Role of hybrid nanostructures and dust particles on transport of heat energy in micropolar fluid with memory effects
- PDF / 1,832,470 Bytes
- 14 Pages / 595.276 x 790.866 pts Page_size
- 62 Downloads / 168 Views
Role of hybrid nanostructures and dust particles on transport of heat energy in micropolar fluid with memory effects Hajra Kaneez1 · M. Nawaz1 · Yasser Elmasry2 Received: 5 April 2020 / Accepted: 21 September 2020 © Akadémiai Kiadó, Budapest, Hungary 2020
Abstract Constitutive models exhibiting viscoelastic and micro-inertia with vortex viscosity effects are used for modeling of transport of heat energy, (angular and linear) with conservation laws for dust phase flow. The governing models are solved via the finite element method. The convergence of numerical solutions is guaranteed and mesh-free results are computed in view of a variation of physical parameters. Micro-rotations have shown a remarkable impact on shear stress and wall heat flux. The momentum relaxation (memory effects) time has shown a remarkable decrease in velocity associated with macro-flow. An increase in vortex viscosity increases angular motion. The Deborah number has shown a decreasing trend on flow. This causes a significant decrease in convective transport of heat energy. The temperature of dust particles increases when the ratio of specific heat and fluid particle interaction parameter for temperature is increased. However, the opposite behavior is noted for the case of increasing the relaxation time of the particle phase. The hybrid nanofluid transports much momentum than the momentum transported by mono-nanofluid. Keywords Viscoelasticity · Micro-inertia · Dusty fluid · Memory effects · Mixed convection · Angular momentum List of symbols u, v Fluid velocity components (m s−1) A Stoke’s resistance g Gravitational acceleration (m s−2) T Fluid temperatures (K) Tw Wall temperature Tp Dust particles temperature T∞ Ambient temperatures u0 Constant N Micro-rotation velocity N0 Number density of dust particles f Dimensionless velocities for fluid Fp Dimensionless velocity dust particles Uw Wall velocity j Micro-inertia per unit mass m Mass of dust particles Cm Specific heat of dust particles (J kg−1 K−1) * Hajra Kaneez [email protected] 1
Department of Applied Mathematics and Statistics, Institute of Space Technology, P.O. Box 2750, Islamabad 44000, Pakistan
Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia
2
DB Deborah number Pr Prandtl number Ec Eckert number cp Specific heat (J kg−1K−1) k Thermal conductivity Subscripts f Fluid p Dust particles s1 Solid particles for Al2O3 s2 Solid particles for CuO nf Nanofluid hnf Hybrid nanofluid Greeks 𝜆0 Relaxation time for Maxwell fluid 𝜇 Dynamic viscosity (kg ms−1) 𝜌 Density (kg m−3) 𝜑D Volume fraction for dust particles 𝜎 Electrical conductivity 𝜏v Relaxation times for dust phase 𝜏T Relaxation times for temperature 𝜑1 Volume fractions of Al2O3 𝜑2 Volume fractions of CuO 𝜖 Mixed convection parameter 𝛼 Relaxation time of the particle phase 𝛽v Interaction parameter for velocity
13
Vol.:(0123456789)
𝜃 Dimensionless temperatures for fluid 𝜃p Dimensionless temperatures for dust particles 𝛽T Par
Data Loading...
