Study of Exponential Thermal Boundary Condition on Unsteady Magnetohydrodynamic Convection in a Square Enclosure Filled with Fe3O4- Water Ferrofluid

In this paper, magnetohydrodynamic convection is analyzed numerically for a square enclosure filled with Fe3O4–water ferrofluid. A time-dependent exponential thermal boundary condition is applied at the bottom wall of the cavity. The ferrofluid is modeled as a single-phase fluid. Maxwell-Garnet model is used for modeling the effective thermal conductivity and viscosity of the ferrofluid. The Galerkin-weighted residuals method of finite-element analysis is adopted for the numerical solutions. The solid volume fraction, f is varied from 2.5 to 10% and the Hartmann number Ha from 0 to 20. Investigations are carried out for Rayleigh number Ra =104 and 105 over dimensionless times τ=0.01–1.0. The present study indicates that Ra, Ha and f, have a significant effect on heat transfer. At τ =1, if Ra=104, a higher solid volume fraction maximizes heat transfer whereas at Ra=105, a lower solid volume fraction maximizes heat transfer. Moreover, at τ =1, incrementing Ha diminishes heat transfer at Ra=104 whereas an optimum value of Ha=10 maximizes heat transfer for Ra=105. The exponential thermal boundary conditions have a certain importance on heat transfer. The present results provide necessary information for further investigation of heat transfer in its different applications

Study of Exponential Thermal Boundary Condition on Unsteady Magnetohydrodynamic Convection in a Square Enclosure Filled with Fe3O4- Water Ferrofluid

In this paper, magnetohydrodynamic convection is analyzed numerically for a square enclosure filled with Fe3O4–water ferrofluid. A time-dependent exponential thermal boundary condition is applied at the bottom wall of the cavity. The ferrofluid is modeled as a single-phase fluid. Maxwell-Garnet model is used for modeling the effective thermal conductivity and viscosity of the ferrofluid. The Galerkin-weighted residuals method of finite-element analysis is adopted for the numerical solutions. The solid volume fraction, f is varied from 2.5 to 10% and the Hartmann number Ha from 0 to 20. Investigations are carried out for Rayleigh number Ra =104 and 105 over dimensionless times τ=0.01–1.0. The present study indicates that Ra, Ha and f, have a significant effect on heat transfer. At τ =1, if Ra=104, a higher solid volume fraction maximizes heat transfer whereas at Ra=105, a lower solid volume fraction maximizes heat transfer. Moreover, at τ =1, incrementing Ha diminishes heat transfer at Ra=104 whereas an optimum value of Ha=10 maximizes heat transfer for Ra=105. The exponential thermal boundary conditions have a certain importance on heat transfer. The present results provide necessary information for further investigation of heat transfer in its different applications

Rotational effect of a cylinder on hydro-thermal characteristics in a partially heated square enclosure using CNT-water nanofluid

Rotating cylinder movement in a cavity flow is an exciting field of study in heat transfer. Considerable research has been carried out on rotating cylinders under MHD mixed convection in various types of enclosures. However, considering partially heated square enclosure and magnetic field using CNT-water nanofluid is very limited. This study's goal is to assess the hydrothermal phenomena in a square enclosure with a rotating cylinder. Simulation has been conducted for different rotational speeds (Ω) and dimensionless times (τ) to observe the thermal and fluid flow behaviour. The Galerkin Residual based finite element method has been used to conduct numerical calculations. The results are shown as isotherms, streamlines, and average Nusselt number at the cylinder wall. Moreover, the drag force at the moving wall, and the fluid properties such as the root mean square (rms) of velocity, the temperature, the vorticity functions, and the average fluid temperature are also presented. The heat transfer rate, drag force, rms velocity, and temperature increase with the rise of rotational speed and dimensionless time rise. Maximum vorticity occurs at Ω = 8 and τ = 1. The maximum vorticity function increases 12 times with the increasing rotational speed. Higher rotational speed leads to increased average fluid temperature. The case of Ω = 8, τ = 1 shows the most temperature variance, while Ω = 1, τ = 0.1 has the least. Increasing rotational speed results in higher drag force on the cylinder's surface. At Ω = 4, the drag force is 2.8 times greater than at Ω = 2. Overall, the fluid flow and thermal performance boost up while the rotating speed of the cylinder is higher