Abstract
The unsteady natural convection heat transfer of nanofluid along a vertical plate embedded in porous medium is investigated. The Darcy-Forchheimer model is used to formulate the problem. Thermal conductivity and viscosity models based on a wide range of experimental data of nanofluids and incorporating the velocity-slip effect of the nanoparticle with respect to the base fluid, i.e., Brownian diffusion is used. The effective thermal conductivity of nanofluid in porous media is calculated using copper powder as porous media. The nonlinear governing equations are solved using an unconditionally stable implicit finite difference scheme. In this study, six different types of nanofluids have been compared with respect to the heat transfer enhancement, and the effects of particle concentration, particle size, temperature of the plate, and porosity of the medium on the heat transfer enhancement and skin friction coefficient have been studied in detail. It is found that heat transfer rate increases with the increase in particle concentration up to an optimal level, but on the further increase in particle concentration, the heat transfer rate decreases. For a particular value of particle concentration, small-sized particles enhance the heat transfer rates. On the other hand, skin friction coefficients always increase with the increase in particle concentration and decrease in nanoparticle size.
Highlights
Natural convection heat transfer in porous media is an important phenomenon in engineering systems due to its wide applications such as cooling of electronics components, heat exchangers, drying processes, building insulations, and geothermal and oil recovery
Choi [10] proposed that the uniform dispersion of small concentration of nano-sized metal/ metal oxides particles into a fluid enhances the thermal conductivity of the base fluid, and such fluids were termed as nanofluids
Corcione [14] analyzed the experimental data of thermal conductivity and viscosity of nanofluids, which were obtained by various researchers for different types of nanoparticles dispersed in different base fluids, and found an empirical correlating equation for the prediction of effective thermal conductivity and dynamic viscosity of nanofluids
Summary
Natural convection heat transfer in porous media is an important phenomenon in engineering systems due to its wide applications such as cooling of electronics components, heat exchangers, drying processes, building insulations, and geothermal and oil recovery. Abu-Nada and Oztop [18] investigated the effects of inclination angle on natural convection in enclosures filled with Cu-water nanofluid All these authors reported that the heat transfer rate increases with the increase in nanoparticle concentration in the base fluid. The effective thermal conductivity was calculated by the model of Chon et al [13], and to formulate the dynamic viscosity of the Al2O3-water nanofluid, the author used the experimental data and found the empirical correlation for the dynamic viscosity as a function of temperature and particle concentration. In the studies of natural convection of nanofluids in porous media, the authors did the parametric study only They did not account any effect of parameters influencing the thermal conductivity and dynamic viscosity, such as particle concentration, particle size, temperature, nature of base fluid, and the nature of nanoparticle, which satisfy the experimental data for the thermal conductivity and dynamic viscosity of the nanofluids. The scope of the current research is to implement the appropriate models for the nanofluid properties, which consist the velocity-slip effects of nanoparticles with respect to the base fluid and the heat transfer flow in the two phases, i.e., through porous medium and nanofluid to be taken into account, and to analyze the effect of nanofluids on heat transfer enhancement in the natural convection in porous media
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