Abstract
In this study, the numerical investigation of the natural convection heat transfer around a hot elliptical cylinder inside a cold rhombus enclosure filled with a nanofluid in the presence of a uniform magnetic field is conducted. An immersed boundary method as a computational tool has been extended and applied to solve the problem. The influence of various parameters such as cylinder diameters (a, b), Hartmann number (Ha = 0, 50 and 100), nanofluid volume fraction (varphi = 0 , 2.5% and 5%), and Rayleigh number (Ra = 103, 104, 105, 106, and 107) has been studied. Streamlines and isotherms contours as well as average Nusselt number have been specified for different modes. An equation for the average Nusselt number as a function of mentioned parameters is presented in this paper. The results show that at lower Ra numbers of Ra = 103 and 104, the magnetic field effect is negligible. However, at higher Rayleigh numbers, the average Nusselt number (Nuave) decreases with the increasing Ha number. The maximum decrease in Nuave at Ra = 105, 106 and 107are calculated −8.15%, −23.4% and −27.3%, respectively. An asymmetry-unsteady flow is observed at {text{Ra}} = 10^{7} for Ha = 0. However, at higher Ha numbers a steady-symmetrical flow is formed.
Highlights
Various engineering applications of natural convection heat transfer inside a nanofluid—filled enclosures are extended
The heat transfer area of study in nanofluids under the influence of a magnetic field could be divided into the two following categories: The first category is the investigation of heat transfer problems in an enclosure
Results show a symmetrical pattern of streamlines and isotherms in Rayleigh numbers of Ra = 103, 104, 105 and 106
Summary
Greek symbols ⃗f Force source to impose velocity boundary condition (m s−2) Thermal diffusivity (m2 s−1) ⃗f Dimensionless force source Coefficient of thermal expansion (oK−1) g⃗ Gravity acceleration vector (m s−2) Θ Dimensionless temperature h Heat source to impose thermal boundary condition Θ∗ Dimensionless intermediate temperature. H Dimensionless heat source ΘΓ Dimensionless temperature on the boundary Ha Hartmann number. I Integration operator Viscosity (kg m−1 s−1) k Thermal conductivity (W m−1 K−1) Density (kg m−3) b Boltzmann’s constant = 1.38066e-23 (JK−1) Nanofluid volume fraction Ls Side length of enclosure (m) Electrical conductivity L2 L 2 Norm ∇ Gradient operator L0 Reference length ∇2 Laplace operator M Molecular mass of base-fluid. Subscripts N Avogadro number nf Nanofluid Nu Local Nusselt number f Pure fluid p Pressure (pa) p Particle P Dimensionless pressure fr Freezing point Pr Prandtl number H Hot Re Reynolds number C Cold S Distance of cylinders (m) M Momentum t Time (s) Θ Thermal T Temperature
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