Dimensional Natural Convection Research Articles

Rayleigh–Bénard convection of carbopol microgels: Are viscoplastic models adequate?

We investigate the adequacy of viscoplastic models in describing the Rayleigh–Bénard convection of yield stress fluids. We conduct numerical simulations of the steady two dimensional natural convection of viscoplastic fluids in a long rectangular cavity to explore how the uncertainties of the rheological properties and the temperature boundary conditions propagate to the uncertainties of steady flow features. A systematic comparison of different nondimensionalization approaches is conducted to motivate our choice of the dimensionless groups. The ratio of the yield stress and buoyancy stress, BY, governs momentum transfer in natural convection flows and measurably improves the collapse of data. We show that the commonly used definitions of modified Rayleigh number can be similarly ineffective in revealing a master curve. For the ideal boundary conditions and BY>0, the motionless state is a steady regime in Rayleigh–Bénard settings irrespective of the value of the other dimensionless groups. The uncertainties in the temperature boundary conditions can eliminate this steady regime. Thus, the observation of flow development in experiments does not necessarily contradict the theoretical predictions based on viscoplastic models. Nevertheless, we show that the experimental estimates of the critical conditions challenge the predicted stabilizing effect of the yield stress: the estimates do not depend on BY in the manner predicted by viscoplastic models.

Heat and Mass Transfer in an Inclined Bi-L-Shaped Layered Porous Media: Effect of Buoyancy Ration

The effect of buoyancy ratio on the two dimensional natural convection heat and mass transfer generated in an inclined square bi-L-shaped layered porous cavity filled with Newtonian fluid has been investigated numerically. Each porous layer is considered isotropic, homogeneous and saturated with the same fluid. The cavity is heated and salted from below where as the vertical walls are assumed to be adiabatic and impermeable. The physical model for the momentum conservation equation makes use of the Darcy-Brinkman-Forcheimer model, and the set of coupled equations is solved using a finite volume approach. The power-law scheme is used to evaluate the flow, heat and mass fluxes across each of the control volume boundaries. Tri diagonal matrix algorithm with under-relaxation is used in conjunction with iterations to solve the nonlinear discretized equations. An in-house code developed for this study is validated using previous studies. The results are presented graphically in terms of streamlines, isotherms and iso-concentrations. In addition, the heat and mass transfer rate in the cavity is measured in terms of the average Nusselt and Sherwood numbers.

A Numerical Study of Three- Dimensional Natural Convection in a Differentially Heated Cubical Enclosure

—A high-resolution, finite difference numerical studyis reported on three-dimensional steady-state natural convectionof air, for two Rayleigh numbers, in a cubical enclosure, which isheated differentially at one side walls. The temperature of thewall is TC except for the right vertical wall, in which is TH.Thedetails of the three-dimensional flow and thermal characteristicsare described.

Numerical analysis of 2-D laminar natural convection heat transfer from solid horizontal cylinders with longitudinal fins

Proper thermal management through an effective cooling mechanism is essential for improving the reliability of operation of various electronic devices. A number of cooling methods are available among which passive cooling by natural convection has been deemed appropriate since it has distinctive advantages over active cooling or forced convection like high reliability, low maintenance cost, energy efficiency and noise-free nature. In the present study, natural convection from solid horizontal cylindrical heat sources of the geometry and dimensions of heat sinks of LED bulbs with external longitudinal plate fins have been modelled. Numerical computations of continuity, momentum and energy equations to solve the two dimensional incompressible natural convection conjugate heat transfer from such cylinders has been studied in the laminar regime (4.5×105<RaD<5.2×105). The diameter of the cylinder is kept at 60 mm whereas the length is kept at 50 mm. The number of fins has been varied from three to 36, the height of fins kept at 10, 20 and 30 mm and thickness at one mm. The effect of fin geometry parameters and Rayleigh number on total heat transfer, heat transfer exclusively from fin surface and from bare cylinder surface, heat transfer per fin and Nusselt number based on cylinder diameter have been studied in detail. Finally, optimum fin spacing for a particular fin height has been evaluated. Contour plots to capture temperature and velocity vectors around the heat source have also been developed. Numerical correlations of Nusselt number as a function of Rayleigh number, non-dimensional fin spacing and non-dimensional fin height reveal that the scaling laws of RaD1∕3 and RaD1∕4 are valid both for the computational data of our present analysis and experimental data even though the experiments are for a slightly different boundary condition.

Three-dimensional numerical study for laminar natural convection within a rectangular solar chimney

A numerical study of three – dimensional, steady, laminar and incompressible natural convection of air (Pr=0.72) within a rectangular solar chimney is presented. Partial differential equations for conservation of mass, momentum and energy equations are solved by finite volume method with staggered grid arrangement. SIMPLE algorithm is applied to solve the set of discretization equations. The numerical results are compared with those of previous published work under the same conditions and gives a good agreement. The influence of changing in chimney dimension (thickness and height) and the inlet air temperature on the amount of induced flow rate is studied. From the presented results the optimal design for the chimney can be achieved

Laminar and turbulent natural convection from a stack of thin hollow horizontal cylinders: A numerical study

Three dimensional natural convection from a stack of thin hollow horizontal cylinders has been investigated numerically in both laminar and turbulent regimes of Rayleigh number (Ra) spanning in the range 104 to 108 and 1010 to 1013, respectively. In the present study, the length to diameter ratio (L/D) of the cylinders is considered in the range 0.5–20. Thin horizontal hollow cylinders of three, six, and ten in numbers are arranged in a triangular manner to form three different types of stacks of same length scale. The full Navier-Stokes equation along with the energy equation are solved to predict the flow pattern and heat loss from the cylinders. The present computational study is able to capture very interesting buoyancy plume structures around the stack of short and long hollow cylinders. The average Nusselt number (Nu) shows a positive dependence on Ra for all L/D. In addition, Nu for a stack of three cylinders is found to be marginally higher than the stack of six cylinders followed by ten cylinders. Empirical correlations are developed for Nu as a function of Ra and L/D, which would be beneficial to academic researchers as well as practicing engineers.

Uncertainty quantification in three dimensional natural convection using polynomial chaos expansion and deep neural networks

This paper analyzes the effects of input uncertainties on the outputs of a three dimensional natural convection problem in a differentially heated cubical enclosure. Two different cases are considered for parameter uncertainty propagation and global sensitivity analysis. In case A, stochastic variation is introduced in the two non-dimensional parameters (Rayleigh and Prandtl numbers) with an assumption that the boundary temperature is uniform. Being a two dimensional stochastic problem, the polynomial chaos expansion (PCE) method is used as a surrogate model. Case B deals with non-uniform stochasticity in the boundary temperature. Instead of the traditional Gaussian process model with the Karhunen-Loève expansion, a novel approach is successfully implemented to model uncertainty in the boundary condition. The boundary is divided into multiple domains and the temperature imposed on each domain is assumed to be an independent and identically distributed (i.i.d) random variable. Deep neural networks are trained with the boundary temperatures as inputs and Nusselt number, internal temperature or velocities as outputs. The number of domains which is essentially the stochastic dimension is 4, 8, 16 or 32. Rigorous training and testing process shows that the neural network is able to approximate the outputs to a reasonable accuracy. For a high stochastic dimension such as 32, it is computationally expensive to fit the PCE. This paper demonstrates a novel way of using the deep neural network as a surrogate modeling method for uncertainty quantification with the number of simulations much fewer than that required for fitting the PCE, thus, saving the computational cost.

Simulation of three dimensional MHD natural convection using double MRT Lattice Boltzmann method

In this study, a three-dimensional mesoscopic simulation of magneto hydrodynamics (MHD) natural convection in a cubic cavity has been studied by new means of the Lattice Boltzmann method with double Multi-Relaxation-Time (MRT) model. In order to solve the momentum and energy equations, two different populations with various lattices have been used. This paper has been conducted for specific values of the Grashof number (Gr=2×103_2×105) and Hartmann number (Ha=0–100), while the Prandtl number is fixed at Pr=0.73. The results are presented in the form of average and local Nusselt number and contours of temperature and velocity at different planes of the cavity. It was found that the double MRT-LBM method is an appropriate approach to solve the studied case. The present results also show that the increase of the Hartmann number causes the heat transfer to drop considerably. Also, the effect of Hartmann number increases by enhancing the Grashof number, as the reduction of average Nusselt number is 12% for Gr=2×103 and 71% for Gr=2×105 when Hartmann number increases from 0 to 100. In contrast with Hartmann number, increasing of Grashof number raises heat transfer rate and the average Nusselt number increases by more than three times by enhancing the Grashof number from 2×103 to 2×105.

Numerical Study of Natural Convective Heat and Mass Transfer in an Inclined Porous Media

In this study, two dimensional natural convection heat and mass transfer generated in an inclined rectangular porous cavity filled with Newtonian fluid has been investigated numerically. The cavity is heated and cooled along horizontal walls while the solutal gradient is imposed horizontally. The physical model for the momentum conservation equation makes use of the Darcy model, and the set of coupled equations is solved using a finite volume approach. The successive-under-relaxation (SUR) method is used in the solution of the stream function equation. The results are presented graphically in terms of streamlines, isotherms and iso-concentrations. The heat and mass transfer rate in the cavity is measured in terms of the average Nusselt and Sherwood numbers for various non-dimensional parameters.

Combined natural convection and thermal radiation in an inclined cubical cavity with a rectangular pins attached to its active wall

Three dimensional combined natural convection and thermal radiation in an inclined cubic enclosure with pins attached to the active wall is investigated numerically. The vertical opposing walls are heated and cooled while the other walls are assumed to be adiabatic. The governing flow, momentum equations and the radiative transfer are solved using Fluent® 6.3 CFD software. In the discretization of the convection terms, the second order upwind scheme and for the solution algorithm SIMPLE is used. The cubic enclosure is filled with air and the flow is considered to be laminar. The properties of air are assumed to be constant except for the density variation for which the Boussinesq approximation is used. The surface to surface (S2S) heat model is used as the radiation transfer model. The computations are performed for Rayleigh number in the range 103≤Ra≤106 and for the surface emissivity (e) 0≤e≤1 while the inclination angle is varied 0°≤φ≤75°. The mean Nusselt number for convection and radiation transfer were evaluated as a function of Rayleigh number, emissivity and inclination angle and for some cases, the fluid flow and the temperature distributions were analyzed. The results showed that the mean total and radiative Nusselt number increases monotonically with increasing Ra number and the surface emissivity.

MHD natural convection of ferrofluid from a fixed vertical plate with aligned, transverse magnetic field and convective boundary condition

The present study analyzed the influence of aligned and transverse magnetic field on two dimensional natural convection boundary layer flow of a ferrofluid over a semi-infinte fixed vertical plate in the presence of convective boundary condition. It is assumed that the left surface of the plate is in contact with a hot fluid while the cold fluid on the right surface. Two different base fluids (water and kerosene) containing magnetite (Fe3O4) as ferroparticle are considered. The governing boundary layer equations along with the appropriate boundary conditions are transformed to a set of ordinary differential equations using similarity variables. The resultant system of equations is then solved numerically by using Keller-Box method. Numerical results for the skin friction coefficient and local Nusselt number were presented whilst the velocity and temperature profiles illustrated graphically and analyzed. The effect of the inclined angle, magnetic field parameter, volume fraction, Grashof number and Biot number on the flow field were discussed. It is found that the heat transfer rate at the plate surface with Fe3O4- kerosene ferrofluid is higher than Fe3O4- water.

3D natural convection in a cubical cavity with a thermally active heater under the presence of an external magnetic field

A numerical study of three dimensional natural convection heat transfer and fluid flow in a cubical cavity induced by a thermally active plate is described under the presence of external magnetic field. The active plate is attached to the center of one vertical wall of the cavity filled with different fluids as mercury, air and dielectric liquid FC-77. It is located at two different positions as vertical or horizontal. The governing equations are solved by using finite volume method. Computations are performed for a wide range of Hartmann number (0 ≤ Ha ≤ 300), Prandtl number (0.025 ≤ Pr ≤ 25) and different aspect ratio of the plate (Ac = 0.5 & 1.0) when the Rayleigh number Ra is fixed to be 107. It is found that the heat transfer rate is strongly suppressed by the X and Y directional magnetic fields and it is weakly suppressed by the Z directional magnetic field.

Numerical investigation of two dimensional natural convection and entropy generation inside a porous square enclosure with sinusoidally heated wall

In this paper, effect of sinusoidal heating on natural convection heat transfer and fluid flow has been studied in two dimensional square cavity saturated with porous medium. The governing equations have been formulated using Darcy-Forchheimer model and Boussinesq approximation. Finite volume method has been used to solve the governing equation. Computations are done for the wide range of Rayleigh number, Ra = 103 − 106 and Darcy number, Da = 105 − 103 considering air (Pr = 0.71) as working fluid. In this analysis, it is observed that in the presence of sinusoidal heating of the bottom wall, transition from conduction to convection mode of heat transfer occurs at 104 ≤ Ra ≤ 105. It is also found that at high Ra and high Da, fluid friction irreversibility dominates the heat transfer irreversibility in the cavity and the maximum entropy generation is found for Da = 103 and Ra = 106 in this parameteric study.

Transient free convection flow past vertical cylinder with constant heat flux and mass transfer

Abstract This paper describes a one dimensional unsteady natural convection flow past an infinite vertical cylinder with heat and mass transfer under the effect of constant heat flux at the surface of the cylinder. Closed form solutions of the dimensionless unsteady linear governing boundary layer equations are obtained in terms of Bessel functions and modified Bessel functions by Laplace transform method. The numerical values of velocity, temperature and concentration profiles are obtained for different values of the physical parameters namely, thermal Grashof number, mass Grashof number, Prandtl number, Schmidt number and time and presented in graphs. Also, skin friction and Sherwood number are shown graphically and discussed. It is observed that the velocity and temperature increase unboundedly with time, while the concentration approaches steady state at larger times.

A New Scheme for the Finite Volume Method Verified with Two Dimensional Laminar Natural Convection in a Square Cavity

A new scheme applied to the finite volume method for solving the partial differential equations of fluid flow is proposed. The Lagrange interpolating polynomial with a setting of zero for the spatial domain at the cell faces, and the present time at the cell center is adopted for the new scheme to estimate the values of the variables at the cell faces, the derivative values of the variables with respect to the spatial domain at the cell faces and the derivative values of the variables with respect to time at the cell center for spatial and temporal discretization of the discretized equation. The new scheme was verified by comparing the solutions of the new scheme to the benchmark numerical solutions and the published numerical solutions of two dimensional laminar natural convection in a square cavity. From the comparison, the results show that the solutions of the new scheme agree well with the benchmark numerical solutions and the published numerical solutions.

Laminar natural convection inside the open, forward-facing stepped rectangular enclosure with a partition and time-variant temperature on the stepped top wall

A finite difference based numerical study of two dimensional laminar natural convection inside the open rectangular forward stepped enclosure with sinusoidal time-variant temperature on the top wall is presented by vorticity–stream function approach. The enclosure is divided by a vertical partition at the middle with a central opening. The aspect ratio of the enclosure is 1.6. The top wall is constructed with a step of 20% of height of the enclosure. Except the top wall, all the outer walls are assumed as hot and maintained at constant temperature. The parameters governing the study are the amplitude (0<a<0.5) and the period (0.001<τ<0.8) of the variable temperature, the Rayleigh number (104<Ra<106), Prandtl number (Pr=0.71), and the step. The effect of the amplitude and period on the heat transfer inside the enclosure is examined for constant temperature (a=0) and varying temperature (a≠0 and τ≠0). The details of fluctuating flow and temperature fields are analyzed and the periodic results are elucidated with streamlines, isotherms and Nusselt number. The result indicates that the heat transfer increases with increasing amplitude and decreases with increasing period of oscillating temperature on the top wall. The heat transfer increases when buoyancy is increased through Rayleigh number. The provision of step increases the heat transfer on the right side of the upper wall due to the increasing buoyancy.

Study of the Transient Natural Convection of a Newtonian Fluid inside an Enclosure Delimited by Portions of Cylinders

Using a bi-cylindrical coordinates system and a vorticity-stream function formulation, the authors study numerically the two dimensional unsteady natural convection of a Newtonian fluid bounded by portions of cylinders. A spatial discretization based on the finite difference method is used to approximate the dimensionless equations. While a purely implicit scheme is adopted for the time discretization. The algebraic systems of equations resulting from the discretization are solved by a Successive under Relaxation (SUR) method. The authors analyzed the effects of the Rayleigh number on the dynamic of the system. The analysis of the thermal and flow field showed that for Rayleigh number greater than 5.106 the transfers inside the enclosure are dominated by convection.

Effects of the Heated Surface on the Unsteady Two Dimensional Natural Convection in Enclosures Bounded by Two Paraboloids of Revolution

Using a paraboloidal coordinates system and a vorticity- stream function formulation, the authors study numerically the two-dimensional unsteady natural convection of a Newtonian fluid confined between two paraboloids of revolution with vertical axes. A certain portion of the opening upward surface is heated up with a constant temperature and the rest remains thermally isolated. The upper surface downwardly open is completely cooled. A spatial discretization based on finite volume method is used to approximate the dimensionless equations. A fully implicit scheme is adopted for time discretization and algebraic systems obtained are solved by a successive under relaxation method. The authors analyzed the effects of the control parameters like the Rayleigh number and the heat factor (ratio between heated surface and total surface of the upwardly open paraboloid) on the dynamic of the system. Local results are presented in the form of streamline and isotherm plots as well as the variation of the average Nusselt number and the friction coefficient on the lower wall. The analysis of these figures showed that for the three values of e, 1/2, 3/4, 1 observed flows are very different

Effects of Natural Convection from an Open Square Cavity Containing a Heated Circular Cylinder

The problem of natural convection heat transfer in a square open cavity containing a heated and conducting circular cylinder at the centre is analyzed in this paper. As boundary conditions of the cavity, the left vertical wall is kept at a constant heat flux, bottom and top wall are kept at different high and low temperature respectively. The remaining side is open. Two dimensional laminar steady state natural convection is considered. This configuration is related in the design of electronic devices, solar energy receivers, uncovered flat plate solar collectors geothermal reservoirs etc. The fluid is concerned with different Prandtl numbers, Grashof numbers and the properties of the fluid are assumed to be constant. The development of Mathematical model is governed by the coupled equations of continuity, momentum and energy and is solved by employing Galerkin weighted finite element method. Flow field and heat transfer were predicted for fluid with Pr = 0.72 , 1.0 ,7.0; Gr = 103, 104, 105 ,106; inclination angles of the cavity are ? = 0°, 15°, 30°, 45° and diameter ratio dr = 0.2.The average Nusselt number increases as the increases of inclination angle of the cavity for lower Pr and lower temperature at bottom wall. The average Nu increases mainly for higher inclinations and for higher Gr. Various vortices and recirculations are formed into the flow field for higher Pr and higher temperature at the bottom wall. DOI: http://dx.doi.org/10.3329/bjsir.v47i1.10718Bangladesh J. Sci. Ind. Res. 47(1), 19-28, 2012

Numerical exploration of 1 + 2 type laminar natural convection in a differentially heated square cavity using Chebyshev spectral collocation method

In this paper, the Chebyshev spectral collocation method is applied to explore the unsteady two dimensional (1+2 type) laminar natural convection in a differentially heated square cavity at a Rayleigh number (Ra) of 107. The method has embedded the traditional Chorin's algorithm so as to avoid the trouble of seeking the pressure field in the buoyancy driven wall-jet flow. The sensitivity of the δ− parameter has been numerically investigated. It is found that when the δ value is over 11.6173, numerical instability occurs. Comparing the maximum horizontal velocity component with the existing numerical data obtained by solving the Poisson's equation of pressure field reveals that the Chorin's algorithm should be inapplicable for the solution of the benchmark problem of natural convection at Ra=107 in thermal science.