Linear temporal stability of Jeffery–Hamel flow of nanofluids

Abstract

Flow stability plays a key role in transition to turbulence in various systems. This transition initiates with disturbances appearing in the laminar base flow, potentially amplifying over time based on flow and fluid parameters. In response to these amplified disturbances, the flow undergoes successive stages of different laminar flows, ultimately transitioning to turbulence. One influential parameter affecting flow stability is the nanoparticle volume fraction ($\varphi$) in nanofluids, extensively employed in thermofluid systems like cooling devices to enhance fluid thermal conductivity and the heat transfer coefficient. Focusing on the impact of nanoparticles on Jeffery–Hamel flow stability, this study assumes fluid properties are temperature- and pressure-independent, exclusively examining the momentum transfer aspect. The analysis commences by deriving the base laminar flow solution. Subsequently, linear temporal stability analysis is employed, imposing infinitesimally-small perturbations on the base flow as a modified form of normal modes. A generalized Orr–Sommerfeld equation is derived and solved using a spectral method. Results indicate that, assuming nanofluid viscosity as ${\mu }_{\mathrm{nf}}={\mu }_f/{(1-\varphi )}^{2.5}$, nanoparticle effects on momentum transfer and flow stability hinge on the ratio of nano-solid particle density to base fluid density ($R_{\rho }={\rho }_s/{\rho }_f$). For $\varphi \in (0,0.1]$, flow stabilization occurs with $\varphi$ when $R_{\rho }<3.5000$, while destabilization is observed when $R_{\rho }>4.0135$. Notably, nanoparticles exhibit a negligible impact on flow stability when $3.5000\le R_{\rho }\le 4.0135$.