Natural convection of non-Newtonian power-law fluid in a square cavity with a heat-generating element (original) (raw)
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Mathematics, 2022
Flow of a liquid in an enclosure with heat transfer has drawn special focus of researchers due to the abundant thermal engineering applications. So, the aim of present communication is to explore thermal characteristics of natural convective power-law liquid flow in a square enclosure rooted with a T-shaped fin. The formulation of the problem is executed in the form of partial differential expressions by incorporating the rheological relation of the power-law fluid. The lower wall of the enclosure along with the fin is uniformly heated and vertical walls are prescribed with cold temperature. For effective heat transfer within the cavity the upper boundary is considered thermally insulated. A finite element based commercial software known as COMSOL is used for simulations and discretization of differential equations and is executed incorporating a weak formulation. Domain discretization is performed by dividing it into triangular and rectangular elements at different refinement level...
Heat Transfer of Non-Newtonian Dilatant Power Law Fluids in Square and Rectangular Cavities
Journal of Applied Fluid Mechanics 4(3):37-42, 2011
ABSTRACT: Steady two-dimensional natural convection in fluid filled cavities is numerically investigated for the case of non- Newtonian shear thickening power law liquids. The conservation equations of mass, momentum and energy under the assumption of a Newtonian Boussinesq fluid have been solved using the finite volume method for Newtonian and non-Newtonian fluids. The computations were performed for a Rayleigh number, based on cavity height, of 10(exponent 5) and a Prandtl number of 100. In all of the numerical experiments, the channel is heated from below and cooled from the top with insulated side-walls and the inclination angle is varied. The simulations have been carried out for aspect ratios of 1 and 4. Comparison between the Newtonian and the non-Newtonian cases is conducted based on the dependence of the average Nusselt number on angle of inclination. It is shown that despite significant variation in heat transfer rate both Newtonian and non-Newtonian fluids exhibit similar behavior with the transition from multi-cell flow structure to a single-cell regime.
Energies
Placement of fins in enclosures has promising utilization in advanced technological processes due to their role as heat reducing/generating elements such as in conventional furnaces, economizers, gas turbines, heat exchangers, superconductive heaters and so forth. The advancement in technologies in power engineering and microelectronics requires the development of effective cooling systems. This evolution involves the utilization of fins of significantly variable geometries enclosed in cavities to increase the heat elimination from heat-generating mechanisms. Since fins are considered to play an effective role in the escalation of heat transmission, the current study is conducted to examine the transfer of heat in cavities embedding fins, as well as the effect of a range of several parameters upon the transmission of energy. The following research is supplemented with the interpretation of the thermo-physical aspects of a power-law liquid enclosed in a trapezoidal cavity embedding a...
2019
The study of heat transfer by natural convection in a square cavity saturated by a fluid is considered. The two vertical walls are heated and cooled and the other two walls are considered adiabatic. A numerical study of this phenomenon was conducted, by solving the complete system of governing equations by a fluent computer code and using the Boussinesq approximation. In order to verify the validity of our results, a numerical confirmation with references is thus obtained. The variation of the dynamic and thermo-convective structures of an airflow was analyzed for an aspect ratio configuration equal to one and for different number of Rayleigh and temperature gradients. The study also confirmed the proportionality of mean Nusselt number and mean heat flux with temperature gradient and Rayleigh number.
Natural convection of power law fluids in inclined cavities
International Journal of Thermal Sciences, 2012
Steady two-dimensional natural convection in rectangular two-dimensional cavities filled with non-Newtonian power law-Boussinesq fluids is numerically investigated. The conservation equations of mass, momentum and energy are solved using the finite volume method for varying inclination angles between 0 and 90 and two cavity height based Rayleigh numbers, Ra ¼ 10 4 and 10 5 , a Prandtl number of Pr ¼ 10 2 and three cavity aspect ratios of 1, 4 and 8. For the vertical inclination of 90 , computations were performed for two Rayleigh numbers Ra ¼ 10 4 and 10 5 and three Prandtl numbers of Pr ¼ 10 2 , 10 3 and 10 4 . In all of the numerical experiments, the channel is heated from below and cooled from the top with insulated side walls and the inclination angle is varied. A comprehensive comparison between the Newtonian and the non-Newtonian cases is presented based on the dependence of the average Nusselt number Nu on the angle of inclination together with the Rayleigh number, Prandtl number, power law index n and aspect ratio dependent flow configurations which undergo several exchange of stability as the angle of inclination ɸ is gradually increased from the horizontal resulting in a rather sudden drop in the heat transfer rate triggered by the last loss of stability and transition to a single cell configuration. A correlation relating Nu to the power law index n for vertically heated cavities for the range 10 4 Ra 10 5 and 10 2 Pr 10 4 and valid for aspect ratios 4 AR 8 is given.
Journal of Heat Transfer, 1992
The phenomenon of natural convection in a square cavity filled with a copper-water nanofluid is investigated numerically. The studied domain is a square cavity with hot and cold isothermal walls at x = 0 and x = L, respectively, while the other walls are adiabatic. The fins are considered perfectly conductive with different lengths (L f) and positioned at different locations. We examined the situation for Rayleigh numbers ranging between 10 4 and 10 6. The governing equations are expressed in the vorticity, stream function, and temperature formulation. The system of equations was solved by the finite difference method, using the upwind scheme. The computation code thus developed was used to analyze the effect of the different locations of the fins on the thermal performances. The obtained results were validated by comparing with those of a previously published work and with those obtained using COMSOL Multiphysics. It has been found that adding fins on the cold and adiabatic walls results in an increase in the average Nusselt number, while it decreases when the fin is located on the hot wall. That is to say, placing the fins on the cold and adiabatic walls increases the thermal performances of the transfer.
Natural convection in a cubical cavity filled with a fluid showing temperature-dependent viscosity
International Journal of Thermal Sciences, 2015
We present a numerical and experimental study of laminar natural convection flow in a fluid filled cubical cavity. The fluid is a dielectric oil used for cooling distribution and power transformers. As most liquids, this oil exhibits temperature-dependent viscosity. The cubical cavity of interest has an imposed temperature difference between two opposite vertical walls while the other walls are insulated. The cavity dimensions are 0.1 m  0.1 m  0.1 m. Four characteristic Rayleigh numbers ranging from 1.7  10 8 to 6.3  10 8 were analyzed. The numerical study was carried out by applying the Finite Element Method to solve the 3D NaviereStokes and heat equations using the in-house developed Par-GPFEP code. The influence of temperature-dependent viscosity on the total transferred heat and on the flow pattern, have been evaluated. Although there are several studies regarding the flow in a square cavity in this configuration, there is limited information in the literature on the 3D flow in cubical cavities with variable properties of the working fluid. We could not find in the open literature experimental measurements that we could use to validate our numerical results. For this reason an experimental setup was developed. The velocity field was visualized and measured by Particle Image Velocimetry (PIV). The temperature profiles in the vertical mid-axis at mid-plane of the cavity were measured and compared with the numerical results. We found reasonable agreement between numerical simulations and experimental measurements.
Laminar free and forced convection cooling of a semi permeable open cavity
Scientific research and essays
Heat transfer inside a semi porous two-dimensional rectangular open cavity was numerically investigated. The open cavity comprises two vertical walls closed to the bottom by an adiabatic horizontal wall. One vertical wall is a porous and an inflow of fluid occurs normal to it. The other wall transfers a uniform heat flux to the cavity. It shows how natural convection effects may enhance the forced convection inside the open cavity. The main motivation for the work is its application for electronic equipment where frequently the devices used for the electronic equipment cooling are based on natural and forced convection. Governing equations are expressed in Cartesian coordinates and numerically handled by a finite volume method. Results are presented for both local and average Nusselt numbers at the heated wall and for the isotherms and streamlines of the fluid flowing inside the open cavity as a function of Reynolds number ranging from 1 to 100, Grashof number ranging from 0 to 10+7...
IJERT-Numerical Investigation of Natural Convection Heat Transfer in a Square Cavity
International Journal of Engineering Research and Technology (IJERT), 2015
https://www.ijert.org/numerical-investigation-of-natural-convection-heat-transfer-in-a-square-cavity https://www.ijert.org/research/numerical-investigation-of-natural-convection-heat-transfer-in-a-square-cavity-IJERTV4IS070206.pdf Natural convection heat transfer in enclosures find many applications such as heating and cooling of building spaces, solar energy utilization, thermal energy storage, cooling of electrical and electronic components etc. In the present study, Numerical Investigation is conducted in a square cavity with one vertical wall maintained at a high temperature and with the opposing vertical wall at a low temperature. The influence of Grashof numbers ranging from 20000 to 200000 for Prandtl number 0.7 (air) is studied. The governing vorticity and energy equations are solved by finite difference methods including Alternating Direction Implicit (ADI) and Successive Over Relaxation (SOR) techniques with C coding. Steady state isothermal lines and streamlines are obtained for all the Grashof numbers considered. In addition, the average Nusselt number, over the hot wall for the range of Grashof numbers is calculated. The contours of streamlines and isothermal lines are presented for all the parameters investigated. Changes in the streamline and isothermal line patterns are observed with the change in Grashof numbers. The results obtained in this study are useful for the design of devices with enclosures subjected to high temperature differences.