Application of a Complex Nusselt Number to Heat Transfer During Compression and Expansion

1994 ◽  
Vol 116 (3) ◽  
pp. 536-542 ◽  
Author(s):  
A. A. Kornhauser ◽  
J. L. Smith
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Temperature Difference ◽  
Rate Of Change ◽  
Transfer Model ◽  
Volume Data ◽  
Piston Cylinder ◽  
Compression And Expansion ◽  
Experimental Pressure

Heat transfer during compression and expansion can be out of phase with bulk gas-wall temperature difference. An ordinary convective heat transfer model is incapable of predicting this phenomenon. Expressions for compression/expansion heat transfer developed from simple conduction models use a complex heat transfer coefficient. Thus, heat flux consists of one part proportional to temperature difference plus a second part proportional to rate of change of temperature. Surface-averaged heat flux was calculated from experimental pressure-volume data for piston-cylinder gas springs over a range of speeds, pressures, gases, and geometries. The complex Nusselt number model proved capable of correlating both magnitude and phase of the measured heat transfer as functions of an oscillation Peclet number.

scholarly journals EFFECT OF CAVITY RATIO ON HEAT TRANSFER BY FREE LOAD FROM HEATED PLATES UPWARD WITH CONSTANT HEAT FLUX

2021 ◽  
Vol 9 (12) ◽  
pp. 686-695
Author(s):  
Waleed Abdulhadiethbayah ◽  
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Free Convection ◽  
Electronic Devices ◽  
Experimental Studies ◽  
Constant Heat Flux ◽  
Rate Of Change ◽  
Constant Heat ◽  
The Difference

Many engineering and industrial applications always seek to find ways to dissipate heat from heated surfaces used in these industries. As it is involved in the cooling of electronic parts and electrical transformers, as well as the design of solar collectors, in addition to being a process of heat exchange between hot surfaces and the fluids in contact with them. Since most electronic devices or their parts are cooled by removing the heat generated inside them by using air as a heat transfer medium and in a free convection way, and the fact that heat transfer by free convection occurs in many fields, so there were many studies that dealt with this topic. The free load is generated by the buoyant force (Bouncy force) As a result of the difference in the density of the fluid adjacent to the heated surface due to the difference in temperatures between the fluid and the surface. The laminar flow along surfaces has been extensively studied analytically [1,2,3,4] In the horizontal, inclined and vertical case, whether by constant heat flux or constant surface temperature, there are also many experimental studies of heat transfer by free convection from horizontal, inclined and vertical surfaces with constant heat flux or constant surface temperature [5,6,7,8]. Some experimental studies have also been conducted on heat transfer by convection from heated surfaces in the form of a disk (ring)The outcome of these studies was to extract an exponential mathematical relationship between the average of Nusselt number and the Kirchhoff number or Rayleigh number and the following formula: (Nu=C(Ra) n It is one of the most suitable formulas for heat transfer by free convection from heated surfaces in all its forms and over a wide range of Rayleigh number . It is noted that not all of these studies dealt with the study of the effect of the cavity ratio on heat transfer by free convection from square-shaped surfaces, which is the form that is more applied in electronic devices. Therefore, the current research means studying the rate of change in the average of Nusselt number, which represents a function of the rate of change in the rate of heat transfer by convection, as well as studying the thermal gradient above the surface, and this was done through using three hollow surfaces in proportions (0.25,0.5,0.75) of the total area.

Heat Transfer During Compression and Expansion of Gas

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Masutaka Ota ◽  
Yoshihiko Haramura
Keyword(s):  
Heat Transfer ◽  
Specific Heat ◽  
Peclet Number ◽  
Volume Data ◽  
Péclet Number ◽  
Surface Areas ◽  
Piston Cylinder ◽  
Wide Range ◽  
Compression And Expansion ◽  
Extended Surface

Abstract Heat transfer during compression and expansion of gas is investigated to obtain a correlation that is easy to use in the design of the reciprocating energy conversion machines. We carried out experiments to measure the heat transfer characteristics to̸from gas during compression and expansion to obtain the correlation. These measurements were performed using a piston-cylinder assembly over a range of volume ratios, frequencies, mean pressures, gases, and internal extended surface areas. The heat transfer was estimated thermodynamically from experimental pressure-volume data. Dimensionless groups for heat transfer are discussed in order to correlate the data. The product of the dimensionless heat transfer and specific heat ratio was found to be optimal and was correlated with only the Peclet number for a wide range of conditions, even for gases having different specific heat ratios. The temperature amplitude of the center of the test space was obtained, and it is found that the penetration depth reached the center when the Peclet number is in the range from 20 to 30.

Experimental Study on the Effect of Low Acute Side Angles on Heat Transfer in Rhombic Shaped Microchannel

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Sunil K. Dwivedi ◽  
Sandip K. Saha
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Experimental Study ◽  
Heat Flux ◽  
Nusselt Number ◽  
Three Dimensional ◽  
Constant Heat Flux ◽  
Numerical Results ◽  
Transfer Model ◽  
Design And Optimization

This experimental study on rhombic shaped microchannels was conducted to understand the effect of a low acute side angle on the Nusselt number and compare the results with the published numerical results for H1 (axially constant heat flux and circumferentially constant temperature) and H2 (constant axial and circumferential wall heat flux) boundary conditions. The hydraulic and heat transfer characteristics of the rhombic geometry with a side angle of 30 deg for different mass flow rates and heat flux inputs are obtained using a three-dimensional (3D) conjugate heat transfer model, which is validated with the experimental results. It is found that the average Nusselt number obtained from the experimental and numerical results can be approximated closely with that computed using the H1 boundary condition. The local Nusselt number of hydrodynamically and thermally developed regions obtained from the numerical analysis is compared with a correlation for the H1 boundary condition. These results will be useful in design and optimization of a rhombic shaped microchannel for electronic cooling applications.

Steady and transient thermal convection in a fluid layer with uniform volumetric energy sources

1977 ◽  
Vol 83 (2) ◽  
pp. 375-395 ◽  
Author(s):  
F. A. Kulacki ◽  
A. A. Emara
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Steady State ◽  
Rayleigh Number ◽  
Time Scales ◽  
Temperature Difference ◽  
Number Range ◽  
Volumetric Heating ◽  
Steady State Temperature

Measurements of the overall heat flux in steady convection have been made in a horizontal layer of dilute aqueous electrolyte. The layer is bounded below by a rigid zero-heat-flux surface and above by a rigid isothermal surface. Joule heating by an alternating current passing horizontally through the layer provides a uniformly distributed volumetric energy source. The Nusselt number at the upper surface is found to be proportional to Ra0[sdot ]227 in the range 1[sdot ]4 ≤ Ra/Rac ≤ 1[sdot ]6 × 109, which covers the laminar, transitional and turbulent flow regimes. Eight discrete transitions in the heat flux are found in this Rayleigh number range. Extrapolation of the heat-transfer correlation to the conduction value of the Nusselt number yields a critical Rayleigh number which is within -6[sdot ]7% of the value given by linearized stability theory. Measurements have been made of the time scales of developing convection after a sudden start of volumetric heating and of decaying convection when volumetric heating is suddenly stopped. In both cases, the steady-state temperature difference across the layer appears to be the controlling physical parameter, with both processes exhibiting the same time scale for a given steady-state temperature difference, or [mid ]ΔRa[mid ]. For step changes in Ra such that [mid ]ΔRa[mid ] > 100Rac, the time scales for both processes can be represented by Fo [vprop ] [mid ]ΔRa[mid ]m, where Fo is the Fourier number of the layer. Temperature profiles of developing convection exhibit a temperature excess in the upper 15–20 % of the layer in the early stages of flow development for Rayleigh numbers corresponding to turbulent convection. This excess disappears when the average core temperature becomes large enough to permit eddy transport and mixing processes near the upper surface. The steady-state limits in the transient experiments yield heat-transfer data in agreement with the results of the steady-state experiments.

The Infrared Characteristics of the Wall Temperature of Boiling Heat Transfer in Microchannel

2011 ◽  
Vol 383-390 ◽  
pp. 811-815
Author(s):  
Hu Gen Ma ◽  
Jian Mei Bai ◽  
Rong Jian Xie ◽  
Wen Jing Tu
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Wall Temperature ◽  
Boiling Heat Transfer ◽  
Transfer Test ◽  
Axial Direction ◽  
Transfer Model ◽  
Micro Channel ◽  
Vapor Quality ◽  
Test Rig

In this paper, the boiling heat transfer test rig was designed and built, while the characteristics of boiling Heat Transfer of refrigerants in micro-channel was researched. The wall temperature of micro-channel was measured by TH5104 Infrared thermography. The results showed that there were obvious variations for wall temperature of micro-channel along the axial direction when boiling heat transfer occurred in the micro-channel. The temperature distribution affected obviously by the heat flux, mass flow rate; vapor quality and heat transfer model.

A Heat Transfer Model of Dropwise Condensation Underneath a Horizontal Substrate

2011 ◽  
Vol 199-200 ◽  
pp. 1604-1608
Author(s):  
Yun Fu Chen
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Contact Angle ◽  
Fractal Model ◽  
Condensation Heat Transfer ◽  
Droplet Growth ◽  
Transfer Model ◽  
Dropwise Condensation ◽  
Small Contact Angle ◽  
Horizontal Substrate

For finding influence of the condensing surface to dropwise condensation heat transfer, a fractal model for dropwise condensation heat transfer has been established based on the self-similarity characteristics of droplet growth at various magnifications on condensing surfaces with considering influence of contact angle to heat transfer. It has been shown based on the proposed fractal model that the area fraction of drops decreases with contact angle increase under the same sub-cooled temperature; Varying the contact angle changes the drop distribution; higher the contact angle, lower the departing droplet size and large number density of small droplets; dropwise condensation translates easily to the filmwise condensation at the small contact angle ;the heat flux increases with the sub-cooled temperature increases, and the greater of contact angle, the more heat flux increases slowly.

A New Nusselt Number for Complicated Configurations

2013 ◽  
Author(s):  
Tom I-Ping Shih ◽  
Srisudarshan Krishna Sathyanarayanan
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Local Heat ◽  
Negative Slope ◽  
Test Problems ◽  
Rectangular Duct ◽  
Circular Duct ◽  
Flow And Heat Transfer ◽  
Local Heat Flux

Convective heat transfer over surfaces is generally presented in the form of the heat-transfer coefficient (h) or its nondimensional form, the Nusselt number (Nu). Both require the specification of the free-stream temperature (Too) or the bulk (Tb) temperature, which are clearly defined only for simple configurations. For complicated configurations with flow separation and multiple temperature streams, the physical significance of Too and Tb becomes unclear. In addition, their use could cause the local h to approach positive or negative infinity if Too or Tb is nearly the same as the local wall temperature (Twall). In this paper, a new Nusselt number, referred to as the SCS number, is proposed, that provides information on the local heat flux but does not use h and hence by-passes the need to define Too or Tb. CFD analysis based on steady RANS with the shear-stress transport model is used to compare and contrast the SCS number with Nu for two test problems: (1) compressible flow and heat transfer in a straight duct with a circular cross section and (2) compressible flow and heat transfer in a high-aspect ratio rectangular duct with a staggered array of pin fins. Parameters examined include: Reynolds number at the duct inlet (3,000 to 15,000 for the circular duct and 15,000 and 150,000 for the rectangular duct), wall temperature (Twall = 373 K to 1473 K for the circular duct and 313 K and 1,173 K for the rectangular duct), and distance from of the inlet of the duct (up to 100D for the circular duct and up to 156D for the rectangular duct). For the circular duct, Nu was found to decrease rapidly from the duct inlet until reaching a minimum and then to rise until reaching a nearly constant value in the “fully” developed region if the wall is heating the gas. If the wall is cooling the gas, then Nu has a constant positive slope in the “fully” developed region. The location of the minimum in Nu and where Nu becomes nearly constant in value or in slope are strong functions of Twall. For the SCS number, the decrease from the duct inlet is monotonic with a negative slope, whether the wall is heating or cooling the gas. Also, different SCS curves for different Twall approach each other as the distance from the inlet increases. For the rectangular duct, Nu tends to oscillate about a constant value in the pin-fin region, whereas SCS tends to oscillate about a line with a negative slope. For both test problems, the variation of SCS is not more complicated than Nu, but SCS yields the local heat flux without need for Tb, a parameter that is hard to define and measure for complicated problems.

Oscillatory Heat Transfer in a Pipe Subjected to a Laminar Reciprocating Flow

1996 ◽  
Vol 118 (3) ◽  
pp. 592-597 ◽  
Author(s):  
T. S. Zhao ◽  
P. Cheng
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Heat Flux ◽  
Nusselt Number ◽  
Numerical Study ◽  
Temperature Cycle ◽  
Uniform Heat Flux ◽  
Fluid Temperature ◽  
Cycle Space ◽  
Reciprocating Flow

An experimental and numerical study has been carried out for laminar forced convection in a long pipe heated by uniform heat flux and subjected to a reciprocating flow of air. Transient fluid temperature variations in the two mixing chambers connected to both ends of the heated section were measured. These measurements were used as the thermal boundary conditions for the numerical simulation of the hydrodynamically and thermally developing reciprocating flow in the heated pipe. The coupled governing equations for time-dependent convective heat transfer in the fluid flow and conduction in the wall of the heated tube were solved numerically. The numerical results for time-resolved centerline fuid temperature, cycle-averaged wall temperature, and the space-cycle averaged Nusselt number are shown to be in good agreement with the experimental data. Based on the experimental data, a correlation equation is obtained for the cycle-space averaged Nusselt number in terms of appropriate dimensionless parameters for a laminar reciprocating flow of air in a long pipe with constant heat flux.

Heat Transfer and Flow Friction Characteristics for Compact Cold Plates

2003 ◽  
Vol 125 (1) ◽  
pp. 104-113 ◽  
Author(s):  
Chang-Yuan Liu ◽  
Ying-Huei Hung
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Thermal Resistance ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Average Nusselt Number ◽  
Cold Plate ◽  
Air Mass

Both experimental and theoretical investigations on the heat transfer and flow friction characteristics of compact cold plates have been performed. From the results, the local and average temperature rises on the cold plate surface increase with increasing chip heat flux or decreasing air mass flow rate. Besides, the effect of chip heat flux on the thermal resistance of cold plate is insignificant; while the thermal resistance of cold plate decreases with increasing air mass flow rate. Three empirical correlations of thermal resistance in terms of air mass flow rate with a power of −0.228 are presented. As for average Nusselt number, the effect of chip heat flux on the average Nusselt number is insignificant; while the average Nusselt number of the cold plate increases with increasing Reynolds number. An empirical relationship between Nu¯cp and Re can be correlated. In the flow frictional aspect, the overall pressure drop of the cold plate increases with increasing air mass flow rate; while it is insignificantly affected by chip heat flux. An empirical correlation of the overall pressure drop in terms of air mass flow rate with a power of 1.265 is presented. Finally, both heat transfer performance factor “j” and pumping power factor “f” decrease with increasing Reynolds number in a power of 0.805; while they are independent of chip heat flux. The Colburn analogy can be adequately employed in the study.

scholarly journals The effect of operating parameters on the heat transfer in the heat pipe

2021 ◽  
Vol 2119 (1) ◽  
pp. 012088
Author(s):  
A. A. Litvintceva ◽  
N. I. Volkov ◽  
N. I. Vorogushina ◽  
V. A. Moskovskikh ◽  
V. V. Cheverda
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Heat Pipe ◽  
Temperature Difference ◽  
Heat Pipes ◽  
Working Fluid ◽  
Operating Parameters ◽  
Temperature Stabilization ◽  
Ir Camera ◽  
Fluid Properties

Abstract Heat pipes are a good solution for temperature stabilization, for example, of microelectronics, because these kinds of systems are without any moving parts. Experimental research of the effect of operating parameters on the heat transfer in a cylindrical heat pipe has been conducted. The effect of the working fluid properties and the porous layer thickness on the heat flux and temperature difference in the heat pipe has been investigated. The temperature field of the heat pipe has been investigated using the IR-camera and K-type thermocouples. The data obtained by IR-camera and K-type thermocouples have been compared. It is demonstrated the power transferred from the evaporator to the condenser is a linear function of the temperature difference between them.

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