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This study explores the numerical investigation of magnetohydrodynamic free convection flow within a rectangular cavity featuring a triangular obstacle near a corner heater. The upper horizontal wall is maintained at a cool temperature, while the right bottom corner is heated, and the remaining walls are kept adiabatic. Solving the governing nonlinear differential equations for general flow problems, along with boundary conditions, is accomplished using the Galerkin weighted residual finite element method. The simulation spans a broad range of parameters, including Rayleigh number Ra(102 = Ra = 104), Hartmann number Ha(0 = Ha = 100), and Prandtl number Pr (0.70 = Pr = 7.00). Results are presented in terms of stream functions, temperature profiles, and Nusselt Numbers. At low Rayleigh numbers (Ra = 103), the isotherms exhibit near-parallel alignment with the upper portion of the triangular obstacle, while higher Ra values lead to more distorted isotherms. An increase in Rayleigh number corresponds to a significant enhancement in flow circulation and heat transfer. Isotherms distributions remain consistent with increasing Hartmann numbers, but higher Hartmann numbers influence streamlines. Validation of the numerical model against previously published results demonstrates good agreement. [ABSTRACT FROM AUTHOR]

Augmentation of heat transfer can be in so many ways, heat transfer of a nanofluid in a porous is one of the most recent methodologies. In this analysis, the physical properties of water as the base fluid and copper as the nanoparticles exercise. The Finite element method is applied to obtain numerical solutions. The effects of the Darcy number, Richardson number and solid volume fraction of nanofluids on the streamlines, isotherms, dimensionless temperature, velocity profiles, and average Nusselt numbers and average fluid temperature examined graphically. It has found that both the Richardson number and solid volume fraction have a noteworthy influence on streamlines and isotherms. Darcy number has a good control parameter for heat transfer in fluid flow through a porous medium in the enclosure. A heat transfer correlation of the average Nusselt number for various Darcy numbers and solid volume fraction presented here. Finally, for the validation of the existing work, the current results are compared with the published results, and a favorable agreement attained. Besides this, heat transfer in the square enclosure remains better than for the other enclosures with the wavy walls or curved walls. [ABSTRACT FROM AUTHOR]

Numerical study of natural convection flow in a hexagonal enclosure with a single vertical fin attached to its heated bottom wall has been carried out. Finite element method based Galerkin weighted residual technique is used to solve the governing equation. The horizontal walls of the enclosure are kept at constant high temperature while the inclined walls are kept at constant cold temperature. A vertical heated fin is attached to the hot bottom wall with a length () at a position () from the left surface having thickness (). The Prandlt number for the flow inside the enclosure is 0.71. The results of the problem are presented in graphical and tabular forms and discussed. The fin efficiency and temperature distribution were examined. The numerical results indicate the strong influence of the mentioned parameters on the flow structure and heat transfer as well as temperature. A set of graphical results are presented in terms of streamlines, isotherms contour, temperature profiles, velocity profiles, local Nusselt number and average Nusselt number. The obtained results indicated that the heat transfer rate increases with the increase of Rayleigh number in a hexagonal enclosure. The results are validated comparing with the published works. [ABSTRACT FROM AUTHOR]

This study investigated the effects of the aspect ratio of the cavity for average fluid temperature at exit port, average Nusselt number, maximum temperature of the fluid in the domain, drag coefficient, isotherms and streamlines on behalf of different Hartmann numbers and Rayleigh numbers. Solution of governing equations of momentum and energy has been made by finite element technique. Above mentioned parameters such as an aspect ratio which is cavity height to cavity length change from Ar = 0.5 to 2 for different Rayleigh numbers and Hartmann numbers which change from Ra = 10² to 105 and Ha = 0 to 50 respectively. Prandt; number Pr = 7 and Reynolds number Re = 100 is fixed in this simulation. It is found that variation of the aspect ratio makes an important effect for higher values of Rayleigh numbers. Heat transfer enhances with increasing of aspect ratio. Increasing of Hartmann number decreases the heat transfer inside the cavity. [ABSTRACT FROM AUTHOR]