Sinusoidal Heat Flux Research Articles

F121 正方容器内熱対流場に対する熱流束振動振幅の影響(自然対流2)

In this paper, the thermal convection field and its resonance phenomena in a square cavity with sinusoidal heat-flux vibration were numerically examined at Pr=0.71, Ra=10^6. When the amplitude of the vibration a is less than unity, i.e. α<1.0, the field has the local maximum of relative amplitude of midplane Nusselt number at a critical angular frequency ω_c=350 in accord with that of the internal gravity wave. In contrast, for a>1.0, we found that the thermal convection field exhibits a nonlinear response to the vibration. ω_c is changed linearly with α, and we observed the nonlinear resonance phenomena which differs from the one induced by the wave.

405 熱流束振動を加えた矩形容器内熱対流場の内部重力波共鳴(G.S.伝熱,九州支部 第58期総会・講演会)

In this paper, the thermal convection field and its resonance phenomena in a rectangular cavity with sinusoidal heat-flux vibration were numerically examined. As angular velocity ω is changed, the thermal convection field at Pr=0.71, Ra=10^5 is found to be classified into 5 regions and, particularly, the field has the local maximum of relative amplitued of midplane Nusselt's number at ω_c=140, which corresponds to the angular velocity of internal gravity wave ω_r estimated by a theoretical equation proposed by Thorpe. This shows the local enhancement is induced by an internal gravity wave resonance. Such correspondence is observed for Ra&ge;10^5, Ra&ge;10^6 for Pr=0.71, 7.1, respectively. For the range of Ra we proposed a correlation equation to estimate the resonant angular velocity which is a function of Pr and Gr only.

Internal Gravity Wave Resonance of Thermal Convection Fields in a Square Cavity with Heat-Flux Vibration

In this paper, the thermal convection field and its resonance phenomena in a square cavity with sinusoidal heat-flux vibration were numerically examined. As angular velocity ω is changed, the thermal convection field at Pγ=0.71, Rα=106 is found to be classified into 5 regions and, particularly, the field has the local maximum of relative amplitude of midplane Nusselt's number at ωc=350, which corresponds to the angular velocity of internal gravity wave ωγ estimated by a theoretical equation proposed by Thorpe. This shows the local enhancement is induced by an internal gravity wave resonance. Such correspondence is observed for Rα≥105, Rα≥106 for Pγ=0.71, 7.1, respectively. For the range of Rα we proposed a correlation equation, a function of Pγ and Gγ only, to estimate the resonant angular velocity.

Analytical solution to the problem of heat transfer in an MHD flow inside a channel with prescribed sinusoidal wall heat flux

An MHD laminar flow through a two dimensional channel subjected to a uniform magnetic field and heated at the walls of the conduit over the whole length with a sinusoidal heat flux of vanishing mean value or not, is studied analytically. General expressions of the temperature distribution and of the local and mean Nusselt numbers are obtained by using the technique of linear operators in the case of negligible Joule and viscous dissipation and by taking into account the axial conduction effect. The principal results show that an increase of the local Nusselt number with Hartmann number is observed, and, far from the inlet section, the average heat transfer between the fluid and the walls shows a significant improvement at all values of Hartmann number used when the frequency of the prescribed sinusoidal wall heat flux is increasing in the case of vanishing mean value of the heat flux and this is true especially at low Peclet numbers.

Large Eddy Simulation of Thermally Induced Oscillations in the Convective Boundary Layer

Mesoscale circulations induced by differential boundary layer heating due to surface inhomogeneities on scales of 5 km and more can significantly change the average properties and the structure of the convective boundary layer (CBL) as well as trigger off temporal oscillations. The results of one of the first numerical case studies using large eddy simulation (LES) on the mesoscale suggest that mesoscale circulations exhibit a considerably larger average kinetic energy than convection under homogeneous conditions. This affects turbulent transport processes and should be accounted for in larger-scale models even if their turbulence parameterizations rely on homogeneous control runs of high-resolution models. This case study uses the Hannover parallelized large eddy simulation model (PALM) with prescribed 1D sinusoidal surface heat flux variations on wavelengths from 2.5 to 40 km. The resulting mesoscale circulations are analyzed by means of domain-averaged cross sections, time averaged and normalized with the boundary layer height, as well as power spectra and domain-averaged time series. The simulated mesoscale circulations were periodic. Vertical profiles and time series demonstrate that the onset of the mesoscale circulation triggers off a temporal boundary layer oscillation, whose period and amplitude depend on the surface heat flux perturbation wavelength and amplitude and on the background wind component perpendicular to the surface inhomogeneity orientation. Spectral analysis shows that the mesoscale circulations damp convection equally in all directions. A hypothesis of the oscillation mechanism is briefly discussed.

Lateral heating effects on the PVT growth process of Hg2Cl2 crystals

Effects of lateral heating on flow profiles and growth rates during the growth of mercurous chloride crystals by the physical–vapour-transport process in vertical ampoules are investigated by a two-dimensional model. The growth conditions of an experimental study available in the open literature are simulated. Lateral thermal boundary condition is modelled by a spatially sinusoidal heat flux. The results of the present computations are in agreement with the earlier experimental results and indicate that an increase in the lateral heating rate can cause a significant decrease in the transport rate while the flow accelerates. In the case of flow bifurcations, the growth rates can become as low as in the case of convectionless flow conditions.

LARGE-EDDY SIMULATION OF THERMALLY INDUCED OSCILLATIONS IN THE CONVECTIVE BOUNDARY LAYER

Abstract Mesoscale circulations induced by differential boundary layer heating due to surface inhomogeneities on scales of 5 km and more can significantly change the average properties and the structure of the convective boundary layer (CBL) as well as trigger off temporal oscillations. The results of one of the first numerical case studies using large eddy simulation (LES) on the mesoscale suggest that mesoscale circulations exhibit a considerably larger average kinetic energy than convection under homogeneous conditions. This affects turbulent transport processes and should be accounted for in larger-scale models even if their turbulence parameterizations rely on homogeneous control runs of high-resolution models. This case study uses the Hannover parallelized large eddy simulation model (PALM) with prescribed 1D sinusoidal surface heat flux variations on wavelengths from 2.5 to 40 km. The resulting mesoscale circulations are analyzed by means of domain-averaged cross sections, time averaged and normali...

Parametric studies on the phase shift method to measure the blood perfusion of biological bodies

To better understand the phase shift method to non-invasively measure the blood perfusion of living tissues in vivo, the dual reciprocity boundary element method (DRBEM) was applied to numerically solve the transient and non-linear two-dimensional bio-heat transfer in biological bodies subject to a sinusoidal heat flux at the skin surface. The influences of the heating flux, the heating oscillation magnitude, the heating frequency, the blood vessel underneath the skin, and the space or temperature dependent blood perfusion to the temperature response and the phase shift between the heat flux and the temperature response at the skin surface were comprehensively examined. The effects of the heating area to the temperature response were also investigated. And a better understanding on the heat transfer behavior of biological bodies under sinusoidal heating was thus obtained. These results are expected to be valuable for constructing the practical instrumentation to non-invasively measure the blood perfusion of biological bodies.

Effects of viscous dissipation on laminar forced convection with axially periodic wall heat flux

The laminar forced convection in a circular duct is investigated in the case of a sinusoidal axial variation of the wall heat flux. The axial heat conduction in the fluid is neglected, while the effect of viscous dissipation is taken into account. The heat transfer in the thermally developed region, where the temperature is the sum of a linear function and a periodic function of the axial coordinate, is analysed. Both the temperature field and the local Nusselt number are evaluated analytically. Comparisons with the solution in the absence of viscous heating are performed. It is shown that the effect of viscous dissipation on the temperature field may be relevant especially in the case of a sinusoidal wall heat flux distribution with a vanishing mean value.

Simulation numérique de la convection naturelle d'un liquide soumis à des conditions pariétales variables

The present work determines numerically and analyses the dynamic and thermal fields resulting from natural convection in vertical cylinders partially filled with a liquid. The finite difference method has been used to solve the equations governing these flows. Two different types of boundary conditions were implemented in the solution of these equations: in the first case, a temperature which varies sinusoidally on all the boundaries of the cylinder was imposed and, in the second case, a sinusoidal heat flux was imposed. In the case of variable wall temperature, it was noticed that the flow becomes more and more complex and passes from a monocellular structure at the beginning of the period to a multicellular structure at the end of the period, provoked by the differences in temperature that appear within the fluid. Also, despite the imposition of the same temperature on all walls, it was observed that the majority of the heat is exchanged through the vertical wall of the cylinder. In the case of variable wall flux, a nearly constant local heat transfer was predicted for all walls but the mean transfer was larger for the transversal wall. The flow is here monocellular and is little perturbed because of the continuous heating. It was also noted the formation of thermal stratification which is not as quickly destroyed as in the case of prescribed variable wall temperature.

Estimation of blood perfusion using phase shift in temperature response to sinusoidal heating at the skin surface.

A closed form analytical solution of the Pennes' bio-heat equation was obtained for temperature distributions in the skin tissue subject to the sinusoidal heat flux. Phase shifts in the surface temperature response were revealed to be related to local blood perfusion rate and heating frequency. The influence of the thermal contact resistance on the perfusion estimation was investigated. It has been proved that this influence is relatively small because of the phase shift based estimation and can be effectively eliminated by application of highly conductive grease. This analysis provides the theoretical foundation for a new noninvasive modality of blood perfusion estimation based on the surface temperature measurement which can have significant applications in future clinical practices.

Mathematical modeling of natural convection in a vertical cylindrical tank with alternating-sign heat flux distribution on the wall

On the basis of a numerical solution of the two-dimensional nonstationary Navier-Stokes equations in the Boussinesq approximation, mathematical modeling of laminar natural convection is carried out for a sinusoidal heat flux distribution on the side wall. For various values of the governing parameters, the spatial and temporal structure of the convective flow is analyzed in detail.

Laminar forced convection with sinusoidal wall heat flux distribution: axially periodic regime

Stationary and laminar forced convection in a circular tube with a sinusoidal axial distribution of wall heat flux is studied under the hypothesis that both axial heat conduction and viscous dissipation in the fluid are negligible. Two cases are considered: a sinusoidal wall heat flux distribution with a vanishing mean value; a sinusoidal wall heat flux distribution which does not change its sign. In both cases, the temperature field and the local Nusselt number are evaluated analytically in the fully developed region, i.e. where the local Nusselt number depends periodically on the axial coordinate. It is shown that, in the first case, the fully developed region presents an infinite sequence of axial positions where the local Nusselt number is singular. In these positions, the wall heat flux has a non-vanishing value even if the wall temperature equals the bulk temperature.

EFFECT OF THERMAL CAPACITY ON THERMOELASTIC INSTABILITY DURING THE SOLIDIFICATION OF PURE METALS

If unidirectional solidification of pure metals at constant cooling rate is perturbed by a small spatially sinusoidal heat flux at the casting / mold interface, corresponding responses with sinusoidal perturbation are obtained for the evolution of the casting / melt interface, for the temperature and stress fields in the solidified casting and for the contact pressure at the mold surface. The results show that the perturbation in contact pressure tends asymptotically to a maximum value at larger values of time. The magnitude of the contact pressure perturbation is decreased by the inclusion of thermal capacity, and this effect is enhanced at higher mean cooling rates. This indicates that materials with higher specific heat (or lower thermal diffusivities) might be less susceptible to thermoelastic instabilities associated with the contact pressure and its dependent thermal contact resistance at the casting / mold interface.

Periodic heat transfer through inhomogeneous media part 3: Hollow sphere

The paper presents the exact analytical solutions for periodic radial heat conduction through an inhomogeneous hollow sphere for a certain class of thermal-conductivity profile. The exact analytical solutions for some of these profiles, (including linear and quadratic) have been compared with those obtained by considering the spherical medium to be made up of a number of homogeneous layers with different thermal conductivities, varying from layer to layer, and using the layered-structure (or matrix-multiplication) method. The numerical results arrived at by the layered-structure method converge rapidly (with increasing number of layers considered) to the values obtained from the exact analytical solutions. It strengthens the confidence in applying the layered-structure method to the case of periodic heat conduction through an inhomogeneous hollow cylinder. Considering the inhomogeneous conducting medium to be made up of a number of spherical layers with a linear profile of thermal conductivity has been shown to be a more effective alternative method of accounting for any type of inhomogeniety; and it saves computation time, as the rate of convergence is much higher than for the homogeneous-layered structure method. The numerical results have been presented in the form of elements of a 2 × 2 matrix, relating the sinusoidal steady-state temperature and heat flux of the two surfaces of the hollow sphere.

Periodic heat transfer through inhomogeneous media. Part 1. Slab

The paper presents exact analytical solutions of one-dimensional periodic heat conduction through an inhomogeneous slab for a certain class of thermal conductivity profiles (including linear and exponential). The exact analytical solutions for some of these profiles have been compared with those obtained by considering the slab to be made up of a number of homogeneous layers with different thermal conductivities varying from layer to layer and using the layered structure (or matrix multiplication) method. The numerical results arrived at by the layered-structure method converge rapidly (with increasing number of layers considered) to the values obtained from the exact analytical solutions. This gives confidence in the application of the layered-structure method to periodic heat conduction through inhomogeneous slabs. The numerical results have been presented in the form of elements of a 2 × 2 matrix, relating the sinusoidal steady-state temperature and heat flux on the two sides of the slab.

Non-Fourier Heat Conduction in a Semi-infinite Solid Subjected to Oscillatory Surface Thermal Disturbances

Many investigators have explored the effect of non-Fourier conduction in transient processes in recent years. Based on a relaxation model for heat conduction in solids and liquids, the traditional heat diffusion equation is replaced with a hyperbolic equation that accounts for the finite thermal propagation speed. The use of the hyperbolic equation removes the nonphysical phenomenon of the diffusion equation analysis that predicts instantaneous temperature disturbances at all points in the medium for a step heat flux at the boundary. It further removes the peculiarity of an infinite temperature gradient at the boundary as time goes to zero. The objective of this work is to show that the non-Fourier conduction effect can be important even at a long-time after the initial transient if the thermal disturbance is oscillatory with the period of oscillation of the same order of the magnitude as the thermal relaxation time. In particular, the thermal response of a semi-infinite solid subjected to a sinusoidal boundary heat flux condition is generated. The present solution illustrates readily that, in many practical situations such as the repeated irradiation of a solid by a laser with very short pulse width, heat transfer analyses using the traditional Fourier heat diffusion equationmore » can result in significant errors. The current results also suggest that the thermal relaxation time of a solid can be determined by measuring the thermal response of the solid can be determined by measuring the thermal response of the solid irradiated by a high-frequency heat flux.« less

An investigation of the gates asynchronous coupling strategy using a simple energy-balance model

A simple globally averaged energy-balance model is used to explore the properties of the asynchronous coupling strategy due to Gates. The model's behaviour in response to (1) a constant (perturbation) heat flux, and (2) a sinusoidal heat flux, is considered. For (1), a new form of the equation for the mixed-layer temperature during asynchronous phases is derived. This allows the effect of varying Dickinson's implicitness parameter to be analyzed in the 3-box case. For (2), it is shown that Gates' strategy can produce an equilibrium seasonal cycle that is not quite correct. Discussion of the reasons for this leads to the suggestion of improvements to the strategy.

Radiant and convective heat transfer for flow of a transparent gas in a short tube with sinusoidal wall heat flux

The present analysis accounts for combined convective and radiant heat transfer to a fluid flowing in a short tube with prescribed wall heat flux. The heat flux distribution used was of sine shape with maximum at the middle of the tube. This solution is known to represent the axial power variation in a nuclear reactor core. The tube wall and gas bulk temperatures were obtained by successive substitutions for the wall and gas energy balance equations. The integrals were approximated by Sympson's rule and initial guesses for the iterative process were based upon limiting cases for pure radiation and pure convection. The results of the combined solution compared with the pure radiation approach show a decrease of 30 percent for the maximum wall temperature using black surface ( ε=1). For this same situation, the increase in the gas temperature along the tube shows a reduction of 58 percent when compared to the pure convection solution.

Single bubble slug expulsion of initially static superheated sodium in a heated pipe and variation of residual film thickness on the channel walls

Transient growth of a single bubble in initially static superheated sodium within a heated pipe, and the variation of the local film thickness around the bubble due to vaporization were numerically time and axial position were obtained for sinusoidal heat flux distribution along the pipe. Results showed that bubble velocity, temperature and pressure increased, and film thickness decreased with increasing initial fluid superheat.