Nodal Topology in Compact Thermal Models

2007 ◽  
Author(s):  
D. H. Greisen ◽  
V. P. Manno
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Flux ◽  
Heat Transfer Coefficient ◽  
Boundary Conditions ◽  
Transfer Coefficient ◽  
Area Ratio ◽  
System Level ◽  
Thermal Models ◽  
Single Boundary

Compact Thermal Models (CTMs) utilize a few connected thermal nodes to represent the thermal characteristics of electronic packages. These models are preferable to highly discretized models in preliminary design and system level analysis because of their computational efficiency. Surface heat flux non-uniformities often make it necessary to subdivide the package surfaces into multiple CTM nodes. This division is often quantified as the surface area ratio. This work assesses CTM performance sensitivity to area ratio changes and variation in heat transfer coefficient boundary conditions. CTMs for benchmark TQFP and BGA packages are developed using an admittance matrix approach. While optimum area ratios are identified, a direct correlation between these optimal values and the heat flux distributions computed from fully-discretized models was not obtained. CTM performance was found to be sensitive to changes in the heat transfer coefficient used to generate the CTM parameter values. A critical generating heat transfer coefficient was determined such that the resulting CTM, when optimized for a single boundary condition, was relatively accurate over the whole set of boundary conditions considered. This single boundary condition also provided an upper bound for error. This finding could be significant in future CTM development procedures.

Alternative and Relevant Representation to Heat Transfer Coefficient for Modeling the Heat Transfer Between a Fluid and a Non-Isothermal Wall in Transient Regime

2010 ◽  
Author(s):  
Benjamin Remy ◽  
Alain Degiovanni
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Heat Transfer Coefficient ◽  
Steady State ◽  
Boundary Conditions ◽  
Transfer Coefficient ◽  
Flat Plate ◽  
Temperature Difference ◽  
Interfacial Heat Transfer ◽  
Thermal Boundary Conditions

This paper deals with the relevant model that can be proposed for modeling the interfacial heat transfer between a fluid and a wall in the case of space and time varying thermal boundary conditions. Usually, for a constant and uniform heat transfer (unidirectional steady-state regime), the problem can be solved introducing a heat transfer coefficient h, uniform in space and constant in time that linearly links the surface heat flux and the temperature difference between the wall temperature Tw and an equivalent fluid temperature Tf. The problem we consider in this work concerns the heat transfer between a steady-state fluid flow and a wall submitted to a transient and non uniform thermal solicitations, as for instance a steady-state flow on a flat plate submitted to a transient and space reduced heat flux. We will show that the more interesting representation for describing the interfacial heat transfer is not to define as usually done a non-uniform and variable heat transfer coefficient h(x,t) because as it depends on the thermal boundary conditions, it is not really intrinsic. We propose an alternative approach, which consists in introducing a generalized impedance Z(ω,p) that links in space and time domain the heat flux and the temperature difference through a double convolution product instead of a scalar product. After the presentation of the general problem, the simple case of a stationary piston flow that can be solved analytically will be considered for validation both in thermal steady-state and transient regimes. To conclude and show the interest of our approach, a comparison between a global approach and a numerical simulation in a more complex and realistic case taking into account the thermal coupling with a flat plate will be presented.

Thermal Spreading Resistance in Flux Channel With Arbitrary Heat Convection in the Sink Plane

2014 ◽  
Author(s):  
Masood Razavi ◽  
Yuri S. Muzychka ◽  
Serpil Kocabiyik
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Transfer Coefficient ◽  
Boundary Conditions ◽  
Thermal Resistance ◽  
Transfer Coefficient ◽  
Fourier Series Expansion ◽  
Arbitrary Distribution ◽  
Spreading Resistance ◽  
Microelectronic Devices

Thermal spreading resistance is one of the key factors for designing the thermal management systems in microelectronic devices. This type of thermal resistance occurs in most of the microelectronic devices and causes some difficulties for thermal engineers to model the system. One of the common geometries in these devices is the flux channel. Different boundary conditions can be applied on the flux channel based on the designing criteria of the system including the arbitrary distribution of heat sinks over the sink plane. This boundary condition is usually simplified as a constant heat transfer coefficient to facilitate the modeling of the system. In this paper, a flux channel with an arbitrary distributed heat transfer coefficient over the sink plane is studied without simplification of the sink boundary condition. Both adiabatic and convective cooling over the edges of the flux channel are considered. Due to the complexity of the sink boundary condition, the conventional analytical solutions are not applicable and the method of least squares is used. By employing this approach, the effect of a non-uniform heat transfer coefficient on thermal spreading resistance is investigated. The solution is presented in form of a Fourier series expansion which can be used to obtain the temperature all over the channel. Results are validated with Finite Element Models, FEM. This approach is useful for thermal engineers who have some difficulty for modeling complex boundary conditions and presents an effective solution for thermal resistance in the flux channels.

scholarly journals Method for Determining the Boundary Condition of Heat Transfer in Mold for Slab Casting

2021 ◽  
Vol 2101 (1) ◽  
pp. 012037
Author(s):  
Junli Guo ◽  
Jin Zou ◽  
Changlin Yang ◽  
Deping Lu ◽  
Lefei Sun
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Flux ◽  
Temperature Field ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Casting Speed ◽  
Cooling Condition ◽  
Average Heat Transfer Coefficient ◽  
Average Heat

Abstract The calculation of temperature field in the mold is important for the study of solidification process of liquid steel. In order to calculate the accurate temperature field of slab in the mod, the boundary condition of heat transfer in the mold should be determined before the calculation of slab temperature. In this paper, the relationship among the average heat transfer coefficient in the mold, the physical properties of steel, the cast condition and the cooling condition is derived according to the energy conservation equation and the Fourier law of heat conduction. Furthermore, the method for determining the parameters related to the formula of boundary heat flux is introduced. Results indicate that the average heat transfer coefficient in the mold ranges from 450 to 2000 W·(m2oC)−1 for conventional caster with a casting speed ranging from 0.8 and 1.8 m·min-1. The average heat transfer coefficient increases with the increase of casting speed. Besides, the casting speed has an effect on the parameters in the formula of calculating boundary heat flux, which indicates that the casting speed and the cooling condition should be taken into consideration for determining parameters related to the formula of calculating surface heat flux in the mold.

scholarly journals Measurements of absorbed heat flux and water-side heat transfer coefficient in water wall tubes

2011 ◽  
Vol 32 (1) ◽  
pp. 77-88 ◽  
Author(s):  
Jan Taler ◽  
Dawid Taler ◽  
Andrzej Kowal
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Heat Transfer Coefficient ◽  
Boundary Conditions ◽  
Transfer Coefficient ◽  
Flux Tube ◽  
Water Flux ◽  
Water Wall ◽  
Water Side ◽  
Steam Boilers

Measurements of absorbed heat flux and water-side heat transfer coefficient in water wall tubes The tubular type instrument (flux tube) was developed to identify boundary conditions in water wall tubes of steam boilers. The meter is constructed from a short length of eccentric tube containing four thermocouples on the fire side below the inner and outer surfaces of the tube. The fifth thermocouple is located at the rear of the tube on the casing side of the water-wall tube. The boundary conditions on the outer and inner surfaces of the water flux-tube are determined based on temperature measurements at the interior locations. Four K-type sheathed thermocouples of 1 mm in diameter, are inserted into holes, which are parallel to the tube axis. The non-linear least squares problem is solved numerically using the Levenberg-Marquardt method. The heat transfer conditions in adjacent boiler tubes have no impact on the temperature distribution in the flux tubes.

Single Phase Heat Transfer In Parallel Micro-Channel Heat Sink

2018 ◽  
pp. 11-16
Author(s):  
R. AL-Khafajy
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Flux ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Test Section ◽  
Single Phase ◽  
Electric Heater ◽  
Micro Channel ◽  
Parallel Channels

A copper parallel channels test piece has built into the test section containing twenty five, one mm by one mm, parallel channels the channels were fifty mm long; the Heat-transfer coefficients for single-phase are reported. Micro- channel was Square shape and the test section has a glass top plate to permit visual observations. The data are taken while the rig is working .The test section is received the heat by an electric heater is associated normally with a boundary condition for constant heat flux. Because the important variation in the single-phase - heat-transfer coefficient in the inlet zone, the interceding copper and aluminum material is shown to make the test section close isothermal wall boundary condition. The heat conduction influence is taken into computation in the data analysis finally; the effective heat flux and the single-phase heat transfer coefficient are reported in this paper experiments and predictions. Key words— Single phase Heat transfer cofficients , Parallel channels ,Heat flux,Mass flux.

scholarly journals Experimental Determination of the Heat Transfer Coefficient of Real Cooled Geometry Using Linear Regression Method

Energies ◽  
2020 ◽  
Vol 14 (1) ◽  
pp. 180
Author(s):  
Asif Ali ◽  
Lorenzo Cocchi ◽  
Alessio Picchi ◽  
Bruno Facchini
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Heat Transfer Coefficient ◽  
Linear Regression ◽  
Surface Temperature ◽  
Transfer Coefficient ◽  
External Surface ◽  
Internal Surface ◽  
Regression Method ◽  
Thermal Transient

The scope of this work was to develop a technique based on the regression method and apply it on a real cooled geometry for measuring its internal heat transfer distribution. The proposed methodology is based upon an already available literature approach. For implementation of the methodology, the geometry is initially heated to a known steady temperature, followed by thermal transient, induced by injection of ambient air to its internal cooling system. During the thermal transient, external surface temperature of the geometry is recorded with the help of infrared camera. Then, a numerical procedure based upon a series of transient finite element analyses of the geometry is applied by using the obtained experimental data. The total test duration is divided into time steps, during which the heat flux on the internal surface is iteratively updated to target the measured external surface temperature. The final procured heat flux and internal surface temperature data of each time step is used to find the convective heat transfer coefficient via linear regression. This methodology is successfully implemented on three geometries: a circular duct, a blade with U-bend internal channel, and a cooled high pressure vane of real engine, with the help of a test rig developed at the University of Florence, Italy. The results are compared with the ones retrieved with similar approach available in the open literature, and the pros and cons of both methodologies are discussed in detail for each geometry.

scholarly journals Darcy-Brinkman free convection about a wedge and a cone subjected to a mixed thermal boundary condition

1992 ◽  
Vol 15 (4) ◽  
pp. 789-794 ◽  
Author(s):  
G. Ramanaiah ◽  
V. Kumaran
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Flux ◽  
Porous Medium ◽  
Heat Transfer Coefficient ◽  
Free Convection ◽  
Transformation Group ◽  
Darcy Number ◽  
Thermal Boundary Condition ◽  
High Porosity

The Darcy-Brinkman free convection near a wedge and a cone in a porous medium with high porosity has been considered. The surfaces are subjected to a mixed thermal boundary condition characterized by a parameterm;m=0,1,∞correspond to the cases of prescribed temperature, prescribed heat flux and prescribed heat transfer coefficient respectively. It is shown that the solutions for differentmare dependent and a transformation group has been found, through which one can get solution for anymprovided solution for a particular value ofmis known. The effects of Darcy number on skin friction and rate of heat transfer are analyzed.

Experimental Evidence of Temperature Ratio Effect on Turbine Blade Tip Heat Transfer

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
H. Jiang ◽  
Q. Zhang ◽  
L. He ◽  
S. Lu ◽  
L. Wang ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Boundary Conditions ◽  
Transfer Coefficient ◽  
Experimental Evidence ◽  
Turbine Blade ◽  
Tip Clearance ◽  
Temperature Ratio ◽  
Thermal Boundary Conditions ◽  
Thermal Measurements

Determination of a scalable Nusselt number (based on “adiabatic heat transfer coefficient”) has been the primary objective of the most existing heat transfer experimental studies. Based on the assumption that the wall thermal boundary conditions do not affect the flow field, the thermal measurements were mostly carried out at near adiabatic condition without matching the engine realistic wall-to-gas temperature ratio (TR). Recent numerical studies raised a question on the validity of this conventional practice in some applications, especially for turbine blade. Due to the relatively low thermal inertia of the over-tip-leakage (OTL) flow within the thin clearance, the fluids' transport properties vary greatly with different wall thermal boundary conditions and the two-way coupling between OTL aerodynamics and heat transfer cannot be neglected. The issue could become more severe when the gas turbine manufacturers are making effort to achieve much tighter clearance. However, there has been no experimental evidence to back up these numerical findings. In this study, transient thermal measurements were conducted in a high-temperature linear cascade rig for a range of tip clearance ratio (G/S) (0.3%, 0.4%, 0.6%, and 1%). Surface temperature history was captured by infrared thermography at a range of wall-to-gas TRs. Heat transfer coefficient (HTC) distributions were obtained based on a conventional data processing technique. The profound influence of tip surface thermal boundary condition on heat transfer and OTL flow was revealed by the first-of-its-kind experimental data obtained in the present experimental study.

Meshless Local Petrov-Galerkin Method for Heat Transfer Analysis

2013 ◽  
Author(s):  
Singiresu S. Rao
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Boundary Conditions ◽  
Transfer Coefficient ◽  
Transfer Problem ◽  
Radiation Heat Transfer ◽  
Heat Transfer Problem ◽  
Radiation Heat ◽  
Mlpg Method ◽  
Transfer Problems

A meshless local Petrov-Galerkin (MLPG) method is proposed to obtain the numerical solution of nonlinear heat transfer problems. The moving least squares scheme is generalized, to construct the field variable and its derivative continuously over the entire domain. The essential boundary conditions are enforced by the direct scheme. The radiation heat transfer coefficient is defined, and the nonlinear boundary value problem is solved as a sequence of linear problems each time updating the radiation heat transfer coefficient. The matrix formulation is used to drive the equations for a 3 dimensional nonlinear coupled radiation heat transfer problem. By using the MPLG method, along with the linearization of the nonlinear radiation problem, a new numerical approach is proposed to find the solution of the coupled heat transfer problem. A numerical study of the dimensionless size parameters for the quadrature and support domains is conducted to find the most appropriate values to ensure convergence of the nodal temperatures to the correct values quickly. Numerical examples are presented to illustrate the applicability and effectiveness of the proposed methodology for the solution of heat transfer problems involving radiation with different types of boundary conditions. In each case, the results obtained using the MLPG method are compared with those given by the FEM method for validation of the results.

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