الفهرس 
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Abstract
The hydrodynamics and heat transfer through isothermal tube entrance region were investigated numerically in the presence of Nano-particles and Porous media each alone or both at the same time. The study was performed by a computer home-code. This code is based on finite volume method. The effects of Reynolds number and Nano-particle concentration on viscous boundary layer thickness, shear stress, coefficient of friction, thermal boundary layer thickness and Nusselt number were presented in case of adding Nano-particles only. Through the study, in case of adding Nano-particles only, Reynolds number varied from 500 to 2000 and Nano-particle concentration varied from o to 10%. Three different Nano-particles Ah03, Ti02 and Cu were studied. While the Prandtl number for the base fluid was kept constant at 7 referring to water.On the other hand, the effects of Darcy number and porosity on local and average Nusselt number were presented in case of adding porous media only. Through the study in case of adding porous media only, Darcy number varies from 10-3 to 0.2, porosity changed from 0.1 to 0.9, carbon steel as porous media, water as base fluid and Reynolds number kept constant at 1500. While the last case of adding both Nano-particles and porous media, the effect of Nano-particle concentration on average Nusselt number was explained. Through the study in case of adding the two methods of enhancing heat transfer at the same time, copper Nano-particle concentration is changed from 2 to 10% while Reynolds number, Prandtl number, Darcy number and porosity were kept constant at 1500, 7, 10-3 and 0.9 respectively. In general, the results showed that an enhancement in Nusselt number by adding Nano-particles especially by using Cu Nano-particles, such that the maximum increase in Nusselt number reached 20.5 % at Re = 1000 at Nano particle concentration = 10 % for copper Nano-particle. Both average coefficient of friction and average Nusselt number were correlated in terms of Reynolds number, Nano-particle concentration, dimensionless entry length and Nano-particle type. The best values when adding porous media is to lower Darcy number and increase porosity as possible. Also, the best case is to add Nano-particles and porous media at the same time. Some of the results were compared with published data, a good agreement was found.