Nusselt Number Changes Research Articles

Variable Property Nusselt Numbers in a Channel with Pin Fins

Nusselt numbers and friction factors are presented that show the effects of temperature ratio and variable properties in a rectangular channel with pin fins and an aspect ratio of 8. The ratio of air inlet stagnation temperature to local surface temperature T 0i /T w varies from 0.68 to 0.93, and Reynolds numbers based on channel height range from 1.8 x 10 4 to 3.38 × 10 4 . The pins are placed in 12 rows, with pin diameter and spacing between adjacent pins in both directions all equal to the channel height. Ratios of globally averaged Nusselt numbers to baseline, constant-property Nusselt numbers, Nu/Nu 0,cp , increase by about 35% as the temperature ratio T 0i /T w decreases, provided that Reynolds number Re H is approximately constant and that the base areas beneath the pins are not considered. When heat transfer from the pin fins is also included, this increase is about the same. Friction factor ratios f/f 0,cp decrease as T 0i /T w decreases over this same range of values. Such global Nusselt number changes are a result of local Nusselt number ratio increases with decreasing temperature ratio, which are especially pronounced beneath the wake and shear layers that are present downstream of each pin and beneath the horseshoe vortex that forms just upstream of each pin fin.

Effects of the Aspect Ratio of Vibrated Enclosures on the Thermal Convection Field and Chaotic Characteristics.

In this paper the time-dependent characteristics of the thermal convection field in rectangular enclosures with large aspect ratio exposed vertical vibration were numerically examined and the results were compared with the ones of square enclosure. In the computation the Prandtl number, the Rayleigh number and the vibration Grashof number were held constant of 0.71, 104 and 106 respectively. The normalized angular frequency of forced vibration was changed in the range between 10 and 7680. As a result, it was ascertained that the five regimes with respect to the angular frequency proposed by Fu and Shieh for the square enclosure captured the change of surface-average Nusselt number when the chaotic characteristics were considered. It was also revealed that the vortices in the enclosure aligned to the vertical direction in the enclosure with large aspect ratio determined the characteristics of the surface-average Nusselt number on hot and cold side walls.

Heat transfer around a circular cylinder in separated air flow

An experimental study has been conducted to determine the heat transfer characteristics around a circular cylinder attached to the separated flow of air shed from a fence. The fence was located vertically to the flow with a height of H = 40 mm. d/H was constant at 0.638, where d is the cylinder diameter of 25.5 mm. X/H were 0.50 and 0.775 and Y/H ranged from 0.525 to 1.50, where X and Y are, respectively, the distances between the axis of the cylinder and the front face of the fence, and the bottom wall of the test section. The Reynolds number based on the cylinder diameter and the velocity of the undisturbed flow ranged from 1.9 × 104 to 6.0 × 104. It was found that the maximum local Nusselt number changes drastically in the vicinity of Y/H = 1.0–1.11 and that the maximum mean Nusselt number occurs in the neighborhood of Y/H = 1.24–1.43 for X/H = 0.50 and 1.3–1.4 for X/H = 0.775. © 1999 Scripta Technica, Heat Trans Asian Res, 28(3): 211–226, 1999

Forced convection of a power-law fluid in a porous channel - numerical solutions

A detailed numerical study of laminar forced convection in a porous channel which contains a fibrous medium saturated with a power-law fluid was performed. Hydrodynamic and heat transfer results are presented for a configuration that has uniform heat flux or uniform temperature heating at the walls. The flow in the porous medium was modeled using the modified Brinkman-Forchheimer-extended Darcy model for power law fluids in which the non-Darcy effects of inertia and boundary were considered. Parametric studies were conducted to examine the effects of Darcy number, power law index, inertia parameter and Prandtl number. The results indicate that when the power law index is decreased, the velocity gradient near the walls increases but these effects are reduced gradually as the Darcy number decreases until the Darcy regime (Da≤10−6) is reached in which case the effects of power law index become negligible. As the power law index is decreased, the thermal boundary layer thickness decreases significantly only in the non-Darcy regime. Consequently, as the power law index decreases, the fully developed Nusselt number increases considerably in the non-Darcy regime whereas in the Darcy regime the change in Nusselt number is very small. As the Prandtl number increases, the local Nusselt number increases and this effect is more significant for shear thinning fluids (n<1.0).

Melting heat transfer characteristics of a horizontal ice cylinder immersed in an immiscible liquid

The melting characteristics of a horizontal ice cylinder immersed in an immiscible liquid were investigated both experimentally and analytically. A clear cylindrical ice layer formed around a horizontal cooling tube with a coaxial outer heated tube was melted in oil as the test immiscible liquid in the annulus between the ice and outer tube. Both the melting behavior of ice and the flow patterns of the immiscible liquid were observed under a variety of outer wall temperature conditions. In the analysis, two boundary layers were introduced for both the melt water film and ambient liquid, respectively. It was found from the experiments that the tendency of the mean Nusselt number changes clearly at Ra = 10 6 , which corresponds to the temperature condition To = 12.0 °C. This analysis might be used to estimate the melting characteristics of such a system during the initial stage oflow temperature conditions.

Melting heat transfer characteristics of a horizontal ice cylinder immersed in an immiscible liquid

The melting characteristics of a horizontal ice cylinder immersed in an immiscible liquid were investigated both experimentally and analytically. A clear cylindrical ice layer formed around a horizontal cooling tube with a coaxial outer heated tube was melted in oil as the test immiscible liquid in the annulus between the ice and outer tube. Both the melting behavior of ice and the flow patterns of the immiscible liquid were observed under a variety of outer wall temperature conditions. In the analysis, two boundary layers were introduced for both the melt water film and ambient liquid, respectively. It was found from the experiments that the tendency of the mean Nusselt number changes clearly at Ra = 106, which corresponds to the temperature condition T0 = 12.0 °C. This analysis might be used to estimate the melting characteristics of such a system during the initial stage of low temperature conditions. © 1998 Scripta Technica, Heat Trans Jpn Res, 27(5): 336–352, 1998

Melting Heat Transfer Characteristics of a Horizontal Ice Cylinder Immersed in Immiscible Liquid.

Melting characteristics of a horizontal ice cylinder immersed within immiscible liquid have been investigated both experimentally and analytically. A clear cylindrical ice layer formed around the horizontal cooling tube with coaxial outer heated tube was melt in the oil as a testing immiscible liquid in the annulus between ice and outer tube. Both the melting behavior of ice and flow pattern of immiscible liquid were observed under a variety of outer wall temperature conditions. In the analysis, a couple of boundary layers were introduced for both melt water film and ambient liquid. respectively. It was found from the experiment that the tendency of mean Nusselt number changes obviously at Ra=105 which corresponds to the temperature condition T0=12.0°C. The present analysis might be utilized to estimate the melting characteristics of such a system for initial stage of low temperature conditions.

Heat Transfer around a Circular Cylinder in Separated Air Flow.

An experimental study has been conducted to determine the heat transfer characteristics around a circular cylinder attached to the separated flow of air shed from a fence. The fence was located vertically to the flow with a height of H=40mm. d/H was constant at 0.638, where d is the cylinder diameter of 25.5mm. X/H were 0.50, 0.775, and Y/H ranged from 0.525 to 1.50, where X and Y are, respectively, the distances between the axis of the cylinder and the front face of the fence, and the bottom wall of the test section. The Reynolds number Re based on the cylinder diameter and the velocity of the undisturbed flow ranged from 1.9×104 to 6.0×104. It was found that the maximum local Nusselt number changes drastically in the vicinity of Y/H=1.0∼1.11, and that the maximum mean Nusselt number occurs in the neighborhood of Y/H=1.24∼1.43 for X/H=0.50, and 1.3∼1.4 for X/H=0.775.

Experimental study of heat and momentum transfer in rotating channel flow

The enhancement of momentum and heat transfer caused by stationary streamwise vortices due to a Coriolis instability in a rotating straight channel is examined. It is shown that the changes in skin friction and Nusselt number depend on changes in the spanwise averaged mean flow and temperature distributions. Hot wire anemometry was used to experimentally determine the streamwise velocity and temperature distributions in a cross stream plane 68 channel widths downstream of the inlet. A technique to accurately compensate the velocity readings for the varying temperature in the channel was developed. It is shown that the streamwise vortices give rise to disturbance profiles which are close to those obtained from linear theory for small rotation numbers and that in this region there is no enhancement of either the averaged momentum or heat transfer. However, even for a disturbance amplitude in the streamwise velocity of the order of 20%, the disturbances are close to linear (both the disturbance distribution and growth rate). In this weakly non-linear region the changes in the mean flow and temperature distributions could be estimated by using the linear eigenfunctions of the disturbances where the amplitude was taken from the measurements. In the fully non-linear (saturated) region the Nusselt number on both the stable and unstable side of the channel was almost twice that at no rotation, however, the skin friction was almost unaffected on the stable side. This shows that the Reynolds analogy between momentum and heat transfer is not valid in this flow situation.

An investigation into a falling film type cooling tower

A model for a falling film type cooling tower has been developed to investigate the effect of tower parameters as well as the effect of liquid-side thermal resistance on the tower performance. The energy equation is used to determine the temperature distribution across the liquid film. The heat and mass transfer processes between the liquid film and air bulk are described using three ordinary differential equations. The energy equation was solved using a finite difference Crank-Nicolson scheme. The heat and mass transfer equations were solved using the Runge-Kutta method. The results obtained show that an increase in tower characteristic KaV/ L under the same conditions improves the tower performance. The converse is true in the case of increased water to air mass flowrate ratio, L/ G. The Lewis number, Le, shows no significant effect on the tower performance. The effect of tower parameters as well as the water inlet temperature on the liquidside Nusselt number and the tower effectiveness was also studied. The results show very insignificant changes in Nusselt number, whereas the effectiveness increases with increasing KaV/ L and reduces with L/ G, but very insignificant changes occur with Le. The present model is also compared with Merkel's equation. Under the same conditions and with Le equal to unity, the results of the Merkel equation shows a smaller approach than that obtained by the present model.

A Two-Dimensional Jet Impinging Heat Transfer on a Circular Cylinder. 2nd Report. Effect of Angles between Two Plates Mounted near the Cylinder.

A circular cylinder of 50 mm diameter (D) was placed in a two-dimensional jet. The flow pattern was changed by mounting two large flat plates symmetrically near the cylinder maintaining a clearance (C) between the cylinder and each plate. The half-angle (ψ) between the plates and the clearance were varied (ψ=20°∼60° ; C/D≤0. 3). The jet velocity and nozzle-to-cylinder distance (L) were also changed. The pressure distribution around the cylinder for the case of C/D≤0. 1 differs markedly from that for the case of C/D≥0. 2. In the former case, pressure fluctuation is suppressed and no peak is observed in the spectrum of velocity fluctuation. Thus, the suppression of self-induced flow oscillation is suggested for the case of C/D≤0. 1. The value of peak Nusselt number changes remarkably with the values of ψ and C/D. The mean Nusselt number is clearly larger in any geometrical condition other than that obtained without an insertion of the plates.

Natural convection heat transfer in horizontal annulus with an open trough (black body solar energy receiver)

An experimental study was carried out to investigate natural convection heat transfer inside a horizontal annulus with an open longitudinal trough that simulates a black body solar energy receiver. The effect of the trough location and annulus eccentricity on Nusselt number is presented. The results indicated that the Nusselt number lies between the two limiting cases of closed annulus and free horizontal cylinder. An enhancement of natural convection takes place by positioning the inner tube below the annulus center line (negative eccentricity). No significant changes in Nusselt number were found to occur when the trough was tilted between the vertical position and 45° from the horizontal.

Natural convection heat transfer in horizontal annulus with an open trough (Black Body Solar Energy Receiver)

An experimental study was carried-out to investigate natural convection heat transfer inside a horizontal annulus with an open longitudinal trough, that simulates a black body solar energy receiver. The effect of Rayleigh number, the annulus eccentricity, and the trough location on Nusselt number is presented. The results indicated that Nusselt number lies between the two limiting cases of closed annulus and and free horizontal cylinder. At low Rayleigh number, convection is relatively weak and Nusselt approaches the value of closed annulus. As Rayleigh increases, Nusselt number approaches the value of free cylinder. An enhancement of natural convection takes place by positioning the inner tube below the annulus center line (negative eccentricity). No significant changes in Nusselt number were found to take place when the trough was titled between the vertical position and 45 degree from the horizontal.

Natural Convection Heat Transfer in an Anisotropic Porous Matrix Heated from Below.

Natural convection heat transfer in a saturated porous matrix whose permeability is anisotropic is analyzed by a finite-element method. A specific problem involves the convection in a square box heated from below. The Rayleigh number is defined at vertical permeability, according to Kvernvold and Tyvand. The calculated critical Rayleigh numbers agree well with the linear stability theory. Variations of the Nusselt numbers with the Rayleigh numbers for various values of the x-to-y permeability ratio and cell number are calculated. It is found that the ratio and cell numbers have a great effect on the properties of natural convection heat transfer and the number of convection cells realized in a square space. Unsteady temperature distribution and Nusselt number changes in the transient state are also calculated.

Computation of Forced Laminar Convection in Rotating Cavities

Finite difference solutions are presented for forced laminar convection in a rotating cylindrical cavity with radial outflow. This forms a simple model of the cooling flow between two compressor disks in a gas turbine engine. If the fluid enters the cavity from a uniform radial source, it is shown that the local Nusselt number changes from that of a “free disk” near the center of the cavity to that for Ekman layer flow at larger radii. With an axial inlet, the flow, and consequently, the heat transfer, is more complex. If vortex breakdown occurs, then the results are very similar to those for the radial inlet case, but otherwise a wall jet forms on the downstream disk, and the heat transfer from this disk may be several times that for the upstream disk. Variation of mean Nusselt number with rotational speed is qualitatively similar to previously published experimental measurements in turbulent flow. The effect of Prandtl number on heat transfer has also been demonstrated.

Heat transfer through a rotating channel in porous medium

A theoretical analysis of the hydrodynamic flow and its temperature distribution in a porous medium is presented for an incompressible viscous fluid in a rotating channel, bounded by two impermeable infinite parallel plates at a constant temperature, under the action of a uniform pressure gradient in the direction of the flow. An exact solution of the governing equations is obtained. The flow is governed by the Darcy’s number σ dependent on the permeabilityk of the medium and the Taylor numberT. The primary and the secondary flows, the temperature distribution, the shear stresses and the Nusselt number at the plates are studied in detail for various values of σ andT. In general, σ is found to have a stronger influence in reducing the mass flux and the temperature of the flow compared to rotation. For large values of σ (σ>10), there is no appreciable change in temperature and Nusselt number with rotation. When σ andT are large, the flow is confined to a boundary layer in the vicinity of the plates.