Convection Phenomena in Fluids Heated from Below

Numerical simulation of free convection of nanofluid in a square cavity with an inside heater

PurposeThe purpose of this paper is to examine numerically the three natural convection of air induced by temperature difference between a cold outer cubic enclosure and a hot inner cylinder. Simulations have been carried out for Rayleigh numbers ranging from 103 to 107 and titled angle of the enclosure from 0° to 90°. The developed mathematical model is governed by the coupled equations of continuity, momentum and energy, and is solved by finite volume method. The effects of cylinder inclination and Rayleigh number on fluid flow and heat transfer are presented. The distribution of isocontours of temperature and isosurfaces of velocity eventually reaches a steady state in the range of Rayleigh numbers between 103 and 107 for titled inclination of 90°; however, for the remaining inclinations, Rayleigh number must be in the range 103-106 to avoid unsteady state, which is manifested by the division of the area containing the maximum local heat transfer rate into three parts for a Rayleigh number equal to 107 and an inclination of 90°. We mention that instability study is not included in the present paper, which is solely devoted to three-dimensional calculations. Results also indicate that optimal average heat transfer rate is obtained for both high Rayleigh number of 106 and high inclination of 90° for the two cases of the inner cylinder and cubical enclosure.Design/methodology/approachThe manuscript deals with prediction of the three-dimensional natural convection phenomena in a cubical cavity induced by an isothermal cylinder at the center with different inclinations by simulating the flow using highly numerical methods such as finite volume method.FindingsIt is found that the local Nusselt number through active walls for titled inclination set at 90°, the symmetry of the flow is conserved and the area containing the maximum heat transfer is divided into three smaller areas situated near the upper portion of the wall, taking the maximum value. That may be due to the preparation of local occurrence of instabilities and bifurcation phenomena that appear for Ra > 107, which is not included in the present paper to save journal space. It was found also that an optimal heat transfer appears when the cylinder orientation becomes vertical (a = 90°). For this inclination, buoyancy forces act upward, corresponding to an aiding situation. In addition, heat transfer rate is increasing with Rayleigh numbers, so correlations of average Nusselt through the cubical cavity and the cylinder are established as function of two parameters (Ra, a). Comparisons of the numerical results with those obtained from all correlations show good agreements.Originality/valueTo the author’s knowledge, studies have thus far adressed three-dimensional cuboids enclosures induced by an inner shape which the location is changed. However, no study has examined three-dimensional natural convection between the inner isothermal cylinder and outer cooled cubical enclosure when the outer enclosure is tilted.

The present research aims to improve the convective thermal transport rate of a hybrid nanofluid within an inverted T‐shaped porous enclosure using strategically placed cold circular cylinders. Different locations of circular cylinders in the physical domain are distinguished with nomenclatures as Cases C0‐C4. The mathematical model, based on the Darcy–Brinkman–Forchheimer equation, is numerically simulated through the penalty finite element method. Fluid flow and heat transfer characteristics are depicted graphically, showcasing streamlines, isotherms, mean Nusselt number (), and heat transfer enhancement percentage (En%) across varied thermo‐physical parameters, including Rayleigh number (), Darcy number (), and porosity values (). Notably, the presence of two circular cylinders at the bottom flow zones (Case C4) demonstrates superior heat transfer compared to other spatial cylinder arrangements with increasing . Furthermore, augmenting flow parameters () in the case C4 model intensifies convective heat and fluid flow phenomena. A comparative analysis of thermal transport activity between Case C4 and the simple physical domain (Case C0) reveals maximum thermal enhancement of 166%, 167%, and 36% across varying , , and values. This comprehensive analysis suggests that two circular cylinders (Case C4) at the bottom flow section of the porous enclosure provide an effective strategy for enhancing convective fluid and thermal transport phenomena in an inverted T‐shaped porous enclosure. Moreover, this research significantly contributes in optimizing the thermal transport engineering of T‐shaped applications like solar collectors, exchangers, and heat storage.

Simulations of compressibility effects in centrifugal buoyancy-induced flow in a closed rotating cavity

Mixed convection in a two-sided elastic walled and SiO2 nanofluid filled cavity with internal heat generation: Effects of inner rotating cylinder and nanoparticle's shape

view Abstract Citations (38) References (12) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The large-scale structure of compressible convection Depassier, M. C. ; Spiegel, E. A. Abstract We study convection of small but finite amplitude in plane-parallel layer of perfect gas. The conductivity is assumed constant, hence the static state is polytropic. The heat flux on the boundaries is held fixed. When the polytropic index is not too large, the critical horizontal wave number for the onset of convection is zero and there is finite-amplitude instability. The finite-amplitude instability persists into the thin-layer limit provided that there are no geometrical limits to the horizontal scale of the convection. This result contradicts conclusions drawn from the strict Boussinesq approximation and it suggests that results based on that approximation are not generic for convection with flux prescribed on the boundaries. For all the Rayleigh numbers and layer thicknesses accessible to our amplitude expansions, convection with very large horizontal extent is expected to be prevalent at significant amplitudes. We suggest ways in which the nonlinear solutions found here may be useful in the interpretation of large-scale solar convection. Publication: The Astronomical Journal Pub Date: March 1981 DOI: 10.1086/112908 Bibcode: 1981AJ.....86..496D Keywords: Compressible Flow; Convective Flow; Convective Heat Transfer; Ideal Gas; Polytropic Processes; Solar Atmosphere; Boundary Layers; Boussinesq Approximation; Finite Element Method; Rayleigh Number; Stellar Evolution; Thermal Conductivity; Thermodynamic Properties; Two Dimensional Flow; Velocity Distribution; Fluid Mechanics and Heat Transfer full text sources ADS |

Natural convection in square enclosure induced by inner circular cylinder with time-periodic pulsating temperature

Development of free thermal convection of fluids in permeable rock domain with two parallel vertical faults is considered. Permeability of the faults is much higher than in the enclosing rocks. Upper and lower boundaries of the rock domain are horizontal. The lower boundary of the domain is impermeable. The upper boundary is open. Temperatures at these boundaries are fixed, and the temperature at the lower boundary is higher than the upper one. Three-dimensional model is considered. The conditions for thermal convection onset were obtained by linear stability analysis. The boundary condition for the convection onset is defined as existence of a steady-state solution of the governing equations for the fluid flow and heat transfer with nonzero convection velocities. This takes place when Rayleigh number exceeds certain critical value. These critical Rayleigh numbers are determined for different values of permeability contrast between the faults and the enclosing rocks and different distances between the faults. It is shown that thermal convection in the considered system can develop at Rayleigh numbers which are lower than the critical value for homogeneous rocks. Influence of Rayleigh number on convection cell pattern is analyzed. The role of the thermal convection in the considered systems in formation of ore deposits is examined.

Natural convection of Cu–water nanofluid in a cavity with partially active side walls

The significant research has seen with nano fluid flow and heat transfer. But still there is a wide scope of research in mass transfer with nano fluids due to Brownian motion of particles. A theoretical investigation has attempted in this paper to study the chemical reaction effects during mass transfer. We have studied convective heat and mass transfer of MHD nano fluid flow past inclined, oscillating permeable flat plate with radiation and Abstract: The significant research has seen with nano fluid flow and heat transfer. But still there is a wide scope of research in mass transfer with nano fluids due to Brownian motion of particles. A theoretical investigation has attempted in this paper to study the chemical reaction effects during mass transfer. We have studied convective heat and mass transfer of MHD nano fluid flow past inclined, oscillating permeable flat plate with radiation and Abstract: The significant research has seen with nano fluid flow and heat transfer. But still there is a wide scope of research in mass transfer with nano fluids due to Brownian motion of particles. A theoretical investigation has attempted in this paper to study the chemical reaction effects during mass transfer. We have studied convective heat and mass transfer of MHD nano fluid flow past inclined, oscillating permeable flat plate with radiation and

Entropy generation minimization has significant importance in fluid flow, heat and mass transfer in an enclosure to get the maximum efficiency of a system and to reduce the loss of energy. In the present study, the analysis of mixed convection fluid flow, heat and mass transfer with heat line and mass line concept and entropy generation due to the effects of fluid flow, heat flow, mass flow and magnetic field in a trapezoidal enclosure with linearly heated and diffusive left wall, uniformly heated and diffusive lower wall, cold and nondiffusive right wall, adiabatic and zero diffusion gradient top wall have been reported. Parametric studies for the wide range of Prandtl number (Pr = 0.7 for air cooling system and Pr = 1000 for the engines filled with olive or engine oils), Rayleigh number (Ra = 103–105), aspect ratio (A = 0.5–1.5) and inclination angle of the cavity (ϕ = 45°–90°) have been performed, which help to construct the perfect shape of cavity in many engineering and physical applications so that the entropy is minimum to get the maximum efficiency of any system. The finite-difference approximation has been used to find out the numerical solutions. Biconjugate Gradient Stabilized (BiCGStab) method is used to solve the discretized nonhomogeneous system of linear equations.

Optical techniques for fluid flow and heat transfer

In this study natural convection heat transfer in a cold outer circular enclosure containing a hot inner sinusoidal circular cylinder is investigated numerically using the Control Volume based Finite Element Method (CVFEM). The fluid in the enclosure is Cu-water nanofluid. Both circular enclosure and inner cylinder are maintained at constant temperature. The governing equations of fluid motion and heat transfer in their vorticity stream function form are used to simulate the fluid flow and heat transfer. The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell–Garnetts (MG) and Brinkman models, respectively. The calculations were performed for different governing parameters such as the Rayleigh number, values of the number of undulations of the inner cylinder and nanoparticle volume fraction. The results show that for all Rayleigh number, increasing number of undulations causes the average Nusselt number to augment except that the average Nusselt number for N = 4 is greater than N = 5.

Fluid flow and heat transfer in a nanochannel may depart from the traditional behavior due to the scale effect, and the velocity slip and temperature jump at the fluid-solid interface must be taken into account. A lot of papers about fluid flows in nanochannels with the same wettability at two surfaces have been published. It is necessary to investigate fluid flow and heat transfer in nanochannels with the asymmetric wettability by the molecular dynamics method. The fluid velocity and temperature distributions, interfacial velocity slip and temperature jump in a rough nanochannel are evaluated. The effects of asymmetric wettability on the velocity slip, temperature jump and internal fluid heat transfer are analyzed. The results indicate that the velocity of the fluid flow under an external force in a nanochannel in a bulk region is of a parabolic distribution, but the parabolic distribution is not centrosymmetric because of the centrosymmetric density profile. The difference in density distribution can affect the fluid flow. Viscous dissipation due to shear flow will increase the fluid temperature. The range that is affected by the interaction between solid and liquid is small. So the wettability of the cold wall hardly affects the velocity of the fluid near the hot wall, and the slip velocity is almost constant. At this time, the negative slip will take place at the fluid-solid interface near the hot wall. But the velocity of the fluid near the cold wall comes up with the increasing hydrophobicity of the cold wall, and the slip velocity increases. The temperature jump on both sides of interface increases with the increasing hydrophobicity of the cold wall, but the degree of temperature jump at a liquid-cold solid interface is higher than that at a liquid-hot solid interface. Then the fluid temperature near the cold wall gradually exceeds the fluid temperature near the hot wall. The internal heat flow of the fluid will be reversed. The inverted temperature profile of the fluid will appear. The inverted temperature profile becomes more obvious when the degree of asymmetric wettability increases.

Purpose The purpose of this paper is to develop a combined method for three-dimensional incompressible flow and heat transfer by the spectral collocation method (SCM) and the artificial compressibility method (ACM), and further to study the performance of the combined method SCM-ACM for three-dimensional incompressible flow and heat transfer. Design/methodology/approach The partial differentials in space are discretized by the SCM with Chebyshev polynomial and Chebyshev–Gauss–Lobbatto collocation points. The unsteady artificial compressibility equations are solved to obtain the steady results by the ACM. Three-dimensional exact solutions with trigonometric function form and exponential function form are constructed to test the accuracy of the combined method. Findings The SCM-ACM is developed successfully for three-dimensional incompressible flow and heat transfer with high accuracy that the minimum value of variance can reach. The accuracy increases exponentially along with time marching steps. The accuracy is also improved exponentially with the increasing of nodes before stable accuracy is achieved, while it keeps stably with the increasing of the time step. The central processing unit time increases exponentially with the increasing of nodes and decreasing of the time step. Research limitations/implications It is difficult for the implementation of the implicit scheme by the developed SCM-ACM. The SCM-ACM can be used for solving unsteady impressible fluid flow and heat transfer. Practical implications The SCM-ACM is applied for two classic cases of lid-driven cavity flow and natural convection in cubic cavities. The present results show good agreement with the published results with much fewer nodes. Originality/value The combined method SCM-ACM is developed, firstly, for solving three-dimensional incompressible fluid flow and heat transfer by the SCM and ACM. The performance of SCM-ACM is investigated. This combined method provides a new choice for solving three-dimensional fluid flow and heat transfer with high accuracy.