2.1. Problem Definition
Figure 1 depicts the geometry, boundary condition and sample element. The bottom wall is hot wall and the top one is melting surface . Other walls are adiabatic. Horizontal magnetic field has been applied. The enclosure is field with nanofluid.
2.2. Governing Equation
2D steady convective nanofluid flow is considered in existence of constant magnetic field. The PDEs are:
(1)(2)(3)(4), and are calculated as:
(5)(6)(7)(8) are calculated via KKL model:
(9)(10)Properties and needed parameters are provided Tables 1 and 2.
Vorticity and stream function should be used to eliminate pressure source terms:
(11)Introducing dimensionless quantities:
(12)The final formulae are:
(13)(14)(15)Boundary conditions are: on top wall on bottom wall on other walls Right, left and bottom walls(16) and in melting surface, we have:
(17) where dimensionless and constants parameters are illustrated as:
(18)It should be mentioned that is related to Stefan numbers.
Local and average Nusselt over the hot wall can calculate as:
(19)(20)