Formulation of a Statistical Model of Heat Transfer in Perfused Tissue

1994 ◽  
Vol 116 (4) ◽  
pp. 521-527 ◽  
Author(s):  
J. W. Baish
Keyword(s):  
Heat Transfer ◽  
Heat Transport ◽  
Drug Transport ◽  
Transfer Problem ◽  
Three Dimensional ◽  
Tissue Temperature ◽  
Statistical Interpretation ◽  
Transfer Equations ◽  
Vascular Geometry ◽  
Steady State Heat

A new model of steady-state heat transport in perfused tissue is presented. The key elements of the model are as follows: (1) a physiologically-based algorithm for simulating the geometry of a realistic vascular tree containing all thermally significant vessels in a tissue; (2) a means of solving the conjugate heat transfer problem of convection by the blood coupled to three-dimensional conduction in the extravascular tissue, and (3) a statistical interpretation of the calculated temperature field. This formulation is radically different from the widely used Pennes and Weinbaum-Jiji bio-heat transfer equations that predict a loosely defined local average tissue temperature from a local perfusion rate and a minimal representation of the vascular geometry. Instead, a probability density function for the tissue temperature is predicted, which carries information on the most probable temperature at a point and uncertainty in that temperature due to the proximity of thermally significant blood vessels. A sample implementation illustrates the dependence of the temperature distribution on the flow rate of the blood and the vascular geometry. The results show that the Pennes formulation of the bio-heat transfer equation accurately predicts the mean tissue temperature except when the arteries and veins are in closely spaced pairs. The model is useful for fundamental studies of tissue heat transport, and should extend readily to other forms of tissue transport including oxygen, nutrient, and drug transport.

scholarly journals Hybrid 1D + 2D Modelling for the Assessment of the Heat Transfer in the EU DEMO Water-Cooled Lithium-Lead Manifolds

Energies ◽  
2020 ◽  
Vol 13 (14) ◽  
pp. 3525
Author(s):  
Antonio Froio ◽  
Andrea Bertinetti ◽  
Alessandro Del Nevo ◽  
Laura Savoldi
Keyword(s):  
Heat Transfer ◽  
Heat Transport ◽  
Transfer Problem ◽  
Computational Cost ◽  
Three Dimensional ◽  
Longitudinal Direction ◽  
Heat Transfer Problem ◽  
Outlet Temperature ◽  
Conductive Heat ◽  
The Eu

The European demonstration fusion power reactor (EU DEMO) tokamak will be the first European fusion device to produce electricity and to include a breeding blanket (BB). In the framework of the design of the EU DEMO BB, the analysis of the heat transfer between the inlet and outlet manifold of the coolant is needed, to assess the actual cooling capability of the water entering the cooling channels, as well as the actual coolant outlet temperature from the machine. The complex, fully three-dimensional conjugate heat transfer problem is reduced here with a novel approach to a simpler one, decoupling the longitudinal and transverse scales for the heat transport by developing correlations for a conductive heat-transfer problem. While in the longitudinal direction a standard 1D model for the heat transport by fluid advection is adopted, a set of 2D finite elements analyses are run in the transverse direction, in order to lump the 2D heat conduction effects in suitable correlations. Such correlations are implemented in a 1D finite volume model with the 1D GEneral Tokamak THErmal-hydraulic Model (GETTHEM) code (Politecnico di Torino, Torino, Italy); the proposed approach thus reduces the 3D problem to a 1D one, allowing a parametric evaluation of the heat transfer in the entire blanket with a reduced computational cost. The deviation from nominal inlet and outlet temperature values, for the case of the Water-Cooled Lithium-Lead BB concept, is found to be always below 1.4 K and, in some cases, even to be beneficial. Consequently, the heat transfer among the manifolds at different temperatures can be safely (and conservatively) neglected.

scholarly journals STEADY-STATE HEAT TRANSFER IN A PLATE WITH TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY (AN EXACT SOLUTION)

2019 ◽  
Vol 18 (2) ◽  
pp. 85
Author(s):  
A. Miguelis ◽  
R. Pazetto ◽  
R. M. S. Gama
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Steady State ◽  
Transfer Problem ◽  
Internal Heat ◽  
Temperature Dependent ◽  
State Heat ◽  
Kirchhoff Transformation ◽  
Steady State Heat ◽  
Steady State Heat Transfer

This work presents the solution of the steady-state heat transfer problem in a rectangular plate with an internal heat source in a context in which the thermal conductivity depends on the local temperature. This generalization of one of the most classical heat transfer problems is carried out with the aid of the Kirchhoff transformation and employs only well known tools, as the superposition of solutions and the Fourier series. The obtained results illustrate how the usual procedures may be extended for solving more realistic physical problems (since the thermal conductivity of any material is temperature-dependent). A general formula for evaluating the Kirchhoff transformation as well as its inverse is presented too. This work has a strong didactical contribution since such analytical solutions are not found in any classical heat transfer book. In addition, the main idea can be used in a lot of similar problems.

Prediction of Local and Integral Turbulent Transport Properties for Liquid-Metal Heat Transfer in Equilateral Triangular Rod Arrays

1975 ◽  
Vol 97 (2) ◽  
pp. 238-243 ◽  
Author(s):  
H. Ramm ◽  
K. Johannsen
Keyword(s):  
Heat Transfer ◽  
Liquid Metal ◽  
Transport Properties ◽  
Turbulence Model ◽  
Transfer Problem ◽  
Turbulent Transport ◽  
Three Dimensional ◽  
Theoretical Method ◽  
Eddy Diffusivity ◽  
Thermal Mixing

A theoretical method based on a phenomenological turbulence model has been applied to evaluate turbulent transport properties for liquid-metal heat transfer in bare equilateral triangular rod bundles. Results obtained for local distributions of thermal eddy diffusivity in the various directions are presented in terms of correlations. From a subsequent solution of the three-dimensional heat transfer problem between two characteristic interior subchannels under conditions characteristic for tracer-type mixing experiments, integral thermal mixing coefficients and thermal length scales have been evaluated. Results demonstrate that the basic concept of subchannel analysis treating molecular conduction and turbulent transport independently of each other tends to underestimate intersubchannel transport. The uncertainties which are involved in principal assumptions of the turbulence-model as well as in the available empirical results are discussed in some detail.

Heat Transfer Normal to Paired Arterioles and Venules Embedded in Perfused Tissue During Hyperthermia

1988 ◽  
Vol 110 (4) ◽  
pp. 277-282 ◽  
Author(s):  
C. K. Charny ◽  
R. L. Levin
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Three Dimensional ◽  
Numerical Data ◽  
Tissue Temperature ◽  
Three Dimensional Model ◽  
Sources And Sinks ◽  
The Mean ◽  
Krogh Cylinder ◽  
Subsequent Incorporation

A numerical model of the heat transer normal to an arteriole-venule pair embedded in muscle tissue has been constructed. Anatomical data describing the blood vessel size, spacing, and density have been incorporated into the model. This model computes temperatures along the vessel walls as well as the temperature throughout the tissue which comprises an infinitely long Krogh cylinder around the vessel pair. Tissue temperatures were computed in the steady-state under resting conditions, while transient calculations were made under hyperthermic conditions. Results show that for both large- (1st generation) and medium-sized (5th generation) vessel pairs, the mean tissue temperature within the tissue cylinder is not equal to the mean of the arteriole and venule blood temperatures under both steady-state and transient conditions. The numerical data were reduced so that a comparison could be made with the predictions of a simple two-dimensional superposition of line sources and sinks presented by Baish et al. [1]. This comparison reveals that the superposition model accurately describes the heat transfer effects during hyperthermia, permitting subsequent incorporation of this theory into a realistic three-dimensional model of heat transfer in a whole limb during hyperthermia.

Three-Dimensional Natural Convection in a Vertical Porous Layer With a Hexagonal Honeycomb Core

1992 ◽  
Vol 114 (4) ◽  
pp. 924-927 ◽  
Author(s):  
Y. Asako ◽  
H. Nakamura ◽  
Y. Yamaguchi ◽  
M. Faghri
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Porous Layer ◽  
Numerical Solutions ◽  
Transfer Problem ◽  
Three Dimensional ◽  
Temperature Fields ◽  
Honeycomb Core ◽  
Thermal Boundary Conditions

Numerical solutions are obtained for a three-dimensional natural convection heat transfer problem in a vertical porous layer with a hexagonal honeycomb core. The porous layer is assumed to be long and wide such that the velocity and temperature fields repeat themselves in successive enclosures. The natural convection problem is solved for only one honeycomb enclosure with periodic thermal boundary conditions. The porous layer is assumed to be homogeneous and isotropic and the flow is obtained by using the Darcian model. The numerical methodology is based on an algebraic coordinate transformation technique, which maps the hexagonal cross section onto a rectangle. The transformed governing equations are solved with the SIMPLE algorithm. The calculations are performed for the Darcy–Rayleigh number in the range of 10 to 103 and for eight values of the aspect ratio (H/L = 0.25, 0.333, 0.5, 0.7, 1, 1.4, 2, and 5). Two types of thermal boundary condition for the honeycomb core wall are considered: conduction and adiabatic honeycomb core wall thermal boundary conditions. The results are presented in the form of average and local heat transfer coefficients and are compared with the corresponding values for two and three-dimensional rectangular enclosures.

A three-dimensional model of transient bioheat transfer in the lower extremity during cryotherapy

2021 ◽  
pp. 095441192110358
Author(s):  
Parvaneh Zare ◽  
Mohammad Ghoraishian ◽  
Ahmadreza Faghih Khorasani
Keyword(s):  
Three Dimensional ◽  
Bioheat Transfer ◽  
Tissue Temperature ◽  
Three Dimensional Model ◽  
Deep Tissue ◽  
Cold Therapy ◽  
Finite Volume Discretization ◽  
Transfer Equations ◽  
Cold Application ◽  
Cold Pack

The purpose of this research was to create a computational model of the human thigh undergoing cryotherapy. The tissue temperatures were measured for five cold pack temperatures of −8°C, −4°C, 0°C, 4°C, and 8°C in addition to six different time intervals of cold application and ice removal. The depth of cold penetration and duration of local tissue cooling were investigated at 10 points during 30 min of application and 7 h of post-application. The model was created in CATIA, using a mid-axial cut of the human thigh MRI without pathology. After validation by the available clinical data, this research applied the finite-volume discretization method to solve bioheat transfer equations. A 16°C decrease in the cold pack temperature reduced the tissue temperatures located 1 and 2 cm below the fat by almost 3.34°C and 1.4°C, respectively, after 30 min of cold application. It took the tissues 10–15 min to start cooling down, and the temperature reached its plateau after 100 min. Thirty minutes of cold application declined the superficial tissue and deep tissue temperatures near the bone by 22.59°C and 0.48°C, respectively. Intense cryotherapy led to an insignificant change in the deep tissue temperature at 2 cm and deeper below the fat tissue. After ice removal, tissues continued cooling down for about 8 min until 40 min, depending on the tissue depth. This study proposed a 100-min cold therapy with 10 min of ice removal to optimize tissue cooling.

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