The set of governing differential equations has been discretized by the control volume method. SIMPLE algorithm was used as pressure–velocity coupling technique and second order upwind method was adopted for convective and diffusive terms. The resulting algebraic system solved by using Gauss–Seidel applied in a line going through all volumes in the computational domain. Convergence criteria for all parameter were restricted to be lower than10−6.
In order to achieve more accuracy grid independence studies were performed on pure water individually in each model. For all cases an inflated grid has been considered spotting for our modeling domain. Schematic of domain grid is illustrated in Fig. ...view middle of the document...
Wall temperature is one of the most important parameter in design and restrictions of this kind of geometries. For examples maximum wall temperature of cladding limits the height of fuel rod in nuclear reactor designs.
3.1. Bulk Temperature
Numerical method predicts temperature in any point of domain. Hence, by reading every height temperature and using balance equation bulk temperature would be calculated (Incropera 1981).
(12) T_m=(∫_A^ ▒ρuT dA_c)/m ̇
Bulk temperature of different flows is illustrated in Fig.4. It is evident from Fig.4 that nanoparticle concentration has no major effect on bulk temperature. Increasing Reynolds number reduce bulk temperature dramatically.
3.2. Wall Temperature Profiles
In Fig.5 and Fig.6 wall temperature and its dependence to Reynolds and nanoparticle concentration is illustrated. Because the heat flux has cosine profile, the temperature will maximize at a point above middle of heating region. It is obvious from Fig.4 that increasing Reynolds number and nanoparticles concentration both decrease the wall temperature. In a specific Reynolds (i.e. Re=3500) adding nanoparticle to 1.5% volume concentration will decrease the wall temperature about 1.5 degrees. Another way to decrease wall temperature is enhancing flow rate (Reynolds number) i.e. increasing Reynolds number from 950 to 4200 will decrease maximum wall temperature about 10 Celsius. It is evident that increasing Reynolds number from 3500 to 4200 has the same effect of adding 1.5% Al2O3 nanoparticles. Both of this two ways decrease maximum wall temperature about 1.5 degrees.
Increasing Reynolds number will flatten wall temperature profiles. It is also evident that for higher Reynolds number profiles are steeper. In other word, in higher Reynolds numbers, effect of nanoparticles on wall temperature is less than lower Reynolds. It might be because of effects of turbulence on heat transfer. Maximum wall temperature is another key parameter in annuli non-uniform heat flux. It is obvious that increasing Reynolds number both peak temperature and its height.
3.3. Local Heat Transfer Coefficients and Nusselt Number
When wall temperature and bulk temperature is determined, one can calculate local heat transfer coefficient. Calculating averaged heat transfer needs a simple integrating. Local heat transfer coefficient profile for different Reynolds number and nanoparticle concentrations is illustrated in Fig.7. Nanoparticles concentration has no major effect on shape of profile but increasing Reynolds number change the profile.
Increasing nanoparticle concentrations to 0.25% and 0.5% have no improving effect on heat transfer coefficient, but addition of nanoparticles to 1% and 1.5% concentrations make heat transfer coefficient...