A numerical study of heat transfer problem by natural convection of a fluid inside a square cavity with two inner bodies is presented. This subject is of great interest in the engineering area, mainly in applications ...A numerical study of heat transfer problem by natural convection of a fluid inside a square cavity with two inner bodies is presented. This subject is of great interest in the engineering area, mainly in applications involving development of heat exchangers and cooling or heating systems of bodies by natural convection mechanism. Two cases have been studied. The inner bodies are square in case 1 and circular in case 2. In both cases, the bodies are solid and thermally conductive, the cavity lower and upper horizontal surfaces are isothermal with high temperature Th and low temperature Tc, respectively. Both vertical surfaces are adiabatic. A FORTRAN code using Finite Element Method (FEM) is developed to simulate the problem and solve the governing equations. The distributions of stream function, ψ, dimensionless temperature, θ, and vorticity, ω, are determined. Heat transfer is evaluated by analyzing the behavior of the average Nusselt number. The Grashof number and thermal diffusivity ratio are considered in range from 2 × 104 to 105 and from 0.1 to 100, respectively. The fluid is air with Prandtl number fixed in 0.733.展开更多
The problem of Magnetohydrodynamic (MHD) free convection heat transfer in a square open cavity containing a heated circular cylinder at the centre has been investigated in this work. As boundary conditions of the cavi...The problem of Magnetohydrodynamic (MHD) free convection heat transfer in a square open cavity containing a heated circular cylinder at the centre has been investigated in this work. As boundary conditions of the cavity, the left vertical wall is kept at a constant heat flux, bottom and top walls are kept at different high and low temperature respectively. The remaining side wall is open. Finite element analysis based on Galerkin weighted Residual approach is used to visualize the temperature distribution and fluid flow solving two-dimensional governing mass, momentum and energy equations for steady state, natural convection flow in presence of magnetic field in side an open square cavity. A uniformly heated circular cylinder is located at the centre of the cavity. The object of this study is to describe the effects of MHD on the thermal fields and flow in presence of such heated circular cylinder by visualization of graph. The investigations are conducted for different values of Rayleigh number (Ra) and Hartmann number (Ha). The results show that the temperature field and flow pattern are significantly dependent on the above mentioned parameters.展开更多
This paper presents the effect of magnetic field, indicated by Hartmann number (Ha), on the free convective flow of Magneto-hydro-dynamic (MHD) fluid in a square cavity with a heated cone of different orientation. Alt...This paper presents the effect of magnetic field, indicated by Hartmann number (Ha), on the free convective flow of Magneto-hydro-dynamic (MHD) fluid in a square cavity with a heated cone of different orientation. Although similar studies abound, the novelty of this work lies in the presence of the heated cone, whose orientation is varied at different angles. The mathematical model includes the system of governing mass, momentum and energy equations. The system is solved by finite element method. The calculations are performed for Prandtl number Pr = 0.71;the Rayleigh number Ra = 10, 1000, 100,000;and for Hartmann number Ha = 0, 20, 50, 100. The results are illustrated with streamlines, velocity profiles and isotherms. From the results, it is found that for the present configuration, magnetic field (Hartmann number) has no effect on the shape of the streamlines for low Rayleigh numbers. However, for high values of Ra, the effect of Ha becomes quite visible. Magnetic field affects the flow by retarding the fluid movement, and thus affects convective heat transfer. At low Ra, the fluid movement and heat transfer rate are already slowing, thus impressing a magnetic field does not produce much effect. At high Ra, fluid particles move at high velocity and change the stream lines, in absence of any magnetic force. Impressing magnetic field in this situation produced noticeable effect by slowing down the fluid movement and changing the streamlines back to low Ra situations. It is noted that a combination of low Ra with zero or low Ha produces similar effects with the combination of high Ra and high Ha. It can be concluded that with increasing Ha, heat transfer mode in MHD fluid gradually changes toward conduction from convection. It can be surmised that sufficiently large Ha can potentially stop the fluid movement altogether. In that case, heat transfer would be fully by conduction.展开更多
In this article, flow and heat transfer inside a corrugated cavity is analyzed for natural convection with a heated inner obstacle. Thermal performance is analyzed for Cu O–water inside a partially heated domain by d...In this article, flow and heat transfer inside a corrugated cavity is analyzed for natural convection with a heated inner obstacle. Thermal performance is analyzed for Cu O–water inside a partially heated domain by defining the constraint along the boundaries. For nanofluid analysis, the Koo and Kleinstreuer Li(KKL) model is implemented to deal with the effective thermal conductivity and viscosity. A heated thin rod is placed inside the corrugated cavity and the bottom portion of the corrugated cavity is partially heated. The dimensionless form of nonlinear partial differential equations are obtained through the compatible transformation along with the boundary constraint. The finite element method is executed to acquire the numerical solution of the obtained dimensional system. Streamlines, isotherms and heat transfers are analyzed for the flow field and temperature distribution. The Nusselt number is calculated at the surface of the partially heated domain for various numerical values of emerging parameters by considering the inner obstacle at cold, adiabatic and heated conditions. The computational simulation was performed by introducing various numerical values of emerging parameters. Important and significant results have been attained for temperature and velocities(in both x-and y-directions) at the vertically and horizontally mean positions of the corrugated duct.展开更多
文摘A numerical study of heat transfer problem by natural convection of a fluid inside a square cavity with two inner bodies is presented. This subject is of great interest in the engineering area, mainly in applications involving development of heat exchangers and cooling or heating systems of bodies by natural convection mechanism. Two cases have been studied. The inner bodies are square in case 1 and circular in case 2. In both cases, the bodies are solid and thermally conductive, the cavity lower and upper horizontal surfaces are isothermal with high temperature Th and low temperature Tc, respectively. Both vertical surfaces are adiabatic. A FORTRAN code using Finite Element Method (FEM) is developed to simulate the problem and solve the governing equations. The distributions of stream function, ψ, dimensionless temperature, θ, and vorticity, ω, are determined. Heat transfer is evaluated by analyzing the behavior of the average Nusselt number. The Grashof number and thermal diffusivity ratio are considered in range from 2 × 104 to 105 and from 0.1 to 100, respectively. The fluid is air with Prandtl number fixed in 0.733.
文摘The problem of Magnetohydrodynamic (MHD) free convection heat transfer in a square open cavity containing a heated circular cylinder at the centre has been investigated in this work. As boundary conditions of the cavity, the left vertical wall is kept at a constant heat flux, bottom and top walls are kept at different high and low temperature respectively. The remaining side wall is open. Finite element analysis based on Galerkin weighted Residual approach is used to visualize the temperature distribution and fluid flow solving two-dimensional governing mass, momentum and energy equations for steady state, natural convection flow in presence of magnetic field in side an open square cavity. A uniformly heated circular cylinder is located at the centre of the cavity. The object of this study is to describe the effects of MHD on the thermal fields and flow in presence of such heated circular cylinder by visualization of graph. The investigations are conducted for different values of Rayleigh number (Ra) and Hartmann number (Ha). The results show that the temperature field and flow pattern are significantly dependent on the above mentioned parameters.
文摘This paper presents the effect of magnetic field, indicated by Hartmann number (Ha), on the free convective flow of Magneto-hydro-dynamic (MHD) fluid in a square cavity with a heated cone of different orientation. Although similar studies abound, the novelty of this work lies in the presence of the heated cone, whose orientation is varied at different angles. The mathematical model includes the system of governing mass, momentum and energy equations. The system is solved by finite element method. The calculations are performed for Prandtl number Pr = 0.71;the Rayleigh number Ra = 10, 1000, 100,000;and for Hartmann number Ha = 0, 20, 50, 100. The results are illustrated with streamlines, velocity profiles and isotherms. From the results, it is found that for the present configuration, magnetic field (Hartmann number) has no effect on the shape of the streamlines for low Rayleigh numbers. However, for high values of Ra, the effect of Ha becomes quite visible. Magnetic field affects the flow by retarding the fluid movement, and thus affects convective heat transfer. At low Ra, the fluid movement and heat transfer rate are already slowing, thus impressing a magnetic field does not produce much effect. At high Ra, fluid particles move at high velocity and change the stream lines, in absence of any magnetic force. Impressing magnetic field in this situation produced noticeable effect by slowing down the fluid movement and changing the streamlines back to low Ra situations. It is noted that a combination of low Ra with zero or low Ha produces similar effects with the combination of high Ra and high Ha. It can be concluded that with increasing Ha, heat transfer mode in MHD fluid gradually changes toward conduction from convection. It can be surmised that sufficiently large Ha can potentially stop the fluid movement altogether. In that case, heat transfer would be fully by conduction.
基金The authors gratefully acknowledge the support given by the University of Tabuk,Ministry of Education in Saudi Arabia.
文摘In this article, flow and heat transfer inside a corrugated cavity is analyzed for natural convection with a heated inner obstacle. Thermal performance is analyzed for Cu O–water inside a partially heated domain by defining the constraint along the boundaries. For nanofluid analysis, the Koo and Kleinstreuer Li(KKL) model is implemented to deal with the effective thermal conductivity and viscosity. A heated thin rod is placed inside the corrugated cavity and the bottom portion of the corrugated cavity is partially heated. The dimensionless form of nonlinear partial differential equations are obtained through the compatible transformation along with the boundary constraint. The finite element method is executed to acquire the numerical solution of the obtained dimensional system. Streamlines, isotherms and heat transfers are analyzed for the flow field and temperature distribution. The Nusselt number is calculated at the surface of the partially heated domain for various numerical values of emerging parameters by considering the inner obstacle at cold, adiabatic and heated conditions. The computational simulation was performed by introducing various numerical values of emerging parameters. Important and significant results have been attained for temperature and velocities(in both x-and y-directions) at the vertically and horizontally mean positions of the corrugated duct.
