The RC Analogy Provides a Versatile Computational Tool for Unsteady, Unidirectional Heat Conduction in Regular Solid Bodies Cooled by Adjoining Fluids

2003 ◽  
Vol 31 (3) ◽  
pp. 233-244
Author(s):  
Antonio Campo ◽  
Francisco Alhama
Keyword(s):  
Heat Transfer ◽  
Initial Conditions ◽  
Simulation Method ◽  
Heat Fluxes ◽  
Total Heat ◽  
Time Dependent ◽  
Total Heat Transfer ◽  
Transfer Rates ◽  
Electric Circuits ◽  
Spatio Temporal

Evaluation of spatio-temporal temperatures and total heat transfer rates in simple bodies (large plate, long cylinder and sphere) has been traditionally explained in undergraduate courses of heat transfer by the Heisler/Gröber or by the Boelter/Gröber charts. These three charts pose some restrictions with respect to the applicable times. Additionally, the charts do not provide information about the time-dependent heat fluxes at the surface. Conversely, evaluation of spatio-temporal temperatures, time-dependent heat fluxes at the surface and total heat transfer rates can be easily done for the entire time domain with the network simulation method (NSM) in conjunction with the commercial code PSPICE. NSM relies on the existing physical analogy between the unsteady transport of electric current and the unsteady transport of unidirectional heat by conduction. This analogy has been named the RC analogy in the specialized literature. The code PSPICE simulates the electric circuits for a specific body together with the imposed boundary and initial conditions, and produces numerical results for the quantities of interest, such as: the spatio-temporal temperature distributions; the time-dependent heat flux distributions at the surface; and the total heat transfer.

An Analytical Study of Heat Transfer in Finite Tissue With Two Blood Vessels and Uniform Dirichlet Boundary Conditions

2005 ◽  
Vol 127 (2) ◽  
pp. 179-188 ◽  
Author(s):  
Devashish Shrivastava ◽  
Benjamin McKay ◽  
Robert B. Roemer
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Source Term ◽  
Dirichlet Boundary ◽  
Total Heat ◽  
Dirichlet Boundary Conditions ◽  
Total Heat Transfer ◽  
Transfer Rates

Counter-current (vessel–vessel) heat transfer has been postulated as one of the most important heat transfer mechanisms in living systems. Surprisingly, however, the accurate quantification of the vessel–vessel, and vessel–tissue, heat transfer rates has never been performed in the most general and important case of a finite, unheated/heated tissue domain with noninsulated boundary conditions. To quantify these heat transfer rates, an exact analytical expression for the temperature field is derived by solving the 2-D Poisson equation with uniform Dirichlet boundary conditions. The new results obtained using this solution are as follows: first, the vessel–vessel heat transfer rate can be a large fraction of the total heat transfer rate of each vessel, thus quantitatively demonstrating the need to accurately model the vessel–vessel heat transfer for vessels imbedded in tissues. Second, the vessel–vessel heat transfer rate is shown to be independent of the source term; while the heat transfer rates from the vessels to the tissue show a significant dependence on the source term. Third, while many previous studies have assumed that (1) the total heat transfer rate from vessels to tissue is zero, and/or (2) the heat transfer rates from paired vessels (of different sizes and at different temperatures) to tissue are equal to each other the current analysis shows that neither of these conditions is met. The analytical solution approach used to solve this two vessels problem is general and can be extended for the case of “N” arbitrarily located vessels.

Rapid Boiling of Droplets in an Ambient Liquid at Partial Superheat

2007 ◽  
Author(s):  
Herman D. Haustein ◽  
Alon Gany
Keyword(s):  
Heat Transfer ◽  
Initial Conditions ◽  
High Heat ◽  
Heat Fluxes ◽  
Liquid Environment ◽  
Transfer Rates ◽  
High Heat Transfer ◽  
High Superheat ◽  
Film Collapse ◽  
Critical Times

This work deals with the dynamics of rapid-boiling of a droplet, at medium-high superheat, rising in a host liquid environment. It considers the heat transfer, the superheat consumption and the hydrodynamics of the droplet as it boils. In the course of the research water-column experiments were conducted, and results are shown. Superheating was implemented by the sudden depressurization of the ambient liquid. Boiling was very rapid, concluding within several milliseconds, and high heat fluxes across the interface were obtained. Additionally, certain critical times in the boiling process were predicted and defined, and a novel criterion for the end of rapid boiling (liquid film collapse), is proposed. These defined critical times agree well with measured points of change in the boiling dynamics. From these results and analysis a deeper understanding of the three-fluid rapid boiling at medium-high superheat has been established, for the first time. In addition, various initial conditions were tested and their effect established qualitatively. This form of boiling, though being very rapid and sustaining high heat transfer rates, is non-explosive in nature, and therefore more designable and widely applicable.

scholarly journals An experimental study of the temperature evolution of a single fin submerged in a phase changing material during melting at different heat fluxes

2021 ◽  
Vol 2116 (1) ◽  
pp. 012047
Author(s):  
R Tassenoy ◽  
W Beyne ◽  
W Plas ◽  
S Lecompte ◽  
M De Paepe
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Temperature Drop ◽  
Melting Process ◽  
Heat Fluxes ◽  
Total Heat ◽  
Temperature Evolution ◽  
Total Heat Transfer ◽  
Steady State Temperature ◽  
State Behaviour

Abstract An experimental setup has been designed to study a single cylindrical fin placed in a cylindrical enclosure filled with phase changing material (PCM). The heat flux to the fin is measured at the top of the fin. The temperature evolution at different fin heights is measured by thermocouples placed internally in the fin. The evolution of these temperatures has been studied for different heat fluxes. This provides insight in the contribution of the different fin heights to the total heat transfer to the PCM during the different stages of the melting process. As such they can be used to assess the effectiveness of the fin over its length. After approximately 6h, the fin temperature stabilizes during melting. Due to the temperature drop over the fin, the bottom temperature reached is significantly lower than the temperature at the top and the contribution of this lower part to the total heat transfer is lower as well. For heat fluxes higher than 3805±75 W/m2, the steady-state temperatures at fin locations in contact with the melting PCM are similar. For low heat fluxes, this steady-state temperature is not reached during a 12h experiment. Longer experiments are thus needed to study the steady-state behaviour at these lower heat fluxes.

Heat Transfer in Thermal Lattice Boltzmann Equation Method

2012 ◽  
Author(s):  
Like Li ◽  
Renwei Mei ◽  
James F. Klausner
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Boltzmann Equation ◽  
Lattice Boltzmann ◽  
Heat Fluxes ◽  
Total Heat ◽  
Lattice Boltzmann Equation ◽  
Thermal Flow ◽  
Total Heat Transfer ◽  
Curved Boundaries

The evaluation of the boundary heat flux and total heat transfer in the lattice Boltzmann equation (LBE) simulations is investigated. The boundary heat fluxes in the discrete velocity directions of the thermal LBE (TLBE) model are obtained directly from the temperature distribution functions at the lattice nodes. With the rectangular lattice uniformly spaced the effective surface area for the discrete heat flux is the unit spacing distance, thus the heat flux integration becomes simply a summation of all the discrete heat fluxes with constant surface areas. The present method for the evaluation of total heat transfer is very efficient and robust for curved boundaries because it does not require the determination of the normal heat flux on the boundary and the surface area. To validate its applicability and accuracy, several numerical tests with analytical solutions are conducted, including 2-dimensional (2D) steady thermal flow in a channel, 1-D transient heat conduction in an inclined semi-infinite solid, 2-D transient conduction inside a circle, and 3-D steady thermal flow in a circular pipe. For straight boundaries perpendicular to one of the discrete velocity vectors, the total heat transfer is second-order accurate. For curved boundaries only first-order accuracy is obtained for the total heat transfer due to the irregularly distributed lattice fractions cut by the curved boundary.

scholarly journals Combined Heat Transfer Mechanisms in the Porous Char Layer Formed from the Intumescent Coatings under Fire

Coatings ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 200
Author(s):  
Lingyun Zhang ◽  
Yupeng Hu ◽  
Minghai Li
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Thermal Conduction ◽  
Total Heat ◽  
Surface Radiation ◽  
Total Heat Transfer ◽  
Char Layer ◽  
Competition Result ◽  
Transfer Mechanisms ◽  
Combined Heat Transfer

This study examines the combined heat transfer by thermal conduction, natural convection and surface radiation in the porous char layer that is formed from the intumescent coating under fire. The results show that some factors, such as the Rayleigh number, conductivity ratio, emissivity, radiation–conduction number, void fraction and heating mode have a certain effect on the total heat transfer. In addition, the natural convection of the air in the cavity always inhibits surface radiation among the solid walls and thermal conduction, and the character of the total heat transfer is the competition result of the three heat transfer mechanisms.

scholarly journals Thermal analysis in thin-film fluid regions of rectangular microgroove

2018 ◽  
Vol 22 (2) ◽  
pp. 899-897
Author(s):  
Xiaohong Gui ◽  
Xiange Song ◽  
Baisheng Nie
Keyword(s):  
Thin Film ◽  
Heat Transfer ◽  
Heat Flux ◽  
Contact Angle ◽  
Film Thickness ◽  
Flux Distribution ◽  
Total Heat ◽  
Heat Flux Distribution ◽  
Total Heat Transfer ◽  
Thin Film Thickness

The effects of contact angle and superheat on thin-film thickness and heat flux distribution occurring in a rectangle microgroove are numerically simulated. Accordingly, physical, and mathematical models are built in detail. Numerical results indicate that meniscus radius and thin-film thickness increase with the improvement of contact angle. The heat flux distribution in the thin-film region increases non-linearly as the contact angle decreases. The total heat transfer through the thin-film region increases with the improvement of superheat, and decreases as the contact angle increases. When the contact angle is equal to zero, the heat transfer in the thin-film region accounts for more than 80% of the total heat transfer. Intensive evaporation in the thin-film region plays a key role in heat transfer for the rectangle capillary microgroove. The liquid with higher wetting performance is more capable of playing the advantages of higher intensity heat transfer in thin- film region. The current investigation will result in a better understanding of thin- -film evaporation and its effect on the effective thermal conductivity in the rectangle microgroove.

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