A Direct Substitution, Equation Error Technique for Solving the Thermographic Tomography Problem

1983 ◽  
Vol 105 (3) ◽  
pp. 237-243 ◽  
Author(s):  
A. M. Kleinman ◽  
R. B. Roemer
Keyword(s):  
Heat Transfer ◽  
Skin Temperature ◽  
Unique Solution ◽  
Transfer Problem ◽  
Subcutaneous Tissue ◽  
Blood Perfusion ◽  
Temperature Data ◽  
Hybrid Technique ◽  
Direct Substitution ◽  
Equation Error

A new technique for solving the combined state and parameter estimation problem in thermographic tomography is presented. The technique involves the direct substitution of known skin temperatures into the finite difference form of the bio-heat transfer equation as formulated for solving an initial value problem with a convection boundary condition at the skin surface. These equations are then used to solve the inverse bio-heat transfer problem for the unknown subcutaneous tissue temperatures and physiological parameters. For a small number of nodal points, closed form algebraic solutions are obtained. For larger sets of equations, a hybrid technique is used in which the problem is initially posed as an unconstrained optimization problem in which the model equation error is minimized using the conjugate gradient descent technique to get close to a solution. Then a generalized Newton-Raphson technique was used to solve the equations. A numerical simulation of a one-dimensional problem is investigated both with and without noise superimposed on the input (transient) skin temperature data. The results show that the technique gives very accurate results if the skin temperature data contains little noise. It is also shown that if the physical properties of the tissue and the metabolism are known, that a given set of proper transient skin temperature inputs yields a unique solution for the unknown internal temperatures and blood perfusion rates. However, the similar problem with known blood perfusion rates and unknown metabolisms does not yield a unique solution for the internal temperatures and metabolisms.

Numerical Simulation of Enhanced Skin Thermal Signature of Female Breast Tumor Subjected to Forced Convection

2003 ◽  
Author(s):  
A. Gupta ◽  
L. Hu ◽  
J. P. Gore ◽  
L. X. Xu
Keyword(s):  
Heat Transfer ◽  
Flow Field ◽  
Skin Temperature ◽  
Forced Convection ◽  
Infrared Imaging ◽  
Transfer Problem ◽  
Blood Perfusion ◽  
Skin Surface ◽  
Temperature Distributions ◽  
Thermal Signature

Early detection is considered to be the best defense against breast cancer and imaging plays a very important role in screening and in the diagnosis of symptomatic women. Infrared thermal imaging of skin temperature changes caused by a malignant tumor in breast is a rapidly developing detection modality with potential for functional detection. Knowledge and control of environmental factors which affect the skin temperature can reduce misinterpretations and false diagnosis associated with infrared imaging. A bio heat transfer based numerical model was utilized to study the energy balance in healthy and malignant breasts subjected to low velocity forced convection in a wind tunnel. Existing estimates of metabolic heating rates and previous measurements of temperature distributions along the radial direction in a region intersecting a known tumor and a comparable region in the healthy breast of the same patient were used to estimate the blood perfusion rates for the tumor. A simplified structural and thermal model was used for representing the changes within and around the tumor. Steady state temperature distributions on the skin surface of the breasts were obtained by numerically solving the conjugate heat transfer problem. Parametric studies on the influences of the airflow on the skin thermal expression of tumors were performed. It was found that the presence of tumor may not be clearly shown due to the irregularity of the skin temperature distribution induced by the flow field. Image processing techniques could be employed to eliminate the effects of the flow field and thermal noise and significantly improve the thermal signature of the tumor on the skin surface.

scholarly journals Solving bio-heat transfer multi-layer equation using Green’s Functions method

2021 ◽  
Vol 2090 (1) ◽  
pp. 012150
Author(s):  
de Oliveira Eduardo Peixoto ◽  
Gilmar Guimaräes
Keyword(s):  
Heat Transfer ◽  
Green's Functions ◽  
Green’S Functions ◽  
Transfer Problem ◽  
Blood Perfusion ◽  
The Body ◽  
Mathematical Background ◽  
Number Of Layers ◽  
Pennes Equation ◽  
Transfer Problems

Abstract An analytical method using Green’s Functions for obtaining solutions in bio-heat transfer problems, modeled by Pennes’ Equation, is presented. Mathematical background on how treating Pennes’ equation and its μ2T term is shown, and two contributions to the classical numbering system in heat conduction are proposed: inclusion of terms to specify the presence of the fin term, μ2T, and identify the biological heat transfer problem. The presentation of the solution is made for a general multi-layer domain, deriving and showing general approaches and Green’s Functions for such n number of layers. Numerical examples are presented to simplify human skin as a two-layer domain: dermis and epidermis, accounting metabolism as a heat source, and blood perfusion only at the dermis. Time-independent summations in the series-solution are written in closed forms, leading to better convergence along the boundaries. Details on obtaining the two-layer solution and its eigenvalues are presented for boundary conditions of prescribed temperature inside the body and convection at the surface, such as its intrinsic verification.

Experimental investigation of wall heat transfer due to spray combustion in a high-pressure/high-temperature vessel

2021 ◽  
pp. 146808742110072
Author(s):  
Karri Keskinen ◽  
Walter Vera-Tudela ◽  
Yuri M Wright ◽  
Konstantinos Boulouchos
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
High Pressure ◽  
High Temperature ◽  
High Speed ◽  
Transfer Problem ◽  
Wall Heat Transfer ◽  
Gas Temperature ◽  
Reference Case ◽  
High Pressure High Temperature

Combustion chamber wall heat transfer is a major contributor to efficiency losses in diesel engines. In this context, thermal swing materials (adapting to the surrounding gas temperature) have been pinpointed as a promising mitigative solution. In this study, experiments are carried out in a high-pressure/high-temperature vessel to (a) characterise the wall heat transfer process ensuing from wall impingement of a combusting fuel spray, and (b) evaluate insulative improvements provided by a coating that promotes thermal swing. The baseline experimental condition resembles that of Spray A from the Engine Combustion Network, while additional variations are generated by modifying the ambient temperature as well as the injection pressure and duration. Wall heat transfer and wall temperature measurements are time-resolved and accompanied by concurrent high-speed imaging of natural luminosity. An investigation with an uncoated wall is carried out with several sensor locations around the stagnation point, elucidating sensor-to-sensor variability and setup symmetry. Surface heat flux follows three phases: (i) an initial peak, (ii) a slightly lower plateau dependent on the injection duration, and (iii) a slow decline. In addition to the uncoated reference case, the investigation involves a coating made of porous zirconia, an established thermal swing material. With a coated setup, the projection of surface quantities (heat flux and temperature) from the immersed measurement location requires additional numerical analysis of conjugate heat transfer. Starting from the traces measured beneath the coating, the surface quantities are obtained by solving a one-dimensional inverse heat transfer problem. The present measurements are complemented by CFD simulations supplemented with recent rough-wall models. The surface roughness of the coated specimen is indicated to have a significant impact on the wall heat flux, offsetting the expected benefit from the thermal swing material.

High-output diesel engine heat transfer: Part 1 - comparison between piston heat flux and global energy balance

2021 ◽  
pp. 146808742110170
Author(s):  
Eric Gingrich ◽  
Michael Tess ◽  
Vamshi Korivi ◽  
Jaal Ghandhi
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Diesel Engine ◽  
Surface Temperature ◽  
Fast Response ◽  
Temperature Data ◽  
Start Of Injection ◽  
Local Measurements ◽  
Surface Temperature Data ◽  
High Output

High-output diesel engine heat transfer measurements are presented in this paper, which is the first of a two-part series of papers. Local piston heat transfer, based on fast-response piston surface temperature data, is compared to global engine heat transfer based on thermodynamic data. A single-cylinder research engine was operated at multiple conditions, including very high-output cases – 30 bar IMEPg and 250 bar in-cylinder pressure. A wireless telemetry system was used to acquire fast-response piston surface temperature data, from which heat flux was calculated. An interpolation and averaging procedure was developed and a method to recover the steady-state portion of the heat flux based on the in-cylinder thermodynamic state was applied. The local measurements were spatially integrated to find total heat transfer, which was found to agree well with the global thermodynamic measurements. A delayed onset of the rise of spatially averaged heat flux was observed for later start of injection timings. The dataset is internally consistent, for example, the local measurements match the global values, which makes it well suited for heat transfer correlation development; this development is pursued in the second part of this paper.

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