Natural convection heat transfer from sinusoidal wavy surfaces

This paper presents the results of an experimental study of the natural convection heat transfer characteristics of sinusoidal wavy surfaces on vertical plates maintained at a constant temperature. Local heat transfer coefficients were obtained with a Mach-Zehnder interferometer. The heat transfer from the wavy surfaces, compared to a plane plate of equal projected area, increased with increasing amplitude-to-wavelength ratio. The heat transfer was increased by about 15 percent at an amplitude-to-wavelength ratio of 0.3; for this case a flow instability was detected. A quantitative comparison with a previously published numerical investigation is also presented. In general, there is agreement between the two studies.     

Natural convection heat transfer along vertical rectangular ducts

Experimental investigations have been reported on steady state natural convection from the outer surface of vertical rectangular and square ducts in air. Seven ducts have been used; three of them have a rectangular cross section and the rest have square cross section. The ducts are heated using internal constant heat flux heating elements. The temperatures along the vertical surface and the peripheral directions of the duct wall are measured. Axial (perimeter averaged) heat transfer coefficients along the side of each duct are obtained for laminar and transition to turbulent regimes of natural convection heat transfer. Axial (perimeter averaged) Nusselt numbers are evaluated and correlated using the modified Rayleigh numbers for laminar and transition regime using the vertical axial distance as a characteristic length. Critical values of the modified Rayleigh numbers are obtained for transition to turbulent. Furthermore, total overall averaged Nusselt numbers are correlated with the modified Rayleigh numbers and the area ratio for the laminar regimes. The local axial (perimeter averaged) heat transfer coefficients are observed to decrease in the laminar region and increase in the transition region. Laminar regimes are obtained at the lower half of the ducts and its chance to appear decreases as the heat flux increases.     

Natural convection heat transfer from round horizontal plate

A new approach to the model of natural convection from a horizontal, isothermal round plate and a simplified analytical solution of this model have been presented. In this model two separate regions with different fluid motions have been distinguished. In the first region, inside the boundary layer, the fluid flows concentrically towards the centre of the plate, while in the second one (stagnation region) the fluid is motionless. The presented theory has been verified experimentally.Ein neuer Lösungsweg für das Modell der freien Konvektion an einer isothermen, kreisförmigen, horizontalen Platte und eine vereinfachte analytische Lösung für dieses Modell werden hier vorgestellt. An diesem Modell wird zwischen zwei Bereichen mit verschiedenen Fluidbewegungen unterschieden. Im ersten Bereich, innerhalb der Grenzschicht, strömt das Fluid konzentrisch in Richtung Plattenmitte, während im zweiten Bereich (Stau-Bereich) die Flüssigkeit in Ruhe ist. Diese Theorie wurde experimentell überprüft.     

Natural convection heat transfer from a horizontal ice cylinder

Heat transfer characteristics passing through the maximum density point around a horizontal ice cylinder immersed in water was studied both theoretically and experimentally. For the sake of a precise comparison, the stagnation point Nusselt number was measured and results then compared with those of the numerical computations that were obtained by solving the full Navier-Stokes equations. A fairly good agreement was seen between the theory and the experiment.At about 6°C of water temperature where the stagnation Nusselt number takes its minimum value, the instability of the flow was observed. It was found that two different computer solutions exist, which shows unstable aspects corresponding to the experimental result.     

Magnetohydrodynamic natural convection heat transfer from radiate vertical porous surfaces

Magnetohydrodynamic natural convection heat transfer from radiate vertical surfaces with fluid suction or injection is considered. The nonsimilarity parameter is found to be the conductive fluid injection or suction along the streamwise coordinate = V{4x/² g(T _w – T )}^1/4. Three dimensionless parameters had been found to describe the problem: the magnetic influence number N = B ² _y /V ², the radiation-conduction parameter R _d = k _R /4aT ³ , and the Gebhart number Ge _x = gx/cp to represent the effect of the viscous dissipation. It is found that increasing the magnetic field strength causes the velocity and the heat transfer rates inside the boundary layer to decrease. Its apparent that increasing the radiation-conduction parameter decreases the velocity and enhances the heat transfer rates. The Gebhart number, i.e, the viscous dissipation had no effect on the present problem.Nomenclature a Stefan-Boltzmann constant - B _y Magnetic field flux density Wb/m² - Cf _x Local skin friction factor - c _p Specific heat capacity - f Dimensionless stream function - Ge _x Gebhart number, gx/cp - g Gravitational acceleration - k Thermal Conductivity - L Length of the plate - N Magnetic influence number, B ² _y /V ² - p Pressure - Pr Prandtl number - q _r Radiative heat flux - q _w (x) Local surface heat flux - Q _w (x) Dimensionless Local surface heat flux - R _d Planck number (Radiation-Conduction parameter), k _R /4aT ³ - T Temperature - T Free stream temperature - T _w Wall temperature - u, v Velocity components in x- and y-directions - V Porous wall suction or injection velocity - V _w Porous wall suction or injection velocity - x, y Axial and normal coordinates - Thermal diffusivity Greek symbols _R Roseland mean absorption coefficient, 4/3R _d - Coefficient of thermal expansion - Nonsimilarity parameter, V{4x/² g(T _w – T )}^1/4 - Peseudo-similarity variable - Dimensionless temperature - _w Ratio of surface temperature to the ambient temperature, T _w /T - Dynamice viscosity - Kinemtic viscosity - Fluid density - Electrical conductivity - _w Local wall shear stress - Dimensional stream function     

黏弹性纳米流体在垂直板上的自然对流与传热分析

基于分数阶Maxwell模型和分数阶Fourier定律构建黏弹性纳米流体在垂直板上的非定常二维边界层自然对流与传热控制方程,利用有限差分和L1算法获得数值稳定解,对不同物理参数下的速度、温度、平均表面摩擦系数和平均Nusselt数的变化趋势进行图形化分析。结果显示,速度和温度边界层均表现出短暂记忆和延迟特性;速度分数导数参数削弱了自然对流,而速度松弛时间的影响却相反;温度分数导数参数削弱了自然对流和热传导,而温度松弛时间的影响却相反。     

Natural convection heat transfer in a uniformly heated horizontal pipe

Natural convection heat transfers inside horizontal pipes were measured. The Rayleigh numbers were varied from 6.8 × 10⁸ to 1.5 × 10¹², while the Prandtl number was fixed at 2,094. Based on the analogy concept, a copper sulfate electroplating system was adopted to measure mass transfer rates in place of heat transfer rates. Test results using single-piece electrodes were in good agreement with the work of Sarac and Korkut. The angle-dependent mass transfer rates, measured using piecewise electrodes, were compared with the results of studies on natural convection in concentric annuli, and showed similar trends. The experiments were expanded to the turbulent region, and a transition criterion was proposed. Angle-dependent natural convection heat transfer correlations for the laminar and turbulent regions were derived.     

A correlation for free convection heat transfer from vertical wavy surfaces

Free convection heat transfer along an isothermal vertical wavy surface was studied experimentally and numerically. A Mach-Zehnder Interferometer was used in the experiment to determine the local heat transfer coefficients. Experiments were done for three different amplitude–wavelength ratios of α = 0.05, 0.1, 0.2 and the Rayleigh numbers ranging from Ra _l = 2.9 × 10⁵ to 5.8 × 10⁵. A finite-volume based code was developed to verify the experimental study and obtain the results for all the amplitude–wavelength ratios between α = 0 to 0.2. It is found that the numerical results agree well with the experimental data. Results indicate that the frequency of the local heat transfer rate is the same as that of the wavy surface. The average heat transfer coefficient decreases as the amplitude–wavelength ratio increases and there is a significant difference between the average heat transfer coefficients of the surface with α = 0.2 and those surfaces with α = 0.05 and 0.1. The experimental data are correlated with a single equation which gives the local Nusselt number along the wavy surface as a function of the amplitude–wavelength ratio and the Rayleigh number.     

Natural convection effects on impulsively started inclined plate with heat and mass transfer

The present investigation, involving the simultaneous heat and mass transfer is concerned with a numerical study of transient natural convection flow past an impulsively started inclined plate. Crank-Nicolson implicit finite difference method is used to solve the unsteady, non-linear and coupled governing equations. In order to check the accuracy of the numerical results, the present study is compared with available exact solution and are found to be in good agreement. Numerical results are obtained for various parameters. The steady-state velocity, temperature and concentration profiles, local and average skin friction, local and average Nusselt number, local and average Sherwood number are shown graphically. It is observed that local wall shear stress decreases as an angle of inclination { decreases.     

Natural convection heat transfer in enclosures with microemulsion phase change material slurry

This paper has dealt with the natural convection heat transfer characteristics of microemulsion slurry composed of water, fine particles of phase change material (PCM) in rectangular enclosures. The microemulsion slurry exhibited non-Newtonian pseudoplastic fluid behavior, and the phase changing process can show dramatically variations in both thermophysical and rheological properties with temperature. The experiments have been carried out separately in three subdivided regions in which the state of PCM in microemulsion is in only solid phase, two phases (coexistence of solid and liquid phases) or only liquid phase. The complicated heat transfer characteristics of natural convection have appeared in the phase changing region. The phase change phenomenon of the PCM enhanced the heat transfer in natural convection, and the Nusselt number was generalized by introducing a modified Stefan number. However, the Nusselt number did not show a linear output with the height of the enclosure, since a top conduction lid or stagnant layer was induced over a certain height of the enclosure. The Nusselt number increased with a decrease in aspect ratio (width/height of the rectangular enclosure) even including the side-wall effect. However, the microemulsion was more viscous while the PCM was in the solid phase, the side-wall effect on heat transfer was greater for the PCM in the solid region than that for the PCM in the liquid region. The correlation generalized for the PCM in a single phase is $ Nu = 1/3(1 - C_1 )Ra^{{1 \over {3.5n + 1}}} , $ where C ₁ = e ^–0.09AR for the PCM in solid phase and C ₁ = e ^–0.33AR for the PCM in liquid phase. For the PCM in the phase changing region, the correlation can be expressed as $ Nu = CRa^{{1 \over {7n + 2}}} Ste^{ - (1.9 - 1.65n)} , $ where C = 1.22 – 0.035AR for AR > 10 and C = 0.55 – 16.4e ^–1.1AR for AR < 10. The enclosure height used in the present experiments was varied from H = 5.5 [mm] to 30.4 [mm] at the fixed width W = 120 [mm] and depth D = 120 [mm]. The experiments were done in the range of modified Rayleigh number 7.0 × 10² ≤ Ra ≤ 3.0 × 10⁶, while the enclosure aspect ratio AR varied from 3.9 to 21.8.     

Natural convection heat transfer in the annular region between porous confocal ellipses

The Darcy–Boussinesq equations are solved in two dimensions and in elliptical cylindrical co‐ordinates using a second‐order‐accurate finite difference code and a very fine grid. For the limiting case of a circular geometry, the results show that a hysteresis loop is possible for some values of the radius ratio, in agreement both with previous calculations using cylindrical co‐ordinates and with the available experimental data. For the general case of an annulus of elliptical cross‐section, two configurations, blunt or slender, are considered. When the major axes are horizontal (blunt case) a hysteresis loop appears for a certain range of Raleigh numbers. For the slender configuration, when the major axes are vertical, a transition from a steady to a periodic regime (Hopf bifurcation) has been evidenced. In all cases, the heat transfer rate from the slender geometry is greater than that obtained in the blunt case. Copyright © 1999 John Wiley & Sons, Ltd.     

Natural convection due to heat and mass transfer in a composite system

A numerical study is performed to analyse heat and mass transfer phenomena due to natural convection in a composite cavity containing a fluid layer overlying a porous layer saturated with the same fluid. The flow in the porous region is modelled using Brinkman–Forchheimer-extended Darcy model that includes both the effect of macroscopic shear (Brinkman effect) and flow inertia (Forchheimer effect). The vertical walls of the two-dimensional enclosure are isothermal whilst the horizontal walls are adiabatic. The two regions are coupled by equating the velocity and stress components at the interface. The resulting coupled equations in non-dimensional form are solved by an alternating direction implicit method by transforming them into parabolic form by the addition of false transient terms. The numerical results show that the amount of fluid penetration into the porous layer depends strongly upon the Darcy, thermal and solutal Rayleigh numbers. Average Nusselt number decreases while average Sherwood number increases with an increase of the Lewis number. The transfer of heat and mass on the heated wall near the interface depends strongly on the Darcy number. Received on 11 May 1998     

An analysis for forced convection heat transfer from external surfaces to non-Newtonian fluids

A theoretical analysis has been proposed for the forced convection heat transfer from external surfaces immersed in non-Newtonian fluids of the power-law model. The integral treatment previously introduced for Newtonian fluids has been successfully extended to the non-Newtonian fluids over a flat plate and a wedge of an arbitrary included angle. The integral momentum and energy equations are transformed into a pair of characteristic equations, which can readily be solved for the velocity shape factor and the boundary layer thickness ratio, once the exponents in the expressions for the power-law model, free stream velocity and wall temperature variation are specified. It has been also found that an asymptotic expression derived under the assumption of large Prandtl number, is valid practically for all power-law fluids, and hence, can be used for a speedy, and yet accurate estimation of the local heat transfer to non-Newtonian fluids.     

Natural convection heat transfer through an enclosed horizontal layer of supercritical carbon dioxide

In natural convection heat transfer through a thin horizontal layer of carbon dioxide, maxima in the equivalent thermal conductivities are obtained in the vicinity of the respective pseudocritical temperatures at pressures of 75.8, 89.6 and 103.4 bar. The maxima are the more pronounced, the closer the critical point is approached.Comparison of experimental results with Nusselt equations shows good agreement except for the immediate vicinity of the pseudocritical temperature.In visual observations a distinct change in flow structure appears in the immediate vicinity of the pseudocritical temperature. A steady state polygon pattern and a boiling-like action could not be observed in this geometry.

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Zusammenfassung Beim Wärmetransport durch freie Konvektion in einer dünnen waagerechten Schicht von Kohlendioxid ergaben sich Maxima der scheinbaren Wärmeleitfähigkeit in der Nähe der pseudokritischen Temperaturen bei Drükken von 75,8, 89,6 und 103,4 bar. Die Maxima sind um so ausgeprägter, je mehr man sich dem kritischen Punkt nähert.Ein Vergleich der Versuchsergebnisse mit Nusseltbeziehungen ergibt gute Übereinstimmung außer in unmittelbarer Umgebung der pseudokritischen Temperatur. Direkte Beobachtungen der Konvektionsmuster zeigen in unmittelbarer Umgebung der pseudokritischen Temperatur eine deutliche Strukturänderung. Ein stationäres Zellmuster und siedeähnliche Vorgänge konnten in dieser Anordnung nicht beobachtet werden.

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Nomenclature A area of the heating or cooling plate - C constant in the correlation - g acceleration of gravity - h heat transfer coefficient - k thermal conductivity of fluid in the gap - k _e equivalent thermal conductivity - m, n exponents of dimensionless numbers - q heat flux - T _C,PC absolute temperature; critical C, pseudocritical PC - Gr Grashof numberg ( _h– _c) ³/ ² - Nu Nusselt numberh/k - Pr Prandtl number/ - thermal diffusivity - coefficient of volume expansion - width of gap - _c,h temperature of cooling (c)-, heating (h)-plate - _m arithmetic mean temperature ( _c+ _h)/2 - kinematic viscosity - _c,h fluid density at the temperature of the cooling (c)- or heating (h)-plate - heat flow rate through the gap     

Natural convection heat transfer in enclosures with conducting multiple partitions and side walls

The flow and heat transfer in enclosures with conducting multiple partitions and side walls were numerically analyzed. Side walls were kept at isothermal conditions, while top and bottom walls were insulated. Employing control volume approach, a computer program based on SIMPLE algorithm was developed. Computations were carried out to investigate the effects of Rayleigh number, number of partitions and cavity aspect ratios on the heat transfer rate. The mean Nusselt numbers were calculated from computed temperature fields. It was observed that, the mean Nusselt number decreases with increasing partition number. It is inversely proportional to (1+N) for N≤4. For all partition numbers, the mean Nusselt number increases with increasing Rayleigh number. On the other hand, the cavity aspect ratio does not affect the mean Nusselt number to a considerable extent for considered aspect ratios in this study.     

Natural convection and conduction heat transfer in open shallow cavities with bounding walls

A numerical study has been carried out on inclined open shallow cavities, which are formed by a wall and horizontal fins. Constant heat flux is applied on the surface of the wall inside the cavity while its other surface was kept isothermal. The wall and the fins are conductive. Conjugate heat transfer by natural convection and conduction is studied by numerically solving equations of mass, momentum and energy. Streamlines and isotherms are produced, heat and mass transfer is calculated. A parametric study is carried out using following parameters: Rayleigh number from 10⁶ to 10¹², conductivity ratio from 1 to 60, open cavity aspect ratio from 1 to 0.125, dimensionless end wall thickness from 0.05 to 0.20, horizontal walls from 0.01 to 0.15 and inclination of the end wall from 90° to 45°. It is found that the volume flow rate and Nusselt number are a decreasing function of the cavity aspect ratio, horizontal fin thickness and conductivity ratio. They are an increasing function of end wall thickness and inclination angle, except in the latter case optima exist at high Rayleigh numbers.