Analysis of critical fluid velocity and heat transfer in temperature-dependent nanocomposite pipes conveying nanofluid subjected to heat generation, conduction, convection and magnetic field

Abstract

In this paper, analysis of critical fluid velocity and heat transfer in the nanocomposite pipes conveying nanofluid is presented. The pipe is reinforced by carbon nanotubes (CNTs) and the fluid is mixed by AL2O3 nanoparticles. The material properties of the nanocomposite pipe and nanofluid are considered temperature-dependent and the structure is subjected to magnetic field. The forces of fluid viscosity and turbulent pressure are obtained using momentum equations of fluid. Based on energy balance, the convection of inner and outer fluids, conduction of pipe and heat generation are considered. For mathematical modeling of the nanocomposite pipes, the first order shear deformation theory (FSDT) and energy method are used. Utilizing the Lagrange method, the coupled pipe-nanofluid motion equations are derived. Applying a semi-analytical method, the motion equations are solved for obtaining the critical fluid velocity and critical Reynolds and Nusselt numbers. The effects of CNTs volume percent, AL2O3 nanoparticles volume percent, length to radius ratio of the pipe and shell surface roughness were shown on the critical fluid velocity, critical Reynolds and Nusselt numbers. The results are validated with other published work which shows the accuracy of obtained results of this work. Numerical results indicate that for heat generation of Q = 10 MW/m3, adding 6% AL2O3 nanoparticles to the fluid increases 20% the critical fluid velocity and 15% the Nusselt number which can be useful for heat exchangers.