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.

A Numerical Study of Three-Dimensional Natural Convective Heat Transfer From a Plate With a “Wavy” Surface

2001 ◽  
Author(s):  
Patrick H. Oosthuizen ◽  
Matt Garrett
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Surface Waves ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Three Dimensional ◽  
Wavy Surface ◽  
Surface Waviness ◽  
Dimensionless Amplitude ◽  
The Mean

Abstract Natural convective heat transfer from a wide isothermal plate which has a “wavy” surface, i.e., has a surface which periodically rises and falls, has been numerically studied. The surface waves run parallel to the direction of flow over the surface and have a relatively small amplitude. Two types of wavy surface have been considered here — saw-tooth and sinusoidal. Surfaces of the type considered are approximate models of situations that occur in certain window covering applications, for example, and are also sometimes used to try to enhance the heat transfer rate from the surface. The flow has been assumed to be laminar. Because the surface waves are parallel to the direction of flow, the flow over the surface will be three-dimensional. Fluid properties have been assumed constant except for the density change with temperature that gives rise to the buoyancy forces, this being treated by means of the Boussinesq type approximation. The governing equations have been written in dimensionless form, the height of the surface being used as the characteristic length scale and the temperature difference between the surface temperature and the temperature of the fluid far from the plate being used as the characteristic temperature. The dimensionless equations have been solved using a finite-element method. Although the flow is three-dimensional because the surface waves are all assumed to have the same shape, the flow over each surface thus being the same, and it was only necessary to solve for the flow over one of the surface waves. The solution has the following parameters: the Grashof number based on the height, the Prandtl number, the dimensionless amplitude of the surface waviness, the dimensionless pitch of the surface waviness, and the form of the surface waviness (saw-tooth or sinusoidal). Results have been obtained for a Prandtl number of 0.7 for Grashof numbers up to 106. The effects of Grashof number, dimensionless amplitude and dimensionless pitch on the mean heat transfer rate have been studied. It is convenient to introduce two mean heat transfer rates, one based on the total surface area and the other based on the projected frontal area of the surface. A comparison of the values of these quantities gives a measure of the effectiveness of the surface waviness in increasing the mean heat transfer rate. The results show that while surface waviness increases the heat transfer rate based on the frontal area, the modifications of the flow produced by the surface waves are such that the increase in heat transfer rate is less than the increase in surface area.

A Study of Three-Dimensional Mixed Convective Heat Transfer From Short Vertical Cylinders in a Horizontal Forced Flow

2000 ◽  
Author(s):  
David A. Scott ◽  
P. H. Oosthuizen
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Three Dimensional ◽  
Forced Flow ◽  
Low Velocity ◽  
Buoyancy Forces ◽  
The Mean ◽  
Mixed Convective Flow ◽  
Comparison Of The Results

Abstract Heat transfer from relatively short vertical isothermal cylinders in a horizontal forced fluid flow has been considered. The flow conditions are such that the buoyancy forces resulting from the temperature differences in the flow are in general significant despite of the presence of a horizontal forced flow of air, that is, mixed convective flow exists. Because the cylinders are short and the buoyancy forces act normal to the forced flow, three-dimensional flow exists. The experiments were performed in a low velocity, open jet wind tunnel. The study involved the experimental determination of the mean heat transfer coefficient and a comparison of the results with a previous numerical analysis. Mean heat transfer rates were determined using the ‘lumped capacity’ method. The mean Nusselt number has the Reynolds number, Grashof number and the height to diameter ratio of the cylinders as parameters. The results have been used to determine the conditions under which the flow departs from purely forced convection and enters the mixed convection regime, i.e., determining the conditions for which the buoyancy effects should be included in convective heat transfer calculations for short cylinders.

scholarly journals AERODYNAMICS OF JETS INTERACTING WITH A FLAT SURFACE

2019 ◽  
Vol 62 (4) ◽  
pp. 263-269
Author(s):  
I. A. Pribytkov ◽  
S. I. Kondrashenko
Keyword(s):  
Heat Transfer ◽  
Critical Point ◽  
Flat Surface ◽  
Stokes Equations ◽  
Thermal State ◽  
Exchange Process ◽  
Three Dimensional ◽  
Internal Diameter ◽  
Three Dimensional Model ◽  
Aerodynamic Properties

In this paper, the development features of a single free jet of hightemperature nitrogen interacting with a flat surface were studied. Calculation of the heat exchange process during heating by the attacking jets is very difficult to implement analytically due to complexity of the gas-dynamic processes occurring both in a single jet and in a system of jets interacting with the metal. The computational difficulties are aggravated by the fact that when interacting with the surface the jet as such disappears. The flat (fan) flow interacts with the surface: form, aerodynamic properties and thermal state of the flow strongly differ from those of the original jet. The studies were conducted on the basis of numerical simulation in the FloEFD software and computing complex for multiphysical simulation based on solution of the equations of gas dynamics and heat transfer. The solved system of equations consisted of Navier-Stokes equations, equations of energy and continuity and was supplemented by k – ε turbulence model. A three-dimensional model was developed for simulation, the necessary properties, initial and boundary conditions were specified. In the study of aerodynamics of a single high-temperature jet interacting with the surface, the main defining values were: nitrogen flow rate from the nozzle U0 , nitrogen temperature T, internal diameter of the nozzle d0 , distance from the nozzle section to the surface h, distance from the critical point (point of intersection of the jet axis with the surface) along the flow radius r. Data on the gas velocity decrease as the jet develops due to the loss of initial energy to engage the motionless surrounding gas in motion, is presented. The studies have shown that increase in the initial velocity of gas outflow brings the area of higher velocities closer to the surface both in the jet itself and in the fan jet. This factor contributes to heat transfer intensification. In addition, high speeds increase the total thickness of the fan flow and reduce the thickness of hydrodynamic boundary layer, which increases with distance from the critical point.

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.

Verification of Finite Volume Computations on Steady-State Fluid Flow and Heat Transfer

2001 ◽  
Vol 124 (1) ◽  
pp. 11-21 ◽  
Author(s):  
J. Cadafalch ◽  
C. D. Pe´rez-Segarra ◽  
R. Co`nsul ◽  
A. Oliva
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Steady State ◽  
Finite Volume ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Independent Solution ◽  
Post Processing ◽  
Square Duct ◽  
Flow And Heat Transfer

This work presents a post-processing tool for the verification of steady-state fluid flow and heat transfer finite volume computations. It is based both on the generalized Richardson extrapolation and the Grid Convergence Index GCI. The observed order of accuracy and a error band where the grid independent solution is expected to be contained are estimated. The results corresponding to the following two and three-dimensional steady-state simulations are post-processed: a flow inside a cavity with moving top wall, an axisymmetric turbulent flow through a compressor valve, a premixed methane/air laminar flat flame on a perforated burner, and the heat transfer from an isothermal cylinder enclosed by a square duct. Discussion is carried out about the certainty of the estimators obtained with the post-processing procedure. They have been shown to be useful parameters in order to assess credibility and quality to the reported numerical solutions.

Conjugate Flow and Heat Transfer Investigation of a Turbo Charger: Part I — Numerical Results

2003 ◽  
Author(s):  
Dieter Bohn ◽  
Tom Heuer ◽  
Karsten Kusterer
Keyword(s):  
Heat Transfer ◽  
Three Dimensional ◽  
Heat Fluxes ◽  
Inlet Temperature ◽  
Three Dimensional Model ◽  
Flow And Heat Transfer ◽  
Turbine Inlet ◽  
Turbo Charger ◽  
Conjugate Calculation

In this paper a three-dimensional conjugate calculation has been performed for a passenger car turbo charger. The scope of this work is to investigate the heat fluxes in the radial compressor which can be strongly influenced by the hot turbine. As a result of this, the compressor efficiency may deteriorate. Consequently, the heat fluxes have to be taken into account for the determination of the efficiency. To overcome this problem a complex three-dimensional model has been developed. It contains the compressor, the oil cooled center housing, and the turbine. 12 operating points have been numerically simulated composed of three different turbine inlet temperatures and four different mass flows. The boundary conditions for the flow and for the outer casing were derived from experimental test data (part II of the paper). Resulting from these conjugate calculations various one-dimensional calculation specifications have been developed. They describe the heat transfer phenomena inside the compressor with the help of a Nusselt number which is a function of an artificial Reynolds number and the turbine inlet temperature.

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