Impact of nanofluid natural convection due to magnetic field in existence of melting heat transfer is simulated using CVFEM in this research. KKL model is taken into account to obtain properties of CuO–H_{2}O nanofluid. Roles of melting parameter
Melting process has various uses such as application like in thermocouple, heat exchangers, and heat engines. Chamkha and Ismael [
Sheremet et al. [
This research intends to present the impact of melting heat transfer on free convection of ferrofluid in the presence of Lorentz forces. CVFEM is selected to find the outputs. Roles of melting parameter, CuO–water volume fraction, and Hartmann and Rayleigh numbers are presented.
Figure
(a) Geometry; (b) sample element.
2D steady convective nanofluid flow is considered in existence of constant magnetic field. The fluid flow is laminar and incompressible. The flow is steady and Newtonian. The viscous dissipation is negligible in this study. The effects of Brownian force and thermophoretic force are not taken into condition. The flow also follows the Boussinesq assumption. The prevailing equations under these constraints can be written as [
Coefficient values of CuO–H_{2}O [
Coefficient values  CuO–water 





















Properties of H_{2}O and CuO [








Water  997.1  4179  0.613  21  — 


6500  540  18  29  45  10^{−10} 
Vorticity and stream function should be used to eliminate pressure source terms:
Local and average Nusselt over the cold wall can be calculated as follows:
CVFEM uses both benefits of two common CFD methods. This method uses triangular element (see Figure
Outputs should not rely on mesh size. Therefore, several grids should be tested. For example, as shown in Table
Mesh independency analysis when
Mesh size 






0.890241  0.895531  0.907145  0.908743  0.909166 





Present work  Rudraiah et al. [ 
Present work  Rudraiah et al. [  
0  2.5665  2.5188  5.093205  4.9198 
10  2.26626  2.2234  4.9047  4.8053 
50  1.09954  1.0856  2.67911  2.8442 
100  1.02218  1.011  1.46048  1.4317 
Validation of present code (Khanafer et al. [
Nanofluid flow in a half sinusoidal annulus due to magnetic field in presence of melting surface is examined.
Impact of adding CuO nanoparticles in water on velocity and temperature contours is depicted in Figure
Impact of adding CuO in water on streamlines and isotherms (nanofluid (
Figures
Isotherms and streamlines for various Ha, Ra when
Isotherms and streamlines for various Ha, Ra when
Figure
Impacts of
Nanofluid free convection due to Lorentz force in existence of melting surface is reported. Combination of FEM and FVM is utilized to solve the PDEs. KKL model is considered for nanofluid. Roles of Hartmann number, CuO–water volume fraction, Rayleigh number, and melting parameter are presented. Outputs depict that temperature gradient improves with augment of melting parameter and Rayleigh number. Adding magnetic field makes the temperature gradient reduce due to domination of conduction mechanism in high Hartmann number.
Magnetic field
Fluid temperature
Nusselt number
Rayleigh number
Gravitational acceleration vector
Hartmann number.
Dimensionless temperature
Thermal diffusivity
Dimensionless vorticity and stream function
Melting parameter
Thermal expansion coefficient
Electrical conductivity
Dynamic viscosity.
Base fluid
Local
Nanofluid.
The authors declare that there are no conflicts of interest regarding the publication of this paper.