Numerical study on MHD mixed convection in a lid driven cavity with a wavy top wall and rectangular heaters at the bottom (original) (raw)
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Effect of Internal Heat Generation or Absorption on MHD Mixed Convection Flow in a Lid Driven Cavity
American Journal of Applied Mathematics, 2015
In the present study the problem of mixed convection flow in the presence of magnetic field in a lid-driven square cavity with internal heat generation or absorption and uniform heating of bottom wall were investigated numerically. The square cavity vertical walls are maintained at cold temperature while the upper wall is insulated. The physical problem is then expressed mathematically by a set of governing equations and the developed mathematical model is solved by employing Galerkin weighted residual method of finite element formulation. Effects of variations of Richardson number, Hartmann number and heat generation or absorption parameter on flow structure and heat transfer rate (Nuesselt number) were studied in details. The significant reduction in the average Nusselt number were produced as the strength of the applied magnetic field was increased. In addition, heat generation predicted to decrease the average Nusselt number whereas heat absorption increases it.
A Numerical Simulation on MHD Mixed Convection in a Lid-driven Cavity with Corner Heaters
Journal of Applied Fluid Mechanics
A numerical investigation on mixed convection in a lid-driven square cavity has been performed in the presence of the uniform magnetic field. From the left-bottom corner of the cavity, three different lengths of heater are varied along bottom and left walls simultaneously. The finite volume method is employed to solve the governing equations. It is observed that the heater length in the x-direction is more effective than that of in the y-direction on the heat transfer and on the flow pattern. The magnetic field affects the average heat transfer rate more on vertical heaters than on the horizontal heaters.
International Journal of Mechanical and Materials Engineering, 2010
The fluid flows and heat transfer induced by the combined effects of mechanically driven lid and buoyancy force within a rectangular cavity is investigated in this paper numerically. The horizontal walls of the enclosure are insulted while the right vertical wall is maintained at a uniform temperature higher than the left vertical wall. In addition, it contains a heat conducting horizontal circular block in its centre. The governing equations for the problem are first transformed into a non-dimensional form and the resulting nonlinear system of partial differential equations are solved by using the finite element formulation based on the Galerkin method of weighted residuals. The analysis is conducted by observing the variations of streamlines and isotherms for different Reynolds number and Prandtl number ranging from 50 to 200 and from 0.071 to 3.0 respectively. The results indicated that both the streamlines and isotherms strongly depend on the Reynolds number and Prandtl number. Moreover, the results of this investigation are also illustrated by the variations of average Nusselt number on the heated surface and average fluid temperature in the enclosure.
MHD Mixed Convection in Two-Sided Lid Driven Open Cavity Including Partition Heat Sources
The effect of magnetic field on mixed convection is numerically investigated in a two sided lid driven open cavity including partition heat sources. The heated partition walls are located at the middle of upper half of the cavity. The vertical moving walls are at constant low temperature while the bottom wall is at constant high temperature. The inclined inlet and outlet are placed at top corner. The cool air is injected in the cavity at an angle of 45º. Steady, laminar, two-dimensional model based on the Galerkin weighted residual finite-element method is used for solving the governing equations. The flow and thermal fields (represented by streamline and isotherm contour) are investigated for fixed Reynolds number (Re=100) with varying Richardson number (Ri = 0.1 ~ 10) and Hartmann number (Ha = 10 ~ 50). The quantitative heat transfer is measured by average Nusselt number (Nu) along the heated surfaces. The computational results indicate that the heat transfer coefficient is strongly affected by Richardson number and Hartmann number. It is observed that convection heat transfer increases with Richardson number while Hartmann number retards it.
Effects of moving lid direction on MHD mixed convection in a linearly heated cavity
International Journal of Heat and Mass Transfer, 2012
Effects of moving lid-direction on MHD mixed convection in a cavity with the bottom wall being linearly heated are analyzed using a numerical technique. Vertical walls of the enclosure are adiabatic and the sliding wall at the top has constant temperature. The lid moves in the negative and positive x-direction. Finite volume method has been used to solve the governing equations. Results are presented for different values of Hartmann number (0 6 Ha 6 30), Reynolds number (100 6 Re 6 1000) and Grashof number (10 4 6 Gr 6 10 6). It is found that direction of lid is more effective on heat transfer and fluid flow in the case of mixed convection than it is the case in forced convection. Heat transfer is also decreased with increasing of magnetic field for all studied parameters.
Mixed convection from a uniform and non uniform sinusoidal heat source on the bottom of a rectangular cavity is studied numerically. Two-dimensional forms of non-dimensional Navier-Stokes equations are solved by using control volume based finite volume technique with staggered grid . Three typical values of the Reynolds numbers are chosen as Re = 10, 100, and 2000 and steady, laminar results are obtained in the values of Richardson number as Ri = 0, 1 and 10, 100 and the values of Prandtl numbers is taken as Pr = 0.71, 7 and 10. The parametric studies for a wide range of governing parameters show consistent performance of the present numerical approach to obtain as stream functions and temperature profiles. Heat transfer rates at the heated walls are presented based on the value of Re and Pr. The computational results indicate that the heat transfer is strongly affected by Reynolds number and Richardson number. In the present investigation, bottom wall is(a) uniformly heated & (b) non –uniformly heated while the two vertical walls are maintained at constant cold temperature and the top wall is well insulated. A complete study on the effect of Ri shows that the strength of circulation increases with the increase in the value of Ri irrespective of Re and Pr. As the value of Ri increases, there occurs a transition from conduction to convection dominated flow at Ri =1. A detailed analysis of flow pattern shows that the natural or forced convection is based on both the parameters Ri and Pr.
Mixed Convection Heat Transfer in a Lid Driven Cavity with Wavy Bottom Surface
American Journal of Applied Mathematics, 2013
The present numerical study is devoted to investigate the mixed convection flow and heat transfer in a lid-driven cavity with wavy bottom surface. The cavity upper wall is moving with a uniform velocity by unity and the other walls are no slip. The cavity vertical walls are insulated while the upper surface is maintained at a uniform temperature higher than the wavy bottom surface. The physical problem is represented mathematically by a set of governing equations and the developed mathematical model is solved by employing Galerkin weighted residual method of finite element formulation. The wide ranges of governing parameters, i. e., the Reynolds number (Re), the Grshof number (Gr) and the number of undulations (λ) on the flow structure and heat transfer characteristics are investigated in detail. It is found that these parameters have significant effect on the flow fields; temperature distributions and heat transfer in the cavity. Furthermore, the trend of skin friction and Nusselt number for different values of the aforementioned parameters are presented in this investigation.
2019
Heat transfer phenomenon in a square cavity with a heated rectangular enclosure is performed numerically. Galerkin weighted residual finite element method is used to solve two-dimensional governing mass, momentum and energy equations for steady state, free convection flow in presence of Magnetohydrodynamic (MHD) effect. The observations are handled for different values of Rayleigh number (Ra) and Hartmann number (Ha). Various characteristics of streamlines, isothermal lines, heat transfer rate in terms of the average Nusselt number (Nu av) and average velocity magnitude (V av) are presented for different parameters. The effect of physical parameter (area of the heated rectangular enclosure, A) is also shown here. The results indicate that the flow models and velocity magnitude field are significantly dependent on the above mentioned parameters.
A Numerical Study on MHD Mixed Convection in an inclined Lid Driven Enclosure
2021
In this work, MHD mixed convection flow and heat transfer in an inclined lid driven enclosure with different angles (φ=0 o to 90 o) for two cases has been studied numerically. Simulations are carried out over a range of parameters: Prandtl numbers (Pr=0.7 and 7.2), Hartmann number(0≤Ha≤100), Richardson number (Ri=0.01,1.0,100) and Reynolds number (Re=100). The governing equations are solved by the finite volume method with a SIMPLE algorithm. It has been found that the average Nusselt number decreases with increasing Hartmann number. It is concluded that on increasing the Richardson number, the overall heat transfer is increased. Also, it is found that existence of the magnetic field suppresses the convective heat transfer and fluid flow in enclosure.
Journal of Heat Transfer, 2012
Magnetohydrodynamic (MHD) mixed-convection flow and heat transfer characteristics inside a square double-lid driven enclosure have been investigated in this study. A heat-generating solid square block is positioned at the centre of the enclosure. Both of its vertical walls are lid-driven and have temperature Tc and uniform velocity V0. In addition, the top and bottom surfaces are kept adiabatic. Discretization of governing equations is achieved using finite element technique based on Galerkin weighted residuals. The computation is carried out for a wide range of pertinent parameters such as Hartmann number, heat-generating parameter, and Richardson number. Numerical results are reported for the effects of aforesaid parameters on the streamline and isotherm contours. In addition, the heat transfer rate in terms of the average Nusselt number and temperature of the fluid as well as block center are presented for the mentioned parametric values. The obtained results show that the flow a...