Abstract
A numerical research on magnetohydrodynamic mixed convection flow in a lid-driven trapezoidal enclosure at non-uniform heating of bottom wall has been studied numerically. The enclosure consists of insulated top wall and cold side walls, too. It also contains a heated triangular block (Rot = 0° - 90°) located somewhere inside the enclosure. The boundary top wall of the enclosure is moving through uniform speed U0. The geometry of the model has been represented mathematically by coupled governing equations in accordance with proper boundary conditions and then a two-dimensional Galerkin finite element based numerical approach has been adopted to solve this paper. The numerical computations have been carried out for the wide range of parameters Prandtl number (0.5 ≤ Pr ≤ 2), Reynolds number (60 ≤ Re ≤ 120), Rayleigh number (Ra = 103) and Hartmann number (Ha = 20) taking with different rotations of heated triangular block. The results have been shown in the form of streamlines, temperature patterns or isotherms, average Nusselt number and average bulk temperature of the fluid in the enclosure at non-uniform heating of bottom wall. It is also indicated that both the streamlines, isotherm patterns strongly depend on the aforesaid governing parameters and location of the triangular block but the thermal conductivity of the triangular block has a noteworthy role on the isotherm pattern lines. Moreover, the variation of Nuav of hot bottom wall and θav in the enclosure is demonstrated here to show the characteristics of heat transfer in the enclosure.
Highlights
Mixed convection heat transfer within a closed enclosure akin to geometry may occur on account of the combined effect of buoyancy along with shear and nowadays has received substantial attention under the lid-driven enclosure problems
According to the above literature review, much studies have been found on mixed convection within a lid-driven square cavity but no attention has been paid to the problem of magneto-hydrodynamic mixed convection flow within a trapezoidal cavity embedded inside heated triangular block of different rotations (Rot = 0 ̊ - 90 ̊) with practical applications which are necessary to investigate
The analysis has been conducted for the various ranges of non-dimensional parameters such as Rayleigh number (Ra = 103), Hartmann number (Ha = 20), Prandtl number (0.5 ≤ Pr ≤ 2), and Reynolds number (60 ≤ Re ≤ 120) as well as various rotations of heated triangular block within trapezoidal cavity
Summary
Mixed convection heat transfer within a closed enclosure akin to geometry may occur on account of the combined effect of buoyancy along with shear and nowadays has received substantial attention under the lid-driven enclosure problems. Heat transfer of mixed convection in a two-dimensional lid-driven trapezoidal enclosure having nanofluids heated from underneath wall is studied by Kareem et al [13] numerically. It is seen from the flow path that the opposing flow is lower than the helping flow which presents Nusselt number. According to the above literature review, much studies have been found on mixed convection within a lid-driven square cavity but no attention has been paid to the problem of magneto-hydrodynamic mixed convection flow within a trapezoidal cavity embedded inside heated triangular block of different rotations (Rot = 0 ̊ - 90 ̊) with practical applications which are necessary to investigate. The Prandtl number has been considered from 0.5 to 2 for fluids
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