A Comparison Between 2-D and 3-D Conduction Shape Factors

2003 ◽  
Author(s):  
Devashish Shrivastava ◽  
Robert Roemer
Keyword(s):  
Heat Transfer ◽  
Temperature Distribution ◽  
Cross Section ◽  
Three Dimensional ◽  
Cylindrical Vessel ◽  
Shape Factors ◽  
Axial Conduction ◽  
Power Deposition ◽  
Tissue Matrix

Conduction shape factors are frequently used in a variety of heat transfer applications to evaluate heat transfer from one three-dimensional body to another three-dimensional body. Previous investigators have used conduction shape factors derived using the 2-D cross-section of the 3-D geometries for non-heating conditions as approximations to 3-D conduction shape factors with heating and no-heating present. This paper investigates the suitability of neglecting the axial conduction and power deposition in deriving expressions for conduction shape factors for the case of a single, cylindrical vessel imbedded concentrically in a cylindrical, uniformly heated tissue matrix. It is shown that 1) conduction shape factors are functions of the deposited power and the temperature distribution and 2) the magnitudes of conduction shape factors are affected significantly by axial conduction.

Analytical Modeling of Temperature Distribution in Interposer-Based Microelectronic Systems

2013 ◽  
Author(s):  
Leila Choobineh ◽  
Dereje Agonafer ◽  
Ankur Jain
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Temperature Field ◽  
Temperature Distribution ◽  
Analytical Modeling ◽  
Three Dimensional ◽  
Heat Transfer Process ◽  
Thermal Design ◽  
Research Attention ◽  
On Chip

Heterogeneous integration in microelectronic systems using interposer technology has attracted significant research attention in the past few years. Interposer technology is based on stacking of several heterogeneous chips on a common carrier substrate, also referred to as the interposer. Compared to other technologies such as System-on-Chip (SoC) or System-in-Package (SiP), interposer-based integration offers several technological advantages. However, the thermal management of an interposer-based system is not well understood. The presence of multiple heat sources in various die and the interposer itself needs to be accounted for in any effective thermal model. While a finite-element based simulation may provide a reasonable temperature prediction tool, an analytical solution is highly desirable for understanding the fundamentals of the heat transfer process in interposers. In this paper, we describe our recent work on analytical modeling of heat transfer in interposer-based microelectronic systems. The basic governing energy conservation equations are solved to derive analytical expressions for the temperature distribution in an interposer-based microelectronic system. These solutions are combined with an iterative approach to provide the three-dimensional temperature field in an interposer. Results are in excellent agreement with finite-element solutions. The analytical model is utilized to study the effect of various parameters on the temperature field in an interposer system. Results from this work may be helpful in the thermal design of microelectronic systems containing interposers.

Heat Transfer for Laminar Flow in Spiral Ducts of Rectangular Cross Section

2005 ◽  
Vol 127 (3) ◽  
pp. 352-356 ◽  
Author(s):  
Michael W. Egner ◽  
Louis C. Burmeister
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Laminar Flow ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Radius Of Curvature ◽  
Dean Number ◽  
Aspect Ratios ◽  
Small Pitch

Laminar flow and heat transfer in three-dimensional spiral ducts of rectangular cross section with aspect ratios of 1, 4, and 8 were determined by making use of the FLUENT computational fluid dynamics program. The peripherally averaged Nusselt number is presented as a function of distance from the inlet and of the Dean number. Fully developed values of the Nusselt number for a constant-radius-of-curvature duct, either toroidal or helical with small pitch, can be used to predict those quantities for the spiral duct in postentry regions. These results are applicable to spiral-plate heat exchangers.

Simulation of Heat Transfer in Bridge-Based Micro Calorimeters

2009 ◽  
Author(s):  
Jun Yu ◽  
Zhen’an Tang ◽  
Zhengxing Huang ◽  
Chong Feng
Keyword(s):  
Heat Transfer ◽  
Heat Capacity ◽  
Temperature Distribution ◽  
Heat Generation ◽  
Silicon Substrate ◽  
Three Dimensional ◽  
Temperature Response ◽  
Differential Method ◽  
Three Dimensional Finite Element ◽  
Micro Calorimeter

Previous studies of bridge-based micro calorimeters have shown that these devices can measure heat capacity and melting point of ultra thin films with pulse scan calorimetry. The bridge-based micro calorimeters consist of a sample region and several beams that connecting the sample region with silicon substrate. Both the sample region and the beams are suspending on the silicon substrate for thermal isolation. The temperature distribution of the micro calorimeter during a heating pulse depends on the joule-heating of the heating resistor, the heat absorption and heat conduct of the bridge. The heat transfer through the beams during a pulse scan measurement is complex because there is heat generation on some beams and the temperature distribution along the beams is not uniform. Using three dimensional finite element analyses (FEA), the thermal-electrical simulations of the heat transfer in the bridge-based micro calorimeters have been performed. The heat consumption and temperature distribution at steady state analyses, the temperature response of the bridge and the heat generation of the heater at transient analyses have been calculated for the bridge-based micro calorimeter with different sample thermal conductivities and heat capacities. The simulation results indicate that for the bridge-based microcalorimeter using pulse calorimetry, when the heat capacity of the sample film is close to or larger than the heat capacity of an empty calorimeter, the differential method of getting the sample heat capacity from the difference between a micro calorimeter with and without the sample is no longer suitable because the heat transfer and temperature distributions of the two calorimeters are no longer comparable to each other.

Effects of Intersection Angles on Flow and Heat Transfer in Corrugated-Undulated Channels With Sinusoidal Waves

2006 ◽  
Vol 128 (8) ◽  
pp. 819-828 ◽  
Author(s):  
Jixiang Yin ◽  
Guojun Li ◽  
Zhenping Feng
Keyword(s):  
Heat Transfer ◽  
Cross Section ◽  
Three Dimensional ◽  
Computational Domain ◽  
Straight Channel ◽  
Flow Area ◽  
Contact Points ◽  
Flow And Heat Transfer ◽  
Different Characteristics ◽  
Steady Laminar

This paper reported three-dimensional numerical simulations of the steady laminar flow and heat transfer in corrugated-undulated channels with sinusoidal waves, aiming to investigate the effects of intersection angles (θ) between corrugated and undulated plate and Reynolds number (Re) on the flow and heat transfer. The simulations are conducted by using multi-channel computational domain for three different geometries. The code is validated against experimental results and then data for Nusselt number (Nu) and friction factor (f) are presented in a Re range of 100-1500, and intersection angle range of 30-150deg. The simulation confirms the changes of Nuu (averaged over undulated plate) and Nuc (averaged over corrugated plate) with θ representing different characteristics. As θ increases, Nu (Nuu or Nuc) is about 2–16 times higher for the corrugated-undulated configurations CP-UH1 and CP-UP1 and the concomitant f is about 4–100 higher, when compared to a straight channel having square cross section. The minimum of local Nu ( Nuu or Nuc ) is situated at the four contact points where the top plate touches the bottom one, and the high Nu is located upstream of the crest of the conjugate duct. Performance evaluation for the CP-UH1 channel shows that the goodness factors (G) are larger than 1 with the straight channel having a square cross section as a reference, and the 30deg geometry channel has optimal flow area goodness.

On the Convective Heat Transfer in a Tube of Elliptic Cross Section Maintained Under Constant Wall Temperature

1986 ◽  
Vol 108 (1) ◽  
pp. 33-39 ◽  
Author(s):  
M. A. Ebadian ◽  
H. C. Topakoglu ◽  
O. A. Arnas
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Temperature Distribution ◽  
Convective Heat Transfer ◽  
Cross Section ◽  
Convective Heat ◽  
Wall Temperature ◽  
Elliptic Cross Section ◽  
Constant Wall Temperature ◽  
Elliptic Cross

The convective heat transfer problem along the portion of a tube of elliptic cross section maintained under a constant wall temperature where hydrodynamically and thermally fully developed flow conditions prevail is solved in this paper. The successive approximation method is used for the solution utilizing elliptic coordinates. Analytical expressions for temperature distribution and Nusselt number corresponding to the first cycle of approximation are obtained in terms of the ellipticity of the cross section. In the case of a circular section, the first cycle approximation of the Nusselt number is obtained as 3.7288 compared to the exact value of 3.6568. Representative temperature distribution curves are plotted and compared to those corresponding with constant wall heat flux conditions.

Numerical Study of Conjugate Heat Transfer Due to Growth of a Vapor Bubble During Flow Boiling of Water in a Microchannel

2007 ◽  
Author(s):  
A. Mukherjee
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Temperature Distribution ◽  
Cross Section ◽  
Vapor Bubble ◽  
Conjugate Heat Transfer ◽  
Flow Boiling ◽  
Wall Heat Flux ◽  
Channel Cross Section ◽  
Flux Boundary Condition

The present study is performed to numerically investigate temperature distribution at the channel walls during growth of a vapor bubble inside a microchannel. The microchannel is of 200 μm square cross section and a vapor bubble nucleates at one of the walls, with liquid flowing in through the channel inlet. Constant heat flux boundary condition is specified at the bottom wall of the microchannel. The complete Navier-Stokes equations along with continuity and energy equations are solved using the SIMPLER method. The liquid vapor interface is captured using the level set technique. The conjugate heat transfer problem is solved at the bottom and side walls. The bubble grows rapidly due to heat transfer from the walls and soon turns into a plug filling the entire channel cross section. The temperature distribution at the channel walls is studied for different values of wall heat flux. The bubble growth rate is found to increase with increase in wall heat flux. High temperatures are noted at the wall below the bubble base due to vapor contact causing axial temperature gradients. Areas of high heat transfer are also seen to exist in the thin layer of liquid between bubble and the channel sidewalls.

Influence Of Relative Size Of The U-Shaped Silicon Rod On Conjugate Heat Transfer In The Regime Of Gas Buayancy Induced Convection

2015 ◽  
Vol 10 (3) ◽  
pp. 76-88
Author(s):  
Vladimir Berdnikov ◽  
Konstantin Mitin ◽  
Alina Mitina
Keyword(s):  
Heat Transfer ◽  
Cross Section ◽  
Solid Body ◽  
Conjugate Heat Transfer ◽  
Relative Size ◽  
Three Dimensional ◽  
Boussinesq Approximation ◽  
Temperature Fields ◽  
Spatial Form ◽  
Section Size

The influence of relative cross-section size of an electrically heated U-shaped silicon rod which is placed in a gas-filled rectangle container with isothermal cold walls on conjugate heat transfer in the regime of buoyancy induced convection was numerically studied in three-dimensional formulation. The natural convection equations in the Boussinesq approximation in term temperature, velocity vortex and velocity vector potential were solved by the finite element method. The spatial form of convective flow and temperature fields in liquid and solid body were studied. It was show that spatial form and intensity of convective flows is significantly depends on the cross-section size of U-shaped silicon rod. This is has strong influence on the temperature field in a solid body.

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