Eugene H. Wissler

A mathematical model of the human thermal system

This paper describes a mathematical model developed to simulate the physical characteristics of the human thermal system in the transient state. Physiological parameters, such as local metabolic heat generation rates, local blood flow rates, and rates of sweating, must be specified as input data. Automatic computation of these parameters will be built into the model at a later date when it is used to study thermal regulation in the human.

Significance of Blood Flow in Calculations of Temperature in Laser Irradiated Tissue

A dimensionless solution of the heat conduction equation for laser irradiation of tissue has been extended to include transport of heat owing to blood flow. The importance of the heat loss term is discussed in relation to the perfusion rate and exposure duration.

A simple theoretical model of heat and moisture transport in multi-layer garments in cool ambient air

Overall resistances for heat and vapor transport in a multilayer garment depend on the properties of individual layers and the thickness of any air space between layers. Under uncomplicated, steady-state conditions, thermal and mass fluxes are uniform within the garment, and the rate of transport is simply computed as the overall temperature or water concentration difference divided by the appropriate resistance. However, that simple computation is not valid under cool ambient conditions when the vapor permeability of the garment is low, and condensation occurs within the garment. Several recent studies have measured heat and vapor transport when condensation occurs within the garment (Richards et al. in Report on Project ThermProject, Contract No. G6RD-CT-2002-00846, 2002; Havenith et al. in J Appl Physiol 104:142–149, 2008). In addition to measuring cooling rates for ensembles when the skin was either wet or dry, both studies employed a flat-plate apparatus to measure resistances of individual layers. Those data provide information required to define the properties of an ensemble in terms of its individual layers. We have extended the work of previous investigators by developing a rather simple technique for analyzing heat and water vapor transport when condensation occurs within a garment. Computed results agree well with experimental results reported by Richards et al. (Report on Project ThermProject, Contract No. G6RD-CT-2002-00846, 2002) and Havenith et al. (J Appl Physiol 104:142–149, 2008). We discuss application of the method to human subjects for whom the rate of sweat secretion, instead of the partial pressure of water on the skin, is specified. Analysis of a more complicated five-layer system studied by Yoo and Kim (Text Res J 78:189–197, 2008) required an iterative computation based on principles defined in this paper.

On the applicability of the Taylor—Aris axial diffusion model to tubular reactor calculations

The relationship between the one dimensional Taylor—Aris model and the more detailed diffusion model for the steady state behavior of a tubular reactor is studied for the case of laminar flow and a first order reaction. It is shown that: (1) the Taylor—Aris model is valid provided that ka2/3·82D < 1; (2) the mean concentration computed using the Taylor—Aris model should be identified as the mean in the plane, Cm, and the net flux across any plane perpendicular to the axis of the reactor is Cm −[(a2U2/48D) + D] (∂Cm/∂z); for large Npe the inlet condition. Cm(0) = 1−(ka2/D)(1/48+1/N2Pe), seems to yield better results than the Wehner—Wilhelm boundary condition; and the zero gradient boundary condition is not the proper one to use at the outlet end of the reactor. It seems to be more appropriate to simply truncate a semi-infinite solution.

Model of human/liquid cooling garment interaction for space suit automatic thermal control.

The Wissler human thermoregulation model was augmented to incorporate simulation of a space suit thermal control system that includes interaction with a liquid cooled garment (LCG) and ventilation gas flow through the suit. The model was utilized in the design process of an automatic controller intended to maintain thermal neutrality of an exercising subject wearing a liquid cooling garment. An experimental apparatus was designed and built to test the efficacy of specific physiological state measurements to provide feedback data for input to the automatic control algorithm. Control of the coolant inlet temperature to the LCG was based on evaluation of transient physiological parameters that describe the thermal state of the subject, including metabolic rate, skin temperatures, and core temperature. Experimental evaluation of the control algorithm function was accomplished in an environmental chamber under conditions that simulated the thermal environment of a space suit and transient metabolic work loads typical of astronaut extravehicular activity (EVA). The model was also applied to analyze experiments to evaluate performance of the automatic control system in maintaining thermal comfort during extensive transient metabolic profiles for a range of environmental temperatures. Finally, the model was used to predict the efficacy of the LCG thermal controller for providing thermal comfort for a variety of regiments that may be encountered in future space missions. Simulations with the Wissler model accurately predicted the thermal interaction between the subject and LCG for a wide range of metabolic profiles and environmental conditions and matched the function of the automatic temperature controller for inlet cooling water to the LCG.

An Analysis of Chorioretinal Thermal Response to Intense Light Exposure

An analytical expression has been obtained for the transient temperature distribution produced when the retina is irradiated by a high-intensity light source. The following factors are included in the analysis: (1) structurally the fundus consists of layers of material which have different physical properties, (2) absorption of energy from the light beam follows the Beer-Lambert law, (3) energy is absorbed in the sclera as well as in the pigment epithelium and choroid, (4) heat is removed from the fundus by blood circulating through the capillaries of the choroid, and (5) intensity of the light source may vary with time. Computed values indicate that absorption of energy in the sclera and removal of heat by convection are both important for longer irradiation times, which agrees with recent experimental observations. The asymptotic response to a train of pulses is presented also.

50 years of computer simulation of the human thermoregulatory system.

This paper presents an updated and augmented version of the Wissler human thermoregulation model that has been developed continuously over the past 50 years. The existing Fortran code is translated into C with extensive embedded commentary. A graphical user interface (GUI) has been developed in Python to facilitate convenient user designation of input and output variables and formatting of data presentation. Use of the code with the GUI is described and demonstrated. New physiological elements were added to the model to represent the hands and feet, including the unique vascular structures adapted for heat transfer associated with glabrous skin. The heat transfer function and efficacy of glabrous skin is unique within the entire body based on the capacity for a very high rate of blood perfusion and the novel capability for dynamic regulation of blood flow. The model was applied to quantify the absolute and relative contributions of glabrous skin flow to thermoregulation for varying levels of blood perfusion. The model also was used to demonstrate how the unique features of glabrous skin blood flow may be recruited to implement thermal therapeutic procedures. We have developed proprietary methods to manipulate the control of glabrous skin blood flow in conjunction with therapeutic devices and simulated the effect of these methods with the model.

On the asymptotic behavior of a tubular reactor in the limit of small axial diffusivity

Abstract An efficient procedure is presented for obtaining the asymptotic form of the longitudinal concentration profile existing in a tubular reactor with small axial diffusivity. The reaction rate expression can be arbitrary. It is shown that longitudinal diffusion causes the concentration at the inlet end to fall below the far-upstream value, causes a modest flattening of the concentration profile along the reactor, and causes the concentration profile at the outlet end to curve upward sufficiently to satisfy the zero-gradient boundary condition.

Turbulent flow of gas through a circular tube with chemical reaction at the wall

Abstract A scheme is developed for computing concentration profiles when an arbitrary reaction occurs at the wall of a tubular reactor. Solutions are constructed using complete sets of orthogonal functions. For reactions which are not first order, it is necessary to solve an integral equation for the concentration of reactant at the wall. A convenient numerical scheme is developed for doing this. Eigenvalues and Fourier coefficients are presented together with computed concentration profiles for several typical cases.

Aerosol characterization using molecular beam techniques

Abstract Molecular beam techniques are applied to measure fundamental properties of aerosol particles. An aerosol-laden gas is sampled with a microprobe or a capillary tube and drawn into a vacuum chamber, where gas molecules are pumped out and an aerosol beam is formed. A surface ionization technique is used to measure the particle number intensity in aerosol beams of alkali metal compounds (primarily potassium iodide). The particle velocity is measured by a time-offlight technique, and the particle mass is measured by electrically charging the particles and subsequently deflecting them in an electrostatic field. Velocity relaxation in a retarding gas is utilized to measure the particle size, and the electric polarizability of neutral aerosol particles is measured by deflecting them in a nonuniform electrostatic field. Particle velocities from 70 to 670 m/sec masses from 1 × 10−20 to 1 × 10−18 kg, and radii from 0.01 to 0.1 μm were measured. Anomalously low mass densities and high electric polarizabilities were observed for these particles. This work demonstrates that aerosol beam techniques are potentially valuable tools for fundamental studies of aerosol particles.