Augmentation of heat transfer via nanofluids in duct flows using Fourier-type conditions: Theoretical and numerical study

Abstract

Motivated by developments in thermal duct processing, an investigation is presented to study the behavior of viscous nanoparticle suspensions flowing in a vertical duct subject to Fourier-type conditions. The left wall temperature is kept lower than that of the right wall. Brownian motion and thermophoresis which are invoked via the presence of nanoparticles are incorporated in the study. Numerical solutions with an efficient Runge–Kutta shooting method are also presented at all values of the control parameters. The impact of thermal Grashof number $(0\le \mathrm{\Lambda }\le 15)$ , Eckert number $(0.01\le Ec\le 0.04)$ , thermophoresis $(0.05\le Nt\le 2)$ , and Brownian motion parameters $(0.05\le Nt\le 2)$ on the velocity, temperature, and nanoparticle concentration distributions for identical $(B{i}_1=B{i}_2=10)$ and differing Biot numbers $(B{i}_1=1,B{i}_2=10)$ (at the duct walls) are computed and visualized graphically. With vanishing thermophoresis and Brownian motion parameters, the solutions match exactly with the earlier Newtonian viscous flow computations. Symmetric and asymmetric wall heat conditions are also acknowledged. Intensifying the thermal Grashof number, Eckert number, thermophoresis parameter, and Brownian parameter serve to amplify magnitudes of the velocity and temperature, whereas the nanoparticle concentration field is suppressed. The skin friction and Sherwood number are also computed with various combinations of the flow control parameters. Nusselt number values at the hot duct wall are enhanced with an increase in thermal buoyancy parameter, Eckert number, Brownian motion parameter, and thermophoresis parameter for equal Biot numbers. The opposite trend is computed for different Biot numbers. For any given values of Biot numbers, the mean velocity and bulk temperature are boosted with increase in thermal buoyancy parameter, Eckert number, Brownian motion parameter, and thermophoresis parameter. Hence, it may be inferred that the transport characteristics computed using Fourier-type boundary conditions are substantially different from those based on isothermal boundary conditions in nanofluid duct flows.