fractional DPL heat conduction model based on materials is considered, which provides a basis for the safe and efficient transportation of high-viscosity and condensable fluids in industrial production.

Citation

Jiang, J., Zhao, H. and Zhang, Y. (2023), "Two dimensional MHD nanofluid flow analysis of fractional dual-phase-lag heat conduction between inclined cylinders with variable thickness", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 33 No. 5, pp. 1637-1660. https://doi.org/10.1108/HFF-05-2022-0264