Effects of Natural Convection from an Open Square Cavity Containing a Heated Circular Cylinder (original) (raw)
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2020
In the current study, the effect of an inner heated circular cylinder placed inside a cooled square enclosure on the heat transfer and fluid flow is numerically studied. The main parameters that were investigated are the position of the inner cylinder which was varied both in the vertical and diagonal directions from -0.2 to +0.2 and the aspect ratio which was from 0.05 to 0.25. The Rayleigh number and the Prandtl number were kept constant at 10 and 0.7, respectively. However, for the comparison study, three Prandtl numbers were examined 10, 10, and 10. The numerical study is conducted using (FORTRAN 90) code which is built to perform the calculations for the Navier-Stokes equation of the stream-vorticity expression using finite-difference approach that relates with the non-orthogonal body-fitted coordinate system. The results revealed that the highest local Nu number was achieved at the top surface of the cylinder when the cylinder is moved both in the vertical and diagonal directi...
2011
BUET for their wise and liberal cooperation in providing me all necessary help from the department during my course of M.Phil. Degree. I would also like to extend my thanks to Prof. Dr. Md. Monirul Alam Sarker and all other teachers and concerned of this department for their thoroughly help and cooperation. Finally I express my devoted affection to my wife Mrs. Tahmina Haque and all my family members and relatives specially my parents for creating a delightful atmosphere as well as excusing me from family duties in order to complete the courses, research studies and final production of the thesis work. vii
Mixed Convection in a Vented Square Cavity with a Heat Conducting Horizontal Solid Circular Cylinder
A finite element method based computational study of steady laminar mixed convection flow inside a vented square cavity with a heat conducting horizontal solid circular cylinder placed at the center of the cavity is carried out in this paper. The developed mathematical model is governed by the coupled equations of continuity, momentum and energy. The present work simulates practical systems such as cooling of electronic devices, ventilation of building etc. The effects of cylinder size and Richardson number on fluid flow and heat transfer performance are investigated. Richardson number is varied from 0.0 to 5.0 and the cylinder diameter is varied from 0.0 to 0.6. The results for the case of without cylinder are compared to those with cylinder to observe the effects cylinder on the flow and heat transfer inside the cavity. The phenomenon inside the cavity for the case of with and without cylinder is analyzed through streamline and isotherm patterns. It is found that the streamlines, isotherms, average Nusselt number at the heated surface, average temperature of the fluid in the cavity and dimensionless temperature at the cylinder center strongly depend on the Richardson number as well as the diameter of the cylinder.
Mathematical and Computational Applications
The present research was developed to find out the effect of heated cylinder configurations in accordance with the magnetic field on the natural convective flow within a square cavity. In the cavity, four types of configurations—left bottom heated cylinder (LBC), right bottom heated cylinder (RBC), left top heated cylinder (LTC) and right top heated cylinder (RTC)—were considered in the investigation. The current mathematical problem was formulated using the non-linear governing equations and then solved by engaging the process of Galerkin weighted residuals based on the finite element scheme (FES). The investigation of the present problem was conducted using numerous parameters: the Rayleigh number (Ra = 103–105), the Hartmann number (Ha = 0–200) at Pr = 0.71 on the flow field, thermal pattern and the variation of heat inside the enclosure. The clarifications of the numerical result were exhibited in the form of streamlines, isotherms, velocity profiles and temperature profiles, lo...
2008
A numerical simulation of two-dimensional laminar steady-state natural convection in a rectangular open cavity has been investigated. An adiabatic circular cylinder is placed at the center of the cavity and the opposite wall to the aperture is heated by a constant heal flux. 'fhe top and bOllomwall> are kept at the constant temperature, The fluid is concerned wilh Prnndtl numbers 0.72, 1.0 and 7.0. The properties of the fluid were assumed to be constant"] he physical problems are rcprcscmcd mathematically by different ,els of goveming equations along with the corresponding boundary conditions. In this the,i" a finite element method for sleady-sMe il1C<Jmpres<iblenatural convection tlows has been developed. The non-dimensional governing equatio", are discreti7ed by using Ga1crkin weighted residual method of finite element formulatiol1. The obtained results are presented in terms of streamline~ and isotherm" heat transfer characteristics Nusseit number...
American Journal of Computational Mathematics, 2015
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.
Mixed Convection in a Square Cavity with a Heat- Conducting Horizontal Square Cylinder
The problem of mixed convection heat transfer in a square cavity with a centered heat conducting horizontal square solid cylinder is analyzed in this paper. As boundary conditions of the cavity, the right vertical wall is kept at constant temperature and the remaining three walls are kept thermally insulated. An external flow enters the cavity through an opening in the left vertical wall and exits from another opening in the right vertical wall. This configuration leads to a conjugate heat transfer problem and simulates the cooling of electronic equipments. Emphasis is placed on the influences of the governing parameters, such as Reynolds number, Richardson number, Prandtl number and the inlet and exit port locations of the cavity. The coupled equations of the simulated model are solved numerically using finite element method. Finally, parametric results are presented in terms of streamlines, isotherms, average Nusselt number at the heated wall, average temperature of the fluid and the temperature at the cylinder center in the cavity. The computational results indicate that both the flow and thermal filed in the cavity strongly depend on the governing parameters and the position of the inlet and outlet port.
International Journal of Heat and Mass Transfer, 2013
A numerical study to investigate the steady laminar natural convection flow in a square cavity with uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls has been performed. A penalty finite element method with bi-quadratic rectangular elements has been used to solve the governing mass, momentum and energy equations. The numerical procedure adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number Ra, 10 3 6 Ra 6 10 5 and Prandtl number Pr, 0.7 6 Pr 6 10) with respect to continuous and discontinuous Dirichlet boundary conditions. Non-uniform heating of the bottom wall produces greater heat transfer rates at the center of the bottom wall than the uniform heating case for all Rayleigh numbers; however, average Nusselt numbers show overall lower heat transfer rates for the non-uniform heating case. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominated regimes, power law correlations between average Nusselt number and Rayleigh numbers are presented.
Journal of Mechanical …, 2009
Numerical simulations are carried out for mixed convection flow in a vented cavity with a heat conducting horizontal square cylinder. A two-dimensional solution for steady laminar mixed convection flow is obtained by using the finite element scheme based on the Galerkin method of weighted residuals for different Richardson numbers varying over the range of 0.0 to 5.0. The study goes further to investigate the effect of the inner cylinder position on the fluid flow and heat transfer in the cavity. The location of the inner cylinder is changed horizontally and vertically along the centerline of the cavity. The effects of both Richardson numbers and cylinder locations on the streamlines, isotherms, average rate of heat transfer from the hot wall, the average temperature of the fluid inside the cavity and the temperature at the cylinder center inside the cavity are investigated. The results indicate that the flow field and temperature distributions inside the cavity are strongly dependent on the Richardson numbers and the position of the inner cylinder.
Effect of Diameter Ratio of Adiabatic Cylinder on Natural Convection from a Square Open Cavity
2011
A numerical analysis is carried out to study the performance of natural convection inside a square open cavity. An adiabatic circular cylinder is placed at the center of the cavity and the sidewall in front of the breathing space is heated by a constant heat flux. The top and bottom walls are kept at the ambient constant temperature. Two-dimensional forms of Navier-Stokes equations along with the energy equations are solved using Galerkin finite element method. Results are obtained for a range of Grashof number from 10 3 to 10 6 at Pr = 0.71 with constant physical properties. 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. The computational results indicate that the heat transfer coefficient is strongly affected by Grashof number. An empirical correlation is developed by using Nusselt number and Grashof number.