A thermal model of the human body exposed to an electromagnetic field

The human body was modeled by numerical procedures to determine the thermal response under varied electromagnetic (EM) exposures. The basic approach taken was to modify the heat transfer equations for man in air to account for thermal loading due to the energy absorbed from the EM field. The human body was represented in an EM model by a large number of small cubical cells of tissue, and the energy density was determined for each cell. This information was then analyzed by a thermal response model consisting of a series of two-dimensional transient conduction equations with internal heat generation due to metabolism, internal convective heat transfer due to blood flow, external interaction by convection and radiation, and cooling of the skin by sweating and evaporation. This model simulated the human body by a series of cylindrical segments. The local temperature at 61 discrete locations as well as the thermoregulatory responses of vasodilatation and sweating were computed for a number of EM field intensities and two frequencies, one near whole-body resonance.     

Intraparticle diffusion alters the dynamic response of immobilized cell/enzyme columns

The effect of intra-particle tracer diffusion on the transient response of a fixed-bed column containing porous Ca-alginate beads is investigated experimentally. Dynamic response experiments are carried out using acetone solutions as tracer, whose concentration in the effluent stream is monitored on-line using a UV analyzer. Comparison of the response of such columns for two particle sizes (radii of 2 and 1?mm) to that of otherwise identical beds filled with solid glass particles of equal size reveals a substantial difference, mainly characterized by a trailing of the effluent concentration-vs-time curves at longer times. This cannot be explained by assuming a change in the effective porosity of the system, nor a change in the hydrodynamic dispersion. Following independent experimental determination of the pertinent physical parameters, a model based on the tanks-in-series concept [1,?2] is implemented on a personal computer and its predictions are compared to the experimental data. The essential assumption of the model is that tracer convection in the bulk liquid is substantially faster than intra-particle diffusion and, as a result, a bead is always surrounded by fluid of uniform (albeit time-dependent) concentration. In the absence of external mass transfer resistances and assuming that the porous nature of the Ca-alginate beads does not substantially alter the hydrodynamic dispersion in the column, the agreement between model and experiment is remarkably good. This leads to the suggestion that the observed response can be explained as the combined result of (fast) tracer convection in the bulk liquid and (slower) tracer diffusion from the bulk liquid to the beads.     

Heat transfer simulation using energy conservative dissipative particle dynamics

Dissipative particle dynamics with energy conservation (eDPD) was used to investigate conduction heat transfer in two dimensions under steady-state condition. Various types of boundary condition were implemented to the conduction domain. Besides, 2D conduction with internal heat generation was studied and the heat generation term was used to measure the thermal conductivity and diffusivity of the eDPD system. The boundary conditions used include both the Neumann and Dirichlet boundary conditions. The Neumann boundary condition was applied via adiabatic surfaces and surfaces exposed to convection heat transfer. The DPD simulations were compared to analytical solutions and finite-difference techniques. It was found that DPD appropriately predicts the temperature distribution in the conduction regime. Details of boundary condition implementation and thermal diffusivity measurement are also described in this paper.     

Computer-based analysis of steady-state and transient heat transfer of small-sized leaves by free and mixed convection

In order to study convective heat transfer of small leaves, the steady‐state and transient heat flux of small leaf‐shaped model structures (area of one side = 1730 mm²) were studied under zero and low (= 100 mm s^?1) wind velocities by using a computer simulation method. The results show that: (1) distinct temperature gradients of several degrees develop over the surface of the model objects during free and mixed convection; and (2) the shape of the objects and onset of low wind velocities has a considerable effect on the resulting temperature pattern and on the time constant τ. Small leaves can thus show a temperature distribution which is far from uniform under zero and low wind conditions. The approach leads, however, to higher leaf temperatures than would be attained by ‘real’ leaves under identical conditions, because heat transfer by transpiration is neglected. The results demonstrate the fundamental importance of a completely controlled environment when measuring heat dissipation by free convection. As slight air breezes alter the temperature of leaves significantly, the existence of purely free convection appears to be questionable in the case of outdoor conditions. Contrary to the prognoses yielded by standard approximations, no quantitative effect of buoyancy on heat transfer under the considered conditions could be detected for small‐sized leaf shapes.     

Air movement and heat loss from sheep. I. Boundary layer insulation of a model sheep, with and without fleece

A model sheep, made from metal cylinders and hemispheres, was heated electrically. Heat loss by forced convection in a wind tunnel was analysed in terms of the dependence of the Nusselt number (Nu) on Reynolds number (Re). For a bare trunk Nu = 0.095 Re0.684, but with fleece covering the trunk to a depth of 3.5 cm, Nu = 0.0112 Re0.875 when the mean radiative temperature of the the coat was taken as the surface temperature. Heat transfer by convection from the whole body, including legs, was described by Nu = 0.029 Re0.80. However, a bulk Nesselt number should not be used to estimate heat loss from a live sheep in a hot environment if the windspeed is below about 4 m s-1 because the relation between mean surface temperature, Nusselt number and convective heat flux is not unique.     

Conditions for equivalency of countercurrent vessel heat transfer formulations.

Previous models of countercurrent blood vessel heat transfer have used one of two, different, equally valid but previously unreconciled formulations, based either on: (1) the difference between the arterial and venous vessels' average wall temperatures, or (2) the difference between those vessels' blood bulk fluid temperatures. This paper shows that these two formulations are only equivalent when the four, previously undefined, "convective heat transfer coefficients" that are used in the bulk temperature difference formulation (two coefficients each for the artery and vein) have very specific, problem-dependent relationships to the standard convective heat transfer coefficients. (The average wall temperature formulation uses those standard coefficients correctly.) The correct values of these bulk temperature difference formulation "convective heat transfer coefficients" are shown to be either: (1) specific functions of (a) the tissue conduction resistances, (b) the standard convective heat transfer coefficients, and (c) the independently specified bulk arterial, bulk venous and tissue temperatures, or (2) arbitrary, user defined values. Thus, they are generally not equivalent to the standard convective heat transfer coefficients that are regularly used, and must change values depending on the blood and tissue temperatures. This dependence can significantly limit the convenience and usefulness of the bulk temperature difference formulations.     

Slip Effects on Mixed Convective Peristaltic Transport of Copper-Water Nanofluid in an Inclined Channel

Peristaltic transport of copper-water nanofluid in an inclined channel is reported in the presence of mixed convection. Both velocity and thermal slip conditions are considered. Mathematical modelling has been carried out using the long wavelength and low Reynolds number approximations. Resulting coupled system of equations is solved numerically. Quantities of interest are analyzed through graphs. Numerical values of heat transfer rate at the wall for different parameters are obtained and examined. Results showed that addition of copper nanoparticles reduces the pressure gradient, axial velocity at the center of channel, trapping and temperature. Velocity slip parameter has a decreasing effect on the velocity near the center of channel. Temperature of nanofluid increases with increase in the Grashoff number and channel inclination angle. It is further concluded that the heat transfer rate at the wall increases considerably in the presence of copper nanoparticles.     

Equations of heat distribution within the body

A vector integral equation describing heat distribution within the body has been derived. The factors considered are heat conduction, forced convection via the circulatory system, environmental exchange, metabolic heat production, and change in heat content. The vector partial differential equation and alternative forms incorporating boundary conditions were also developed. A difference equation based on a first-order approximation to the fundamental equations was derived to form the basis of a model for heat distribution within the body. It has been shown that factors involving conduction and convection must be considered independently unless the temperature of the blood flowing from a region of the body is equal to the average temperature of the tissue in that region. If this relation between tissue and blood temperature does exist, only a single temperature from each eleeent is needed to describe the heat distribution. In this latter case, models which ascribe all heat transfer to “equivalent” conduction or to convection can give valid predictions.     

Respiratory heat loss in the sheep: a comprehensive model

A model is presented for the respiratory heat loss in sheep, considering both the sensible heat lost by convection ( C(R)) and the latent heat eliminated by evaporation ( E(R)). A practical method is described for the estimation of the tidal volume as a function of the respiratory rate. Equations for C(R) and E(R) are developed and the relative importance of both heat transfer mechanisms is discussed. At air temperatures up to 30 degrees C sheep have the least respiratory heat loss at air vapour pressures above 1.6 kPa. At an ambient temperature of 40 degrees C respiratory loss of sensible heat can be nil; for higher temperatures the transfer by convection is negative and thus heat is gained. Convection is a mechanism of minor importance for the respiratory heat transfer in sheep at environmental temperatures above 30 degrees C. These observations show the importance of respiratory latent heat loss for thermoregulation of sheep in hot climates.     

Heat transfer modeling of the tongue

The heat transfer mechanism of tongue was investigated on the basis of experimental and theoretical research. Firstly, the relationship between tongue temperature and blood perfusion was obtained from animal experiment that mainly carried out on porcine tongue, subordinate on human tongue. Secondly, a one-dimensional variable coefficients second-order inhomogeneous heat transfer equation is developed by simplifying tongue as fin cube and the analytical solution is got. The results show that the change regulations of temperature by blood perfusion rate are the same in human and porcine tongue, and also, there is a good agreement between calculation and experimental results. When checking the model with corresponding properties of human tongue, the result is also satisfied. In conclusion, predicting temperature distribution of tongue is feasible with the fin cube model.     

An advanced computational bioheat transfer model for a human body with an embedded systemic circulation

In the present work, an elaborate one-dimensional thermofluid model for a human body is presented. By contrast to the existing pure conduction-/perfusion-based models, the proposed methodology couples the arterial fluid dynamics of a human body with a multi-segmental bioheat model of surrounding solid tissues. In the present configuration, arterial flow is included through a network of elastic vessels. More than a dozen solid segments are employed to represent the heat conduction in the surrounding tissues, and each segment is constituted by a multilayered circular cylinder. Such multi-layers allow flexible delineation of the geometry and incorporation of properties of different tissue types. The coupling of solid tissue and fluid models requires subdivision of the arterial circulation into large and small arteries. The heat exchange between tissues and arterial wall occurs by convection in large vessels and by perfusion in small arteries. The core region, including the heart, provides the inlet conditions for the fluid equations. In the proposed model, shivering, sweating, and perfusion changes constitute the basis of the thermoregulatory system. The equations governing flow and heat transfer in the circulatory system are solved using a locally conservative Galerkin approach, and the heat conduction in the surrounding tissues is solved using a standard implicit backward Euler method. To investigate the effectiveness of the proposed model, temperature field evolutions are monitored at different points of the arterial tree and in the surrounding tissue layers. To study the differences due to flow-induced convection effects on thermal balance, the results of the current model are compared against those of the widely used modelling methodologies. The results show that the convection significantly influences the temperature distribution of the solid tissues in the vicinity of the arteries. Thus, the inner convection has a more predominant role in the human body heat balance than previously thought. To demonstrate its capabilities, the proposed new model is used to study different scenarios, including thermoregulation inactivity and variation in surrounding atmospheric conditions.     

Millimeter‐Wave Heating in In Vitro Studies: Effect of Convection in Continuous and Pulse‐Modulated Regimes

Shallow penetration of millimeter waves (MMW) and non‐uniform illumination in in vitro experiments result in a non‐uniform distribution of the specific absorption rate (SAR). These SAR gradients trigger convective currents in liquids affecting transient and steady‐state temperature distributions. We analyzed the effect of convection on temperature dynamics during MMW exposure in continuous‐wave (CW) and pulsed‐wave (PW) amplitude‐modulated regimes using micro‐thermocouples. Temperature rise kinetics are characterized by the occurrence of a temperature peak that shifts to shorter times as the SAR of the MMW exposure increases and precedes initiation of convection in bulk. Furthermore, we demonstrate that the liquid volume impacts convection. Increasing the volume results in earlier triggering of convection and in a greater cooling rate after the end of the exposure. In PW regimes, convection strongly depends on the pulse duration that affects the heat pulse amplitude and cooling rate. The latter results in a change of the average temperature in PW regime. Bioelectromagnetics. 2019;40:553–568. © 2019 Bioelectromagnetics Society.     

Attrition-free pyrolysis to produce bio-oil and char

Experiments are performed on a laboratory scale setup where beech wood chips are heated by gas convection and walls radiation. This study shows that it is possible to obtain high bio-oil and char yields with relatively low external heat transfer coefficients. The main advantage of this convection/radiation heat transfer mode compared to solid–solid collisions, applied in fluidized bed or twin screw reactors, is the reduction of solid attrition (char and sand). Thus tricky gas–solid separation through hot cyclones and/or hot filters could be avoided or reduced. It should be possible to recover directly bio-oil with less char particles and char free of sand dust. These qualities would allow easier use of these bio-products in different applications.     

Numerical simulation of the pyrolysis zone in a downdraft gasification process

Models of the gasification process are mostly based on lumped analysis with distinct zones of the process treated as one entity. The study presented here was conducted to develop a more useful model specifically for the pyrolysis zone of the reactor of a downdraft gasifier based on finite computation method. Applying principles of energy and mass conservation, governing equations formed were solved by implicit finite difference method on the node of 100 throughout the length of the considered pyrolysis range (20 cm). Heat transfer considered convection, conduction, and the influence of solid radiation components. Chemical kinetics concept was also adopted to simultaneously solve the temperature profile and feedstock consumption rate on the pyrolysis zone. The convergence criteria were set at 10⁻⁶ and simulation used Fortran Power Station 4.0. Validation experiments were also conducted resulting in maximum deviation of 24 °C and 0.37 kg/h for temperature and feedstock feed rate, respectively.     

Combined discrete particle and continuum model predicting solid-state fermentation in a drum fermentor

The development of mathematical models facilitates industrial (large-scale) application of solid-state fermentation (SSF). In this study, a two-phase model of a drum fermentor is developed that consists of a discrete particle model (solid phase) and a continuum model (gas phase). The continuum model describes the distribution of air in the bed injected via an aeration pipe. The discrete particle model describes the solid phase. In previous work, mixing during SSF was predicted with the discrete particle model, although mixing simulations were not carried out in the current work. Heat and mass transfer between the two phases and biomass growth were implemented in the two-phase model. Validation experiments were conducted in a 28-dm3 drum fermentor. In this fermentor, sufficient aeration was provided to control the temperatures near the optimum value for growth during the first 45-50 hours. Several simulations were also conducted for different fermentor scales. Forced aeration via a single pipe in the drum fermentors did not provide homogeneous cooling in the substrate bed. Due to large temperature gradients, biomass yield decreased severely with increasing size of the fermentor. Improvement of air distribution would be required to avoid the need for frequent mixing events, during which growth is hampered. From these results, it was concluded that the two-phase model developed is a powerful tool to investigate design and scale-up of aerated (mixed) SSF fermentors.     

CFD simulation of mass transfer and flow behaviour around a single particle in bioleaching process

The pathway to reach a certain target in many processes such as bioleaching, due to the complex and poorly understood hydrodynamics, reaction kinetics, and chemistry knowledge involved is not apparent. An investigation of the interactions between the parameters in bioleaching process can be applied to optimize the rate of metal extraction from sulphide minerals. Such investigations can be carried out with the aid of numerical simulations. In this study, a computational fluid dynamics (CFD) model was developed to better understand the mass transfer phenomenon and complex flow field around a single particle. The commercial software FLUENT 6.2 has been employed to solve the governing equations. Volume of fluid (VOF) method was used to predict the fluid volume fraction in a 3D geometry. The computational model has successfully captured the results observed in the experiments. Simulation results indicate that concentrations of species in a thin layer of liquid on the particle surface are much higher than their concentrations in the liquid bulk and significant gradients in the ion concentrations between the surface of the particle and the liquid bulk were observed.     

Theoretical and Experimental Studies of Energy Exchange from Jackrabbit Ears and Cylindrically Shaped Appendages

Convection properties of jackrabbit ears were examined in a wind tunnel and in the field in an attempt to study the possible thermal role of the large ears. This work was part of a study on energy exchange of appendages. Cylindrical copper models of various shapes, aluminum castings of domestic and jackrabbit ears, and an amputated jackrabbit ear were studied in a wind tunnel (a) to define the range for convective heat loss for appendages of various shapes, and (b) to study the effect on convection of model shape and orientation to the wind. Shape, i.e. length and closure, proved important. Orientation to the wind produced no consistent or significant variation in the convection coefficient. The convection coefficients from the ear castings fell within the range generated from the cylindrical models. The convection coefficients for the amputated rabbit ear fell partially within the range. Net thermal radiation loss at midday from the jackrabbit ears was found to be small. Convection from the ears, however, could account for the loss of over 100% of the animal's metabolic heat at an air temperature of 30°C. If air temperature exceeds body temperature, the animal must either store heat or resort to the evaporation of water.     

Heat and water transfer in a rotating drum containing solid substrate particles

In previous work we reported on the simulation of mixing behavior of a slowly rotating drum for solid-state fermentation (SSF) using a discrete particle model. In this investigation the discrete particle model is extended with heat and moisture transfer. Heat transfer is implemented in the model via interparticle contacts and the interparticle heat transfer coefficient is determined experimentally. The model is shown to accurately predict heat transfer and resulting temperature gradients in a mixed wheat grain bed. In addition to heat transfer, the addition and subsequent distribution of water in the substrate bed is also studied. The water is added to the bed via spray nozzles to overcome desiccation of the bed during evaporative cooling. The development of moisture profiles in the bed during spraying and mixing are studied experimentally with a water-soluble fluorescent tracer. Two processes that affect the water distribution are considered in the model: the intraparticle absorption process, and the interparticle transfer of free water. It is found that optimum distribution can be achieved when the free water present at the surface of the grains is quickly distributed in the bed, for example, by fast mixing. Alternatively, a short spraying period, followed by a period of mixing without water addition, can be applied. The discrete particle model developed is used successfully to examine the influence of process operation on the moisture distribution (e.g., fill level and rotation rate). It is concluded that the extended discrete particle model can be used as a powerful predictive tool to derive operating strategies and criteria for design and scale-up for mixed SSF and other processes with granular media.     

Numerical modelling of conductive and convective heat transfers in retinal laser applications

The control of the temperature increase is an important issue in retinal laser treatments. Within the fundus of the eye heat, generated by absorption of light, is transmitted by diffusion in the retinal pigment epithelium and in the choroid and lost by convection due to the choroidal blood flow. The temperature can be spatially and temporally determined by solving the heat equation. In a former analytical model this was achieved by assuming uniform convection for the whole fundus of the eye. A numerical method avoiding this unrealistic assumption by considering convective heat transfer only in the choroid is used here to solve the heat equation. Numerical results are compared with experimental results obtained by using a novel method of noninvasive optoacoustic retinal temperature measurements in rabbits. Assuming global convection the perfusion coefficient was evaluated to 0.07 s^?1, whereas a value of 0.32 s^?1 – much closer to values found in the literature (between 0.28 and 0.30 s^?1) – was obtained when choroidal convection was assumed, showing the advantage of the numerical method. The modelling of retinal laser treatment is thus improved and could be considered in the future to optimize treatments by calculating retinal temperature increases under various tissues and laser properties. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Parametric studies on the three-layer microcirculatory model for surface tissue energy exchange

The new three-layer microvascular mathematical model for surface tissue heat transfer developed in, which is based on detailed vascular casts and tissue temperature measurements in the rabbit thigh, is used to investigate the thermal characteristics of surface tissue under a wide variety of physiological conditions. Studies are carried out to examine the effects of vascular configuration, arterial blood supply rate, distribution of capillary perfusion, cutaneous blood circulation and metabolic heat production on the average tissue temperature profile, the local arterial-venous blood temperature difference in the thermally significant countercurrent vessels, and surface heat flux.