Melting heat transfer in hybrid nanofluid flow along a moving surface
- PDF / 1,420,804 Bytes
- 12 Pages / 595.276 x 790.866 pts Page_size
- 30 Downloads / 207 Views
Melting heat transfer in hybrid nanofluid flow along a moving surface Najiyah Safwa Khashi’ie1,2 · Norihan Md Arifin1,3 · Ioan Pop4 · Roslinda Nazar5 Received: 4 April 2020 / Accepted: 10 September 2020 © Akadémiai Kiadó, Budapest, Hungary 2020
Abstract The impact and capability of Cu–Al2O3/water nanoliquid as the heat transfer fluid are numerically investigated along a moving surface with melting heat transfer. The reduced differential equations are solved and presented in the figures and tables. The percent error between present and previous numerical values is 0% which supports the model validation. The volumetric concentration of both Al2O3 and Cu nanoparticles is chosen at most 4% to avoid the instability of the nanofluid. The dual solutions are only seen when the external flow and solid surface move in an opposite direction. Remarkably, the use of hybrid nanofluid assists the boundary layer separation in the presence of melting heat transfer. However, the heat transfer rate of Cu–Al2O3/water is inevitably greater than the pure water and Cu–water. An increase in melting parameter reduces the heat transfer rate and accelerates the separation of boundary layer. The stability analysis supports the initial hypothesis from the graphical results that the second solution is unstable. Keywords Boundary layer flow · Hybrid Cu–Al2O3/water · Melting surface · Dual solutions · Stability analysis List of symbols A Surface area of the heat transfer ( m2) f (𝜂) Dimensionless stream function h Heat transfer coefficient ( W m−2 K−1) k Fluid thermal conductivity ( W m−1 K−1) qw Surface heat flux ( W m−2) s1 First solid nanoparticle (Alumina/Al2O3) s2 Second solid nanoparticle (Copper/Cu) t Time (s) u, v Velocity components along the x, y directions, respectively ( m s−1) x, y Cartesian coordinates Cf Skin friction coefficient
( J kg−1 K−1) (Cp ) Specific heat at constant temperature −1 −3 𝜌Cp Heat capacity of the fluid ( J K m ) Me Melting parameter Nb Brownian motion parameter Nt Thermophoresis parameter Nux Local Nusselt number Pr Prandtl number Rex Local Reynolds number T Fluid temperature (K) T0 Temperature of the solid surface (K) Tm Melting surface temperature (K) T∞ Ambient temperature (K) Uw Velocity of the moving surface ( m s−1) U∞ Free stream velocity ( m s−1)
* Norihan Md Arifin [email protected]
Greek symbols 𝜆 Moving parameter 𝜂 Similarity variable 𝜓 Stream function 𝜃 Dimensionless temperature 𝜇 Dynamic viscosity ( kg m−1 s−1) 𝜈 Kinematic viscosity ( m2 s−1) 𝜌 Fluid density ( kg m−3) 𝛾 Eigenvalue 𝛾1 Smallest eigenvalue 𝜏 Dimensionless time variable
1
Institute for Mathematical Research, Universiti Putra Malaysia (UPM), 43400 Serdang, Selangor, Malaysia
2
Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, 76100 Durian Tunggal, Melaka, Malaysia
3
Department of Mathematics, Faculty of Science, Universiti Putra Malaysia (UPM), 43400 Serdang, Selangor, Malaysia
4
Department of Mathematics, Babe-Bolyai Un
Data Loading...
