Unsteady conjugate thermogravitational convection in a cylindrical region with local energy source

The mathematical modelling of unsteady regimes of natural convection in a closed cylindrical region with a heat-conducting shell of finite thickness was carried out in the presence of a local heat source under the conditions of convective heat exchange with the ambient medium. The mathematical model was constructed in dimensionless variables “stream function — vorticity vector — temperature” in the cylindrical coordinate system. The influence of the Rayleigh number, 10⁴ ≤ Ra ≤ 10⁶, of the unsteadiness factor 0 < τ < 300, of the thermal conductivity ratio λ _2,1 = 5.7·10⁻⁴, 4.3·10⁻², and the energy source sizes on both local characteristics (streamlines and temperature fields) and on the integral complex (the mean Nusselt number on typical boundaries) was analysed in detail. Thermohydrodynamic peculiarities due to the geometry of the object of research were established.     

Surface radiation influence on the regimes of conjugate natural convection in an enclosure with local energy source

A numerical analysis of the unsteady regimes of the natural convection and thermal radiation in a square enclosure with heat-conducting walls has been carried out in the presence of a heat source of finite sizes located in the base zone under the conditions of convective exchange with the ambient medium. The mathematical model formulated in the dimensionless variables “stream function — vorticity — temperature” has been implemented numerically by a finite difference method. The influence of the reduced emissivity of internal surfaces of bounding walls on the local characteristics (the streamlines and temperature fields) and on the integral complex (the mean Nusselt number on typical boundaries) has been analyzed in detail for 0 ≤ ? < 1, the location of the heat source 0.1 ≤ l/L ≤ 0.4, and its length 0.2 ≤ l _hs /L ≤ 0.6 for Ra = 10⁶, Pr = 0.7. The approximation relations have been derived for the mean convective and radiation Nusselt numbers depending on the reduced emissivity of the internal surfaces of bounding walls and the energy source location relative to vertical walls.     

Heat transfer at a laminar free convection and separated flow past a rib in a vertical channel with isothermal walls

The results of numerical computations of a free laminar convection and heat transfer between two parallel isothermal plates in the presence of a single rib on the channel surface are presented. The investigations have been conducted for a channel with the aspect ratio AR = L/w = 10, where L is the channel height, and w is the distance between the plates. An infinitely thin adiabatic rib was located on one of the channel walls in the middle of its height. The relative rib height l/w was varied in the range 0÷0.8. The wall temperature was higher than the ambient temperature, and the Rayleigh number was varied in the range Ra = 10²÷10⁵. The main attention has been paid to the study of the influence of the rib height and the Rayleigh number on local and integral heat transfer and the Reynolds number in the channel (the convective thrust). A fundamental difference in the heat transfer over the channel height has been shown on the ribbed wall and on a smooth surface. The computational results have been compared with the case of a symmetric distribution of the ribs on the both walls with the integral height equal to a single rib.     

Mesoscopic analysis of heatline and massline during double-diffusive MHD natural convection in an inclined cavity

Double-diffusive natural convection in an inclined cavity with the presence of magnetic field is studied numerically via heatline and massline approach. The governing equations are discretized using the Lattice Boltzmann Method (LBM). In this investigation, the controlling parameters involved are Rayleigh number (10³ ≤ Ra ≤ 10⁵), buoyancy ratio (−5 ≤ N ≤ 5), cavity inclination angle (0° ≤ Ø ≤ 180°), Lewis number (2 ≤ Le ≤ 10), Prandtl number (Pr = 5.0) and Hartmann number (0 ≤ Ha ≤ 50). The numerical results obtained by the effect of parameters mentioned above are reported as contours of streamlines, isotherms, isoconcentrations, heatlines, and masslines. The obtained results are compared with the existing literature to validate the coding. The heat and mass transfer rate decrease with increasing the magnetic field and increase with an increase in Rayleigh number. The impact of Ø is maximum for higher Ra and negligible for lower Ra (10³). Increasing Le influences the mass transfer rate to increase and heat transfer to reduce for both opposing and aiding flow.     

Experimental Study of Natural Convection from Electrically Heated Vertical Cylinders Immersed in Air

Abstract

An experimental study of laminar steady-state natural convection heat transfer from electrically heated vertical cylinders immersed in air has been undertaken. Three stainless steel (316 SS) test sections of different slenderness ratios were employed. Surface temperature profiles along the vertical cylinders were obtained using miniature thermocouples when the cylinders were heated with different power levels resulting in different total wall heat fluxes. After the mandatory corrections for the radiation heat fluxes were made, three correlation equations relating the local Nusselt number Nu_y with the local modified Rayleigh number Ra^* _y and the position-to-cylinder diameter y/d were developed. The correlation equations are valid for Ra^* _y ≤ 2 × 10¹².     

Effect of thermodiffusion on convective heat and mass transfer in enclosures with heat-conducting walls

The influence of Soret effect on thermogravitational convection in an enclosure with heat-conducting walls of finite thickness in the presence of local heat and mass sources is numerically analyzed. The mathematical model is formulated in dimensionless variables of streamfunction-vorticity vector. Streamlines and temperature fields representing the influence of the Rayleigh number Ra = 10⁵, 10⁶ and the nonstationarity factor 0 < τ < 3000 are obtained.     

Mathematical simulation of conjugate turbulent natural convection in an enclosure with local heat source

A numerical analysis of turbulent regimes of the natural convection in a closed rectangular region with heat-conducting walls of finite thickness was carried out in the presence of a locally concentrated heat source under the conditions of the radiative-convective heat exchange with the ambient medium on one of the external boundaries. The mathematical model was constructed on the basis of the Reynolds equations in dimensionless variables stream function — vorticity vector — temperature. Special attention was paid to the investigation of the influence of the Grashof number er 10⁸≤Gr<10¹⁰, of the unsteadiness factor 0< τ <1000, and the thermal conductivity ratio λ _2,1 = 5.7·10⁻⁴, 6.8·10⁻⁵ on both the local and integral characteristics of the problem.     

Forced and mixed convection heat transfer from an array of cylinders to a liquid submerged jet

The results of an experimental investigation concerning the heat transfer from three cylindrical heaters to a water jet are reported in the form of correlating equations, which express the Nusselt number versus the Reynolds, Prandtl and Grashof numbers and some dimensionless ratios characterising the configuration. As the experienced range of the thermal flux is wide (2·10⁴ ≤ q̇ ≤ 6·10⁵ W·m⁻²), the influence of the free convection, which was shown to be negligible in previous studies, is carefully investigated in the present one. This influence appears still negligible up to the maximum value of q̇ for the heater impinged by the jet; on the contrary it is remarkable for the heaters lying in its wake. Another aspect which is carefully studied is the influence both of the ratios characterising the configuration and of the impingement direction: accordingly the values of these ratios and the kind of impingement which yield the maximum Nusselt number are clearly singled out. The investigation is completed by some visualization experiments which allow us to qualitatively clarify some aspects of the interaction between the dynamic and thermal fields.     

Laminar free convection heat transfer between vertical isothermal plates

The paper represents results on numerical investigation of flow and heat transfer between two isothermal vertical plates under laminar natural convection. A system of complete Navier–Stokes equations is solved for a two-dimensional gas flow between the plates along with additional rectangular regions (connected to inlet and outlet sections), whose characteristic sizes are much greater than the spacing between the plates. The calculations were performed over very wide ranges of Rayleigh number Ra = 10 ÷ 10⁵ and a relative channel length AR = L/w = 1 ÷ 500. The influence of the input parameters on the gas-dynamic and thermal structure of thermogravitational convection, the local and mean heat transfer, and also the gas flow rate between the plates (convective draft. We determined sizes of the regions and regime parameters when the local heat flux on the walls tends to zero due to the gas temperature approach to the surface temperature. It is shown that the mean heat transfer decreases as the relative channel length AR grows, whereas the integral gas flow rate (convective draft) and Reynolds number in the channel Re = 2wUm/ν increase. The use of a modified Rayleigh number Ra* = Ra · (w/L) (Elenbaas number) leads to generalization of calculation data on mean heat transfer. These data are in good agreement with the correlations for heat transfer [1, 2] and gas flow rate [3]. The reasons of variation of the data in the range of low Rayleigh numbers are discussed in detail.     

A numerical study of laminar natural convective heat transfer inside a closed cavity with different aspect ratio

Two-dimensional steady-state laminar natural convection was studied numerically for differentially heated air-filled closed cavity with adiabatic top and bottom walls. The temperature of the left heated wall and cooled right wall was assumed to be constant. The governing equations were iteratively solved using the control volume approach. In this paper, the effects of the Rayleigh number and the aspect ratio were examined. Flow and thermal fields were exhibited by means of streamlines and isotherms, respectively.Variations of the maximum stream function and the average heat transfer coefficient were also shown. The average Nusselt number and was correlated to the Rayleigh number based on curve fitting for each aspect ratio. The investigation covered the range 10⁴ ≤ RA ≤ 10⁷ and is done at Prandtl number equal to 0.693. The result shows the average Nusselt number is the increasing function of Rayleigh number. As the aspect ratio increases, Nusselt number decreases along the hot wall of the cavity. As Rayleigh number increases, Nusselt number increases. Result indicates that at constant aspect ratio, with increase in Rayleigh number the heat transfer rate increases.     

Lattice Boltzmann simulation of 3-dimensional natural convection heat transfer of CuO/water nanofluids

The present study investigated fluid flow and natural convection heat transfer in an enclosure embedded with isothermal cylinder. The purpose was to simulate the three-dimensional natural convection by thermal lattice Boltzmann method based on the D3Q19 model. The effects of suspended nanoparticles on the fluid flow and heat transfer analysis have been investigated for different parameters such as particle volume fraction, particle diameters, and geometry aspect ratio. It is seen that flow behaviors and the average rate of heat transfer in terms of the Nusselt number (Nu) are effectively changed with different controlling parameters such as particle volume fraction (5 % ≤ φ ≤ 10 %), particle diameter (d _p = 10 nm to 30 nm) and aspect ratio (0.5 ≤ AR ≤ 2) with fixed Rayleigh number, Ra = 10⁵. The present results give a good approximation for choosing an effective parameter to design a thermal system.     

Experimental and Numerical Study of Free Convection on an Isothermal Downward Cone

Abstract

The laminar free-convection heat transfer from an isothermal downward cone in air is investigated experimentally and numerically. The experimental investigation is carried out by Mach-Zehnder interferometery technique and the numerical simulation was done by Fluent. The cone tip angle has been kept constant to 45° and it was suspended from its base throughout the experiment. This article focuses on the effect of Rayleigh number variation on the local and average free-convection heat transfer coefficient over the conical surface. The local and average Nusselt numbers were determined for the Rayleigh number range of 4.9×10⁵ to 1.1×10⁶. Also, the experiment and the numerical simulation were carried out on a vertical isothermal cylinder of circular cross section in order to compare results with other researchers for the verification of our experimental and numerical results. The significant influence of the upper end surface of the cone, both in the experimental and numerical studies, indicated a recirculation region above the upper end surface which affects the local convection heat transfer at the slant trailing edge and causes it to increase. Also, a correlation for the calculation of the local Nusselt number over the cone is proposed.     

Natural convection in a square cavity containing a nanofluid and an adiabatic square block at the center

The problem of free convection fluid flow and heat transfer of Cu–water nanofluid inside a square cavity having adiabatic square bodies at its center has been investigated numerically. The governing equations have been discretized using the finite volume method. The SIMPLER algorithm was employed to couple velocity and pressure fields. Using the developed code, a parametric study was conducted and the effects of pertinent parameters such as Rayleigh number, size of the adiabatic square body, and volume fraction of the Cu nanoparticles on the fluid flow and thermal fields and heat transfer inside the cavity were investigated. The obtained results show that for all Rayleigh numbers with the exception of Ra = 10⁴ the average Nusselt number increases with increase in the volume fraction of the nanoparticles. At Ra = 10⁴ the average Nusselt number is a decreasing function of the nanoparticles volume fraction. Moreover at low Rayleigh numbers (10³ and 10⁴) the rate of heat transfer decreases when the size of the adiabatic square body increases while at high Rayleigh numbers (10⁵ and 10⁶) it increases.     

Spectroscopic studies of a plasma temperature and radiation standard based on a wall-stabilized arc

The absolute determination of the axial temperature (12,000 K ≤ T ≤ 14,500 K, 0.9×10²³ m^-3 ≤ N_e ≤2.5×10^-3 m^-3 of a 3 mm bore wall-stabilized arc operating in argon at 1.75×10⁵ Pa is described using spectroscopic techniques both in the visible and vacuum u.v. spectral regions. Computer simulation techniques to predict the line wing correction for the A(I) line at 430 nm and a detailed study of sources of systematic error have been applied. The reproducibility of the temperature results and the establishment of LTE demonstrates the suitability of the source as a plasma temperature and radiation standard. A detailed study of the Stark broadening of H_β and the comparison of the experimental profiles with the theories of Kepple and Griem and Vidal, Cooper and Smith has shown the former giving N_e values some 11% lower and the latter 1% higher than the pure argon diagnostics at N_e ? 2 × 10²³ m^-3. New values for the argon transition probabilities of two lines and continuum factors at two wavelengths are presented.     

Prediction of minimum water amount to stop thermal decomposition of forest fuel

Presented are results of experimental studies of the heat transfer processes in suppression of thermal decomposition of typical forest fuels (FFs) (spruce needles, birch leaves, aspen twigs, or amixture thereof) due to the effect of aerosol water flow (drop radii: 0.01–0.12 mm; concentration: 3.8 · 10^?5 m³ drop/m³ of gas). The experiments have been carried out with FF samples in the form of cylinders of a thickness of 40–100 mm and a diameter of 20–150 mm. The times required to stop the thermal decomposition of FF have been found, as well as amounts of water necessary to lower in a given time the temperature in a layer of material to the point of decomposition beginning. A dimensionless complex has been derived for prediction of water spraying parameters (amount and time of supply) that ensure sustainable termination of FF decomposition within a specified time interval.     

Mixed convection and entropy generation in a square cavity using nanofluids

In this work, two-dimensional mixed convection and entropy generation of water-(Cu, Ag, Al₂O₃, and TiO₂) nanofluids in a square lid-driven cavity containing two heat sources, have been numerically investigated. The upper lid and bottom wall of the cavity are maintained at a cold temperature T_C, respectively. The governing equations along with boundary conditions are solved using the finite volume method. Comparisons with the previous results were performed and found to be in excellent agreement. The effects of the solid volume fraction (0≤φ≤0.10), Rayleigh (10³≤Ra≤10⁵) and Reynolds (1≤Re≤500) numbers, and different types of nanofluids on the total entropy generation S_t and on entropy generation due to heat transfer S_h are presented and discussed. Moreover, the heat sources positions have an effect on the total entropy generation and Bejan number. It was found that S_t and S_h decrease with increase of φ, Ra, and Re.     

Laminar free convection heat transfer and separated flow structure in a vertical channel with isothermal walls and two adiabatic opposing fins

Results of numerical study of laminar free convection and heat transfer in a vertical plane-parallel channel with two thin adiabatic fins on its walls are presented. The channel has the open inlet and outlet, and its surfaces are maintained at the same temperature. The channel height is unchanged with elongation parameter A = L/w = 10, and the fins are located in the middle of the channel toward each other. Fin height l/w = 0 ÷ 0.4 and Rayleigh number Ra = 10² ÷ 10⁵ are varied in calculations. The effect of these parameters on the flow structure, temperature field, local and integral heat transfer, and gas flow caused by gravitational forces are analyzed in detail. Numerical analysis is based on solving the full Navier–Stokes and energy equations in twodimensional statement and Boussinesq approximation. To determine the dynamic and thermal parameters at the inlet and outlet, the calculation is carried out with two large volumes attached to the inlet and outlet. The features of the flow and heat transfer at separated flow around the channel fins are studied in detail in this work.     

A thermoelastic method to accurately measure the grüneisen parameter and thermal diffusivity

A homogeneous thermoelastic heat source is fed, in a cylindrical sample, by compression; the amount of generated heat is controlled by the Grüneisen parameter. The heating process is followed by a thermal relaxation controlled by the thermal diffusivity. The temperature transient is detected by a miniature temperature sensor mounted on the lateral surface of the sample. The value obtained for the Grüneisen parameter of a technological steel is 1.14±0.03, the thermal diffusivity turning out to be (6.1±0.1)·10⁻⁶ m² s⁻¹.     

Laminar natural convection between vertical isothermal heated plates with different temperatures

Numerical investigation of laminar free convection heat transfer in the vertical parallel plate channel with asymmetric heating is presented. Both inlet and exit effects are included into the analysis. A numerical solution is obtained for a Prandtl number of 0.71 and for modified Rayleigh number [`(Ra)]\overline {Ra} = 10⁻¹ ÷ 10⁵, and varying heating ratio T_R = 0 ÷ 1 and aspect ratio A = 10. Fully elliptic Navier-Stokes and energy equations are solved using the finite volume techniques with staggered grid arrangements. The obtained results show a strong influence of the temperature ratio on local and average heat transfer coefficient on the hot and cold plates. With reduction of T_R the heat transfer parameter on the hot wall grows, and on the cold one, on the contrary, it decreases. As a result, the total heat exchange from two plates depends poorly on the parameter T_R.