Investigation on Nanoparticle Velocity in Two Phase Approach

Numerical investigation on the generality of nanoparticle velocity equation had been done on the previous published work. The three dimensional governing equations (continuity, momentum and energy) were solved using finite volume method (FVM). Parametric study of thermal performance between pure water-cooled and nanofluid-cooled are evaluated for volume fraction in the range of 1% to 4%, and nanofluid type of gammaAl2O3 at Reynolds number range of 67.41 to 286.77. The nanofluid is modeled using single and two phase approach. Three different existing Brownian motion velocities are applied in comparing the generality of the equation for a wide parametric condition. Deviation in between the Brownian motion velocity is identified to be due to the different means of mean free path and constant value used in diffusion equation. Keywords—Brownian nanoparticle velocity, heat transfer enhancement, nanofluid, two phase model. NOMENCLATURE cp specific heat, J/kgK dp particle diameter, nm D diffusion coefficient Dh hydraulic diameter, mm De Dean number, / . h heat transfer coefficient, k thermal conductivity, W/mK M Molecular weight of water, kg/kgmol N Avogadro number of water Nu Nusselt number, / Po Poiseuille number, q” heat flux, kW/cm R radius, nm Rc curvature radius, mm Re Reynolds Number, / Rth Thermal resistance, C/ W, ∆ / T temperature, C u, v, w Velocity component, m/s x,y, z Cartesian coordinate Greek symbols β thermal expansion, 1/K ρ density, kg/m κB Boltzman constant ø solid volume fraction μ viscosity, Ns/m λ curvature ratio, λ D /R E. Mat Tokit is with the Faculty of Mechanical Engineering, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, 76100 Durian Tunggal, Melaka, Malaysia (phone: 606-2332430; fax: 606-2332429 e-mail: ernie@ utem.edu.my). Yusoff M. Z is with the Department of Mechanical Engineering, College of Engineering, Universiti Tenaga Nasional, Jalan IKRAM-UNITEN, 43000 Kajang, Selangor, Malaysia (e-mail: [email protected]). Mohammed H. is with the Department of Thermofluids, Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, 81310 UTM, Skudai, Johor Bahru, Malaysia (e-mail: [email protected]). Subscripts f fluid nf nanofluid np nanoparticle pw pure water rms root mean square s solid