Study on Contact Melting Inside an Elliptical Tube With Nonisothermal Wall

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Yuansong Zhao ◽  
Wenzhen Chen ◽  
Fengrui Sun
Keyword(s):  
Temperature Distribution ◽  
Aspect Ratio ◽  
Wall Temperature ◽  
Film Theory ◽  
Closed Form Solution ◽  
Cylindrical Tube ◽  
Melting Process ◽  
Contact Melting ◽  
Form Solution ◽  
Basic Equations

The problem of contact melting inside an elliptical tube with nonisothermal wall is investigated. A theoretical model, which the inner wall temperature of source varied with angle ϕ, is established by applying film theory. The basic equations of the melting process are solved theoretically, and a closed-form solution is obtained. Under certain cases, comparisons of results for the melting velocity with those of contact melting inside a horizontal cylindrical tube with nonisothermal wall and an elliptical tube with constant temperature are reported for the validity of the solution in this paper. Effects of aspect ratio J and inner wall temperature distribution are critically assessed. It is found that the smaller the elliptical aspect ratio J is, the greater the effect of wall temperature distribution on melting velocity, and the time to complete melting increases with the augment of coefficient c in temperature distribution.

Natural Convection in a Vertical Annulus Containing Water Near the Density Maximum

1987 ◽  
Vol 109 (4) ◽  
pp. 899-905 ◽  
Author(s):  
D. S. Lin ◽  
M. W. Nansteel
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Aspect Ratio ◽  
Density Distribution ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Vertical Flow ◽  
Density Maximum ◽  
Vertical Annulus

Steady natural convection of water near the density extremum in a vertical annulus is studied numerically. Results for flow in annuli with aspect ratio 1≤A≤8 and varying degrees of curvature are given for 103≤Ra≤105. It is shown that both the density distribution parameter R and the annulus curvature K have a strong effect on the steady flow structure and heat transfer in the annulus. A closed-form solution for the vertical flow in a very tall annulus is compared with numerical results for finite-aspect-ratio annuli.

A New Analytical Method for Calculating Maximum Junction Temperature of Packaged Devices Incorporating the Temperature Distribution at the Base of the Substrate

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
J. H. L. Ling ◽  
A. A. O. Tay
Keyword(s):  
Finite Element ◽  
Temperature Distribution ◽  
Analytical Method ◽  
Analytical Methods ◽  
Thermal Analyses ◽  
Closed Form Solution ◽  
Form Solution ◽  
Junction Temperature ◽  
Uniform Temperature ◽  
Element Analysis

All current analytical methods for calculating junction temperature of field effect transistor (FET) and monolithic microwave integrated circuits (MMIC) devices have assumed a constant uniform temperature at the base of the substrate. In a packaged device, however, where the substrate is attached to a carrier, finite element thermal analyses have shown that the temperature distribution along the base of the substrate is not uniform but has a bell-shaped distribution. Consequently, current analytical methods which attempt to predict the junction temperature of a packaged MMIC device by assuming a constant uniform temperature at the base of the substrate have been found to be inaccurate. In this paper, it is found that the temperature distribution along the base of a substrate can be well approximated by a Lorentz distribution which can be determined from a few basic parameters of the device such as the gate length, gate pitch, number of gates, and length of substrate. By incorporating this Lorentz temperature distribution at the base of the substrate with a new closed-form solution for the three-dimensional temperature distribution within the substrate, a new analytical method is developed for accurately calculating the junction temperature of MMIC devices. The accuracy of this new method has been verified with junction temperatures of MMIC devices measured using thermoreflectance thermography (TRT) as well as those calculated using finite element analysis (FEA).

scholarly journals Analytic-Numerical Solution of Random Boundary Value Heat Problems in a Semi-Infinite Bar

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
M.-C. Casabán ◽  
J.-C. Cortés ◽  
B. García-Mora ◽  
L. Jódar
Keyword(s):  
Stochastic Process ◽  
Temperature Distribution ◽  
Numerical Solution ◽  
Closed Form ◽  
Boundary Value ◽  
Closed Form Solution ◽  
Form Solution ◽  
Mean Square ◽  
Random Boundary ◽  
Numerical Examples

This paper deals with the analytic-numerical solution of random heat problems for the temperature distribution in a semi-infinite bar with different boundary value conditions. We apply a random Fourier sine and cosine transform mean square approach. Random operational mean square calculus is developed for the introduced transforms. Using previous results about random ordinary differential equations, a closed form solution stochastic process is firstly obtained. Then, expectation and variance are computed. Illustrative numerical examples are included.

Heat-Conduction Problems With Melting or Freezing

1969 ◽  
Vol 91 (3) ◽  
pp. 421-426 ◽  
Author(s):  
S. H. Cho ◽  
J. E. Sunderland
Keyword(s):  
Temperature Distribution ◽  
Phase Change ◽  
Closed Form Solution ◽  
Form Solution ◽  
Rate Of Change ◽  
Phase Changes ◽  
Transient Temperature ◽  
Infinite Body ◽  
Two Phase ◽  
Transient Temperature Distribution

An exact solution is presented for the temperature distribution and rate of change of phase for a semi-infinite body where the change of phase occurs over a range of temperatures. The surface temperature is instantaneously changed to and held at a temperature different from the phase-change temperature range and the initial temperature. The transient temperature distribution and rate of melting are also determined for a finite slab in which one or two phase changes take place. The slab is initially at a constant temperature and the temperature of one face is instantaneously changed so that a phase change takes place. The other surface of the slab is insulated. An exact closed form solution is presented for the temperature distribution in the newly formed phase and Goodman’s integral technique is used to find the temperature distribution in the initially existing phase.

Melting of a Free Solid in a Spherical Enclosure: Effects of Subcooling

1989 ◽  
Vol 111 (1) ◽  
pp. 32-36 ◽  
Author(s):  
Sanjay K. Roy ◽  
Subrata Sengupta
Keyword(s):  
Temperature Gradient ◽  
Moving Boundary ◽  
Solid Phase ◽  
Closed Form Solution ◽  
Melting Process ◽  
Form Solution ◽  
Solid Core ◽  
Infinite Domain ◽  
Thermal Systems ◽  
Time Step

The melting process within a spherical enclosure with the solid phase uniformly subcooled initially has been studied. The preliminary analysis of the problem is similar to a previous study where the degree of subcooling was zero. However, the heat transfer equation has been modified to include the effects of a temperature gradient in the solid core. As a result, a closed-form solution cannot be obtained. At every time step, the unsteady conduction equation has been solved numerically using a toroidal coordinate system, which has been suitably transformed to immobilize the moving boundary and to transform the infinite domain into a finite one. The temperature gradient at the surface is now used to solve the film equation numerically. The melt time, Nusselt number, and melt flux distributions have been obtained over a range of the parameters (Sb, Ste/Cp*, and 1 /Prα*) normally encountered in solar thermal systems.

scholarly journals A Computational Study on Magnetic Nanoparticles Hyperthermia of Ellipsoidal Tumors

2021 ◽  
Vol 11 (20) ◽  
pp. 9526
Author(s):  
Nickolas D. Polychronopoulos ◽  
Apostolos A. Gkountas ◽  
Ioannis E. Sarris ◽  
Leonidas A. Spyrou
Keyword(s):  
Aspect Ratio ◽  
Computational Model ◽  
Thermal Damage ◽  
Computational Study ◽  
Closed Form Solution ◽  
Magnetic Hyperthermia ◽  
Form Solution ◽  
Aspect Ratios ◽  
Tissue Region ◽  
Spherical Tumor

The modelling of magnetic hyperthermia using nanoparticles of ellipsoid tumor shapes has not been studied adequately. To fill this gap, a computational study has been carried out to determine two key treatment parameters: the therapeutic temperature distribution and the extent of thermal damage. Prolate and oblate spheroidal tumors, of various aspect ratios, surrounded by a large healthy tissue region are assumed. Tissue temperatures are determined from the solution of Pennes’ bio-heat transfer equation. The mortality of the tissues is determined by the Arrhenius kinetic model. The computational model is successfully verified against a closed-form solution for a perfectly spherical tumor. The therapeutic temperature and the thermal damage in the tumor center decrease as the aspect ratio increases and it is insensitive to whether tumors of the same aspect ratio are oblate or prolate spheroids. The necrotic tumor area is affected by the tumor prolateness and oblateness. Good comparison is obtained of the present model with three sets of experimental measurements taken from the literature, for animal tumors exhibiting ellipsoid-like geometry. The computational model enables the determination of the therapeutic temperature and tissue thermal damage for magnetic hyperthermia of ellipsoidal tumors. It can be easily reproduced for various treatment scenarios and may be useful for an effective treatment planning of ellipsoidal tumor geometries.

scholarly journals Mechanism of Continuous Melting and Secondary Contact Melting in Resistance Heating Metal Wire Additive Manufacturing

Materials ◽  
2020 ◽  
Vol 13 (5) ◽  
pp. 1069
Author(s):  
Chengwei Yuan ◽  
Shujun Chen ◽  
Fan Jiang ◽  
Bin Xu ◽  
Shanwen Dong
Keyword(s):  
Temperature Distribution ◽  
Melting Process ◽  
Contact Melting ◽  
Metal Wire ◽  
Secondary Contact ◽  
Dynamic Resistance ◽  
Resistance Heating ◽  
Contact Interface ◽  
Resistance Change ◽  
Continuous Melting

Resistance heating metal wire materials additive manufacturing technology is of great significance for space environment maintenance and manufacturing. However, the continuous deposition process has a problem in which the metal melt is disconnected from the base metal. In order to study the difference between the second contact melting of the disconnected metal melt and the continuous melting of the metal wire as well as eliminate the problem of the uneven heat dissipation of the base metal deposition on the melting process of the metal wire, the physical test of melting the metal wire clamped by the equal diameter conductive nozzle was carried out from the aspects of temperature distribution, temperature change, melting time, dynamic resistance change, and the microstructure. The current, wire length, and diameter of the metal wire are used as variables. It was found that the dynamic resistance change of the wire can be matched with the melting state. During the solid-state temperature rise, due to the presence of the contact interface, the continuous melting and secondary contact melting of metal wires differ in dynamic resistance and the melting process. The continuous melting of the metal wire was caused by the overall resistance of the wire to generate heat and melt, and the temperature distribution is “bow-shaped”. In the second contact melting, the heat generated by the contact interface resistance was transferred to both ends of the metal wire to melt, and the temperature distribution is “inverted V”. The microstructure of the metal wire continuous melting and secondary contact melting solidification is similar. The continuous melting length of the metal wire is greater than the melting length of the secondary contact.

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