scholarly journals Modelling and investigation of temperature field in the boundary layer of biological bodies

2017 ◽  
pp. 90-99
Author(s):  
Bogdan Khapko
Keyword(s):  
Boundary Layer ◽  
Integral Equation ◽  
Temperature Field ◽  
Temperature Distribution ◽  
Heat Generation ◽  
Transfer Problem ◽  
Blood Perfusion ◽  
Metabolic Heat ◽  
Metabolic Heat Generation ◽  
Equation Analysis

A problem on finding temperature field in the boundary layer of biological body when blood perfusion coefficient depends on coordinate is solved. Temperature distribution is caused by the temperature differences between the inside and outside of a body and by the outside heat sources and metabolic heat generation. Heat transfer problem is formulated by using generalized Heaviside functions. Applying the variation of constants method this problem is reduced to the Fredholm integral equation of the second kind. Numerical method of Simpson quadratures was used to solve integral equation. Analysis of temperature distribution in the boundary layer for some cases of boundary conditions is performed. Dependence on temperature inside body from metabolic heat generation and outside heat source is analyzed.

Effect of Physiological Parameters on the Temperature Distribution of a Layered Head Model

2002 ◽  
Author(s):  
Obdulia Ley ◽  
Yildiz Bayazitoglu
Keyword(s):  
Blood Flow ◽  
Temperature Distribution ◽  
Heat Generation ◽  
Brain Temperature ◽  
Blood Perfusion ◽  
Physiological Parameters ◽  
Head Model ◽  
Metabolic Heat ◽  
Metabolic Heat Generation ◽  
The Brain

Brain temperature control is important in clinical therapy, because moderate temperature reduction of brain temperature increases the survival rate after head trauma. A factor that affects the brain temperature distribution is the cerebral blood flow, which is controlled by autoregulatory mechanisms. To improve the existing thermal models of brain, we incorporate the effect of the temperature over the metabolic heat generation, and the regulatory processes that control the cerebral blood perfusion and depend on physiological parameters like, the mean arterial blood pressure, the partial pressure of oxygen, the partial pressure of carbon dioxide, and the cerebral metabolic rate of oxygen consumption. The introduction of these parameters in a thermal model gives information about how specific conditions, such as brain edema, hypoxia, hypercapnia, or hypotension, affect the temperature distribution within the brain. Existing biological thermal models of the human brain, assume constant blood perfusion, and neglect metabolic heat generation or consider it constant, which is a valid assumption for healthy tissue. But during sickness, trauma or under the effect of drugs like anesthetics, the metabolic activity and organ blood flow vary considerably, and such variations must be accounted for in order to achieve accurate thermal modeling. Our work, on a layered head model, shows that variations of the physiological parameters have profound effect on the temperature gradients within the head.

TEMPERATURE DISTRIBUTION AND THERMAL DAMAGE OF PERIPHERAL TISSUE IN HUMAN LIMBS DURING HEAT STRESS: A MATHEMATICAL MODEL

2016 ◽  
Vol 16 (05) ◽  
pp. 1650064 ◽  
Author(s):  
MIR AIJAZ ◽  
M. A. KHANDAY
Keyword(s):  
Finite Element ◽  
Temperature Distribution ◽  
Heat Generation ◽  
Thermal Damage ◽  
Subcutaneous Tissue ◽  
The Body ◽  
Bioheat Equation ◽  
Metabolic Heat ◽  
Metabolic Heat Generation ◽  
Living Tissues

The physiological processes taking place in human body are disturbed by the abnormal changes in climate. The changes in environmental temperature are not effective only to compete with thermal stability of the system but also in the development of thermal injuries at the skin surfaces. Therefore, it is of great importance to estimate the temperature distribution and thermal damage in human peripherals at extreme temperatures. In this paper, the epidermis, dermis and subcutaneous tissue were modeled as uniform elements with distinct thermal properties. The bioheat equation with appropriate boundary conditions has been used to estimate the temperature profiles at the nodal points of the skin and subcutaneous tissue with variable ambient heat and metabolic activities. The model has been solved by variational finite element method and the results of the changes in temperature distribution of the body and the damage to the exposed living tissues has been interpreted graphically in relation with various atmospheric temperatures and rate of metabolic heat generation. By involving the metabolic heat generation term in bioheat equation and using the finite element approach the results obtained in this paper are more reasonable and appropriate than the results developed by Moritz and Henriques, Diller and Hayes, and Jiang et al.

Estimation of Blood Perfusion and Metabolic Heat Generation of Lung Tumor During Cryosurgery

2018 ◽  
Author(s):  
Haile Baye Kassahun ◽  
Henok Tadesse Moges ◽  
Amanuel Shigut Dinsa ◽  
Wubshet Shimels Negussie ◽  
Okebiorun Michael Oluwaseyi ◽  
...  
Keyword(s):  
Heat Generation ◽  
Lung Tumor ◽  
Blood Perfusion ◽  
Metabolic Heat ◽  
Metabolic Heat Generation

Combined Solution of the Inverse Stefan Problem for Successive Freezing/Thawing in Nonideal Biological Tissues

1997 ◽  
Vol 119 (2) ◽  
pp. 146-152 ◽  
Author(s):  
Y. Rabin ◽  
A. Shitzer
Keyword(s):  
Phase Transition ◽  
Heat Generation ◽  
Thermal Effects ◽  
Blood Perfusion ◽  
Biological Tissues ◽  
Initial Condition ◽  
Freezing Front ◽  
Metabolic Heat ◽  
Metabolic Heat Generation ◽  
Combined Solution

A new combined solution of the one-dimensional inverse Stefan problem in biological tissues is presented. The tissue is assumed to be a nonideal material in which phase transition occurs over a temperature range. The solution includes the thermal effects of blood perfusion and metabolic heat generation. The analysis combines a heat balance integral solution in the frozen region and a numerical enthalpy-based solution approach in the unfrozen region. The subregion of phase transition is included in the unfrozen region. Thermal effects of blood perfusion and metabolic heat generation are assumed to be temperature dependent and present in the unfrozen region only. An arbitrary initial condition is assumed that renders the solution useful for cryosurgical applications employing repeated freezing/thawing cycles. Very good agreement is obtained between the combined and an exact solution of a similar problem with constant thermophysical properties and a uniform initial condition. The solution indicated that blood perfusion does not appreciably affect either the shape of the temperature forcing function on the cryoprobe or the location and depth of penetration of the freezing front in peripheral tissues. It does, however, have a major influence on the freezing/thawing cycle duration, which is most pronounced during the thawing stage. The cooling rate imposed at the freezing front also has a major inverse effect on the duration of the freezing/thawing.

scholarly journals Mathematical Model of a Three-Dimensional Non-Isothermal Glacier

1976 ◽  
Vol 16 (74) ◽  
pp. 308-309
Author(s):  
S.S. Grigoryan ◽  
M.S. Krass ◽  
P.A. Shumskiy
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Conduction ◽  
Temperature Distribution ◽  
Small Parameter ◽  
Heat Generation ◽  
Curvilinear Coordinates ◽  
Shear Stresses ◽  
System Of Equations ◽  
Equation Of Heat Conduction

Abstract In the case of a non-isothermal glacier it is necessary to integrate the equations of dynamics together with the equation of heat conduction, heat transfer, and heat generation because of the interdependence (1) of strain-rate of ice on its temperature, and (2) of ice temperature on the rate of heat transfer by moving ice and on the intensity of heat generation in its strain. In view of the complexity of the whole system of equations, simplified mathematical models have been constructed for dynamically different glaciers. The present model concerns land glaciers with thicknesses much less than their horizontal dimensions and radii of curvature of large bottom irregularities, so that the method of a thin boundary layer may be used. The principal assumption is the validity of averaging over a distance of the order of magnitude of ice thickness. Two component shear stresses parallel to the bottom in glaciers of this type considerably exceed the normal stresses and the third shear stress, so the dynamics are described by a statically determined system of equations. For the general case, expressions for the stresses have been obtained in dimensionless affine orthogonal curvilinear coordinates, parallel and normal to the glacier bottom, and taking into account the geometry of the lower and upper surfaces. The statically undetermined problem for ice divides is solved using the equations of continuity and rheology, so the result for stresses depends considerably on temperature distribution. In the case of a flat bottom the dynamics of an ice divide is determined by the curvature of the upper surface. The calculation of the interrelating velocity and temperature distributions is made by means of the iteration of solutions (1) for the components of velocity from the stress expressions using the rheological equations (a power law or the more precise hyberbolic one) with the assigned temperature distribution, and (2) for the temperature with the assigned velocity distribution. The temperature distribution in the coordinate system used is determined by a parabolic equation with a small parameter at the principal derivative. Its solution is reduced to the solution of a system of recurrent non-uniform differential equations of the first order by means of a series expansion of the small parameter: the right part for the largest term of the expansion contains a function of the heat sources, and for the other terms it contains the second derivative along the vertical coordinate from the previous expansion term. Thus advection makes the main contribution to the heat transfer, and temperature in a glacier is distributed along the particle paths, changing simultaneously under the influence of heat generation. A relatively thin conducting boundary layer adjoins the upper and lower surfaces of a glacier, playing the role of a temperature damper in the ablation area. The equation of heat conduction (at the free surface) or of heat conduction and heat transfer (at the bottom) with the boundary conditions, and with the condition of the connection with the solution of the problem for the internal temperature distribution, is being solved for the boundary layer because of its small thickness. Beyond the limits of the boundary layer, heat conduction makes a small change in the temperature distribution, which can be calculated with any degree of accuracy.

Estimation of the kidney metabolic heat generation rate

2019 ◽  
Vol 35 (9) ◽  
Author(s):  
Helcio R.B. Orlande ◽  
Nelson Afonso Lutaif ◽  
José Antonio Rocha Gontijo
Keyword(s):  
Heat Generation ◽  
Generation Rate ◽  
Heat Generation Rate ◽  
Metabolic Heat ◽  
Metabolic Heat Generation

scholarly journals Mathematical Model of a Three-Dimensional Non-Isothermal Glacier

1976 ◽  
Vol 16 (74) ◽  
pp. 308-309
Author(s):  
S.S. Grigoryan ◽  
M.S. Krass ◽  
P.A. Shumskiy
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Conduction ◽  
Temperature Distribution ◽  
Small Parameter ◽  
Heat Generation ◽  
Curvilinear Coordinates ◽  
Shear Stresses ◽  
System Of Equations ◽  
Equation Of Heat Conduction

AbstractIn the case of a non-isothermal glacier it is necessary to integrate the equations of dynamics together with the equation of heat conduction, heat transfer, and heat generation because of the interdependence (1) of strain-rate of ice on its temperature, and (2) of ice temperature on the rate of heat transfer by moving ice and on the intensity of heat generation in its strain. In view of the complexity of the whole system of equations, simplified mathematical models have been constructed for dynamically different glaciers. The present model concerns land glaciers with thicknesses much less than their horizontal dimensions and radii of curvature of large bottom irregularities, so that the method of a thin boundary layer may be used. The principal assumption is the validity of averaging over a distance of the order of magnitude of ice thickness.Two component shear stresses parallel to the bottom in glaciers of this type considerably exceed the normal stresses and the third shear stress, so the dynamics are described by a statically determined system of equations. For the general case, expressions for the stresses have been obtained in dimensionless affine orthogonal curvilinear coordinates, parallel and normal to the glacier bottom, and taking into account the geometry of the lower and upper surfaces. The statically undetermined problem for ice divides is solved using the equations of continuity and rheology, so the result for stresses depends considerably on temperature distribution. In the case of a flat bottom the dynamics of an ice divide is determined by the curvature of the upper surface.The calculation of the interrelating velocity and temperature distributions is made by means of the iteration of solutions (1) for the components of velocity from the stress expressions using the rheological equations (a power law or the more precise hyberbolic one) with the assigned temperature distribution, and (2) for the temperature with the assigned velocity distribution. The temperature distribution in the coordinate system used is determined by a parabolic equation with a small parameter at the principal derivative. Its solution is reduced to the solution of a system of recurrent non-uniform differential equations of the first order by means of a series expansion of the small parameter: the right part for the largest term of the expansion contains a function of the heat sources, and for the other terms it contains the second derivative along the vertical coordinate from the previous expansion term.Thus advection makes the main contribution to the heat transfer, and temperature in a glacier is distributed along the particle paths, changing simultaneously under the influence of heat generation. A relatively thin conducting boundary layer adjoins the upper and lower surfaces of a glacier, playing the role of a temperature damper in the ablation area. The equation of heat conduction (at the free surface) or of heat conduction and heat transfer (at the bottom) with the boundary conditions, and with the condition of the connection with the solution of the problem for the internal temperature distribution, is being solved for the boundary layer because of its small thickness. Beyond the limits of the boundary layer, heat conduction makes a small change in the temperature distribution, which can be calculated with any degree of accuracy.

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