A Theoretical Model for Peripheral Tissue Heat Transfer Using the Bioheat Equation of Weinbaum and Jiji

1987 ◽  
Vol 109 (1) ◽  
pp. 72-78 ◽  
Author(s):  
Wei Jie Song ◽  
Sheldon Weinbaum ◽  
Latif M. Jiji
Keyword(s):  
Heat Transfer ◽  
Numerical Solutions ◽  
Quantitative Model ◽  
Peripheral Tissue ◽  
Whole Body ◽  
Bioheat Equation ◽  
One Dimensional ◽  
Physiological Conditions ◽  
Tissue Organization ◽  
Body Heat

In this paper the new bioheat equation derived in Weinbaum and Jiji [7] is applied to the three layer conceptual model of microvascular surface tissue organization proposed in [1]. A simplified one-dimensional quantitative model of peripheral tissue energy exchange is then developed for application in limb and whole body heat transfer studies. A representative vasculature is constructed for each layer and the enhancement in the local tensor conductivity of the tissue as a function of vascular geometry and blood flow is examined. Numerical solutions for the boundary value problem coupling the three layers are presented and these results used to study the thermal behavior of peripheral tissue for a wide variety of physiological conditions from supine resting state to maximum exercise.

scholarly journals Safe Duration Of A Person Soaking Inside A Hot Tub: Theoretical Prediction of Temperature Elevations in Human Bodies Using A Whole Body Heat Transfer Model

2020 ◽  
Author(s):  
Myo Min Zaw ◽  
Manpreet Singh ◽  
Ronghui Ma ◽  
Liang Zhu
Keyword(s):  
Heat Transfer ◽  
Human Body ◽  
Energy Balance Equation ◽  
The Body ◽  
Whole Body ◽  
Equation Modeling ◽  
Transient Temperature ◽  
Transfer Model ◽  
Bioheat Equation ◽  
Arterial Blood

In this study, we first develop a whole body model based on measurements of a human body, with realistic boundary conditions incorporated before and after a person jumps into a hot tub. For the transient heat transfer simulation, the initial condition is the established steady state temperature field of the human body with appropriate clothing layer to ensure the thermal equilibrium of the body with its surroundings. Once the person is inside a hot tub, the Pennes bioheat equation is used to simulate the transient temperature elevations of the body, and the rising of the arterial blood temperature is solved by an energy balance equation modeling thermal exchange between body tissue and the blood in the body. The safe duration of soaking in hot tubs is then determined as affected by the hot tub water temperatures.

Use of a Zener Approximation for Heat Transfer Analyses of Quasi One-Dimensional Welding Problems

2018 ◽  
Vol 941 ◽  
pp. 2313-2318
Author(s):  
Jerry E. Gould
Keyword(s):  
Heat Transfer ◽  
Numerical Solutions ◽  
One Dimensional ◽  
Copper Electrodes ◽  
Wide Range ◽  
Linear Friction ◽  
Diffusion Transfer ◽  
Cooling Behavior ◽  
Transfer Problems ◽  
Analytical Approaches

Most welding methods in use today involve heating and subsequent cooling of the substrates for joining. Not surprisingly, understanding of associated thermal cycles implicit with the various processes has been a key facet of welding research. While the tools are available for sophisticated numerical solutions, much insight can be gained from simplified analytical approaches. A wide range of joining technologies in use today can be addressed by nominal one-dimensional heat transfer analyses. These include, for example, resistance spot, flash-butt, and linear friction welding. In addressing heat transfer problems, the mathematical constructs for heat transfer are analogous to those for mass (diffusion) transfer. Not surprisingly, one dimensional heat transfer problems can be greatly simplified by adapting the Zener approximation from mass transfer. The work described here employs the Zener approximation to address the direct spot welding of aluminum to steel. The Zener approximation is used to understand heat flow progressively from the steel into the aluminum and finally the copper electrodes. The results are used to understand weld morphology and implicit cooling behavior

Determination of time of death in forensic science via a 3-D whole body heat transfer model

2016 ◽  
Vol 62 ◽  
pp. 109-115 ◽  
Author(s):  
Catherine Bartgis ◽  
Alexander M. LeBrun ◽  
Ronghui Ma ◽  
Liang Zhu
Keyword(s):  
Heat Transfer ◽  
Forensic Science ◽  
Heat Transfer Model ◽  
Whole Body ◽  
Transfer Model ◽  
Time Of Death ◽  
Body Heat

Free-swimming swordfish, Xiphias gladius, alter the rate of whole body heat transfer: morphological and physiological specializations for thermoregulation

2017 ◽  
Vol 75 (2) ◽  
pp. 858-870 ◽  
Author(s):  
Ashley Stoehr ◽  
Joshua St. Martin ◽  
Scott Aalbers ◽  
Chugey Sepulveda ◽  
Diego Bernal
Keyword(s):  
Heat Transfer ◽  
Blood Flow ◽  
Whole Body ◽  
Vertical Movements ◽  
Pelagic Fishes ◽  
Xiphias Gladius ◽  
Flow Pathways ◽  
Body Heat ◽  
Transfer Models

Abstract Swordfish (Xiphias gladius) are large, highly-migratory pelagic, fishes that make diel, vertical excursions from the warm, surface layer (e.g. 18–24 °C) to the cold waters (∼8 °C) below the thermocline (300–600 m). They possess anatomical traits [e.g. medial red muscle (RM) position and an associated vascular rete] that could enable metabolic heat-retention and result in RM temperature elevation above ambient, or RM endothermy. We herein provide: (i) expanded anatomical descriptions of the RM-associated vasculature (i.e. central rete and lateral blood vessels), (ii) new measurements of in vivo temperature, and (iii) heat transfer models to assess the capacities for RM endothermy and physiological thermoregulation during vertical movements. Despite the presence of a medial RM and two associated blood-flow pathways (one of which forms a rete), swordfish exhibited a limited capacity for RM endothermy, with muscle temperatures approaching ambient during prolonged periods above or below the thermocline. Our heat transfer models suggest, however, that swordfish may control rates of heat loss or gain during vertical movements, possibly by altering the route of blood flow supplying the RM. Such physiological thermoregulation likely contributes to the ability of swordfish to capitalize on food resources below the thermocline, which are out of range for most other active, pelagic fishes.

Differential Approximation of Radiative Heat Transfer in a Gray Medium: Axially Symmetric Radiation Field

1980 ◽  
Vol 102 (4) ◽  
pp. 719-723 ◽  
Author(s):  
J. Higenyi ◽  
Y. Bayazitogˇlu
Keyword(s):  
Heat Transfer ◽  
Radiation Field ◽  
Radiative Heat ◽  
Numerical Solutions ◽  
Radiant Energy ◽  
Axially Symmetric ◽  
Differential Approximation ◽  
Emissive Power ◽  
One Dimensional ◽  
Gray Medium

The differential approximation is used to analyze an axially symmetric radiation field for a gray medium within a finite, cylindrical enclosure. The medium emits, absorbs, and isotropically scatters radiant energy and is subject to a specified heat generation. Numerical solutions are obtained for the radiative heat flux and emissive power distributions. It is found that the accuracy of the differential approximation is of the same order for the axially symmetric and one-dimensional problems.

scholarly journals A New Mixed Nonpolynomial Spline Method for the Numerical Solutions of Time Fractional Bioheat Equation

2020 ◽  
pp. 1724-1732
Author(s):  
Ammar Muslim Abdullhussein ◽  
Hameeda Oda Al-Humedi
Keyword(s):  
Fractional Derivative ◽  
Numerical Approximation ◽  
Numerical Solutions ◽  
Spline Method ◽  
Bioheat Equation ◽  
Present Scheme ◽  
Von Neumann ◽  
One Dimensional ◽  
Transfer Paradigm ◽  
Time Fractional Derivative

In this paper, a numerical approximation for a time fractional one-dimensional bioheat equation (transfer paradigm) of temperature distribution in tissues is introduced. It deals with the Caputo fractional derivative with order for time fractional derivative and new mixed nonpolynomial spline for second order of space derivative. We also analyzed the convergence and stability by employing Von Neumann method for the present scheme.

A Comparison of Numerical Solutions of the Unsteady Flow Equations Applied to Reciprocating Compressor Systems

1975 ◽  
Vol 17 (5) ◽  
pp. 271-279 ◽  
Author(s):  
J. F. T. MacLaren ◽  
A. B. Tramschek ◽  
A. Sanjines ◽  
O. F. Pastrana
Keyword(s):  
Heat Transfer ◽  
Numerical Solutions ◽  
Computer Time ◽  
Hyperbolic Partial Differential Equations ◽  
Reciprocating Compressor ◽  
Characteristic Form ◽  
Heat Transfer Area ◽  
One Dimensional ◽  
Flow Equations ◽  
Compressible Fluid Flow

The paper reviews briefly a number of methods which are now available to facilitate solutions to the hyperbolic partial differential equations describing unsteady compressible fluid flow. Various schemes are considered and their merits and disadvantages discussed. Equations describing unsteady one-dimensional flow with heat transfer, area change and friction are presented in conservation-law, normal and characteristic forms. Pulsations in a compressor system are predicted using both the two-step Lax-Wendroff scheme and a scheme based on the characteristic form of the equations. The Lax-Wendroff scheme was simpler to apply, required less computer time, and gave better agreement with experimental results obtained from a single-stage reciprocating air-compressor system.

scholarly journals The Numerical Approximation of the Bioheat Equation of Space-Fractional Type Using Shifted Fractional Legendre Polynomials

2020 ◽  
pp. 875-889
Author(s):  
Firas A. Al-Saadawi ◽  
Hameeda Oda Al-Humedi
Keyword(s):  
Legendre Polynomials ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Dimensional Space ◽  
Bioheat Equation ◽  
One Dimensional ◽  
Good Convergence ◽  
The Matrix ◽  
The One ◽  
Fractional Type

The aim of this paper is to employ the fractional shifted Legendre polynomials (FSLPs) in the matrix form to approximate the fractional derivatives and find the numerical solutions of the one-dimensional space-fractional bioheat equation (SFBHE). The Caputo formula was utilized to approximate the fractional derivative. The proposed methodology applied for two examples showed its usefulness and efficiency. The numerical results showed that the utilized technique is very efficacious with high accuracy and good convergence.

Theory and Experiment for the Effect of Vascular Microstructure on Surface Tissue Heat Transfer—Part II: Model Formulation and Solution

1984 ◽  
Vol 106 (4) ◽  
pp. 331-341 ◽  
Author(s):  
L. M. Jiji ◽  
S. Weinbaum ◽  
D. E. Lemons
Keyword(s):  
Heat Transfer ◽  
Analytic Solution ◽  
Blood Perfusion ◽  
Skin Surface ◽  
Quantitative Model ◽  
Number Density ◽  
Model Formulation ◽  
Physiological Conditions ◽  
Vascular Geometry ◽  
Theory And Experiment

In this paper the conceptual three-layer representation of surface tissue heat transfer proposed in Weinbaum, Jiji and Lemons [I], is developed into a detailed quantitative model. This model takes into consideration the variation of the number density, size and flow velocity of the countercurrent arterio-venous vessels as a function of depth from the skin surface, the directionality of blood perfusion in the transverse vessel layer and the superficial shunting of blood to the cutaneous layer. A closed form analytic solution for the boundary value problem coupling the three layers is obtained. This solution is in terms of numerically evaluated integrals describing the detailed vascular geometry, a capillary bleed-off distribution function and parameters describing the shunting of blood to the cutaneous layer. Representative heat transfer results for typical physiological conditions are presented.

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