Temperature control in solid substrate fermentation through discontinuous rotation

A laboratory-scale system for controlled dynamic solid substrate fermentation was developed and tested. The fermentation takes place in a stainless steel discontinuously rotating drum reactor, under controlled conditions of temperature, gas composition, relative humidity and direction and rate of rotation. The system was tested on a model fermentation of soya beans with Rhizopus oligosporus. In contrast to the traditional tempe fermentation, a granular product is obtained and build-up of heat and mass gradients is restricted. Despite the discontinuous rotation, the fungal growth continues, as evidenced by the production of heat. The rate of cooling depends on the temperature of the gas flushed through the reactor, the gas flow rate and the lenght of the rotation period. As a consequence of the homogeneous temperature control, the fungal heat development continued up to 70 h of fermentation. This is in clear contrast with the traditional tempe fermentation, which is already limited after 36 h by its own heat accumulation. Correspondence to: M. J. R. Nout     

A combined macro and microvascular model for whole limb heat transfer

A new prototype model for whole limb heat transfer is proposed wherein the countercurrent heat exchange from the large central arteries and veins in the core of the limb is coupled to microvascular models for the surrounding muscle and the cutaneous tissue layers. The local microvascular temperature field in the muscle tissue is described by the bioheat equation of Weinbaum and Jiji. The new model allows for an arbitrary axial variation of cross-sectional area and blood distribution between the muscle and cutaneous tissue, accounts for the blood flow to and heat loss from the hand and treats the venous return temperature and surface temperature distribution as unknowns that are determined as part of the solution to the overall boundary value problem. Representative solutions are presented for a wide range of environmental conditions for a limb in both the resting state and during exercise.     

The motion of the left ventricle—III

We use the concept of a layered wall, where each separate layer is to be homogeneous, isotropic, and incompressible, to derive stress-strain relations for the middle layer muscle ring at the transverse midsection of the left ventricle; a convenient method of formulation is that based on the elastic potential function. The hoop or circumferential stress in all three layers is found using dimensional and mechanical parameters derived earlier. The various parameters are expressed as Fourier series so that their behavior over a complete ventricular cycle is known analytically. The cases of simple elongation and what we termcurvilinear simple elongation are considered for the middle layer muscle ring strain, and the resulting stress-strain relations are derived. The results are compared with an incompressible rubber-like material known as a Mooney material.     

A three-dimensional variable geometry countercurrent model for whole limb heat transfer.

A new formulation of the combined macro and microvascular model for heat transfer in a human arm developed in Song et al. [1] is proposed using a recently developed approximate theory for the heat exchange between countercurrent vessels embedded in a tissue cylinder with surface convection [2]. The latter theory is generalized herein to treat an arm with an arbitrary variation in cross-sectional area and continuous bleed off from the axial vessels to the muscle and cutaneous tissue. The local microvascular temperature field is described by a "hybrid" model which applies the Weinbaum-Jiji [3] and Pennes [4] equations in the peripheral and deeper tissue layers, respectively. To obtain reliable end conditions at the wrist and other model input parameters, a plethysmograph-calorimeter has been used to measure the blood flow distribution between the arm and hand circulations, and hand heat loss. The predictions of the model show good agreement with measurements for the axial surface temperature distribution in the arm and confirm the minimum in the axial temperature variation first observed by Pennes [4] for an arm in a warm environment.     

Finite-element solution of thermal conductivity of muscle during cold water immersion

The in vivo or effective thermal conductivity (keff) of muscle tissue of the human forearm was determined through a finite-element (FE) model solution of the bioheat equation. Data were obtained from steady-state temperatures measured in the forearm after 3 h of immersion in water at temperatures (Tw) of 15 (n = 6), 20 (n = 5), and 30 degrees C (n = 5). Temperatures were measured every 0.5 cm from the longitudinal axis of the forearm to the skin approximately 9 cm distal from the elbow. Heat flux was measured at two sites on the skin adjacent to the temperature probe. The FE model is comprised of concentric annular compartments with boundaries defined by the location of temperature measurements. Through this approach, it was possible to include both the metabolic heat production and the convective heat transfer between blood and tissue at two levels of blood flow, one perfusing the compartment and the other passing through the compartment. Without heat exchange at the passing blood flow level, the arterial blood temperature would be assumed to have a constant value everywhere in the forearm muscles, leading to a solution of the bioheat equation that greatly underpredicts keff. The extent of convective heat exchange at the passing blood flow level is estimated to be approximately 60% of the total heat exchange between blood and tissue. Concurrent with this heat exchange is a decrease in the temperature of the arterial blood as it flows radially from the axis to the skin of the forearm, and this decrease is enhanced with a lowered Tw.(ABSTRACT TRUNCATED AT 250 WORDS)     

The bleed off perfusion term in the Weinbaum-Jiji bioheat equation.

The microvascular organization and thermal equilibration of the primary and secondary arteries and veins that comprise the bleed off circulation to the muscle fibers from the parent countercurrent supply artery and veins are analyzed. The blood perfusion heat source term in the tissue energy equation is shown to be related to this vascular organization and to undergo a fundamental change in behavior as one proceeds from the more peripheral tissue, where the perfusion term is proportional to the Ta--Tv difference in the parent supply vessels, to the deeper tissue layers where the bleed off vessels themselves form a branching countercurrent system for each muscle tissue cylinder and the venous return temperature can vary between the local tissue temperature and Ta. The consequences of this change in behavior are examined for the Weinbaum-Jiji bioheat equation and a modified expression for the effective conductivity of perfused tissue is derived for countercurrent bleed off exchange.     

Prediction of temperature profiles in the human skin and subcutaneous tissues

Exact mathematical solutions in terms of confluent hypergeometric and Airy's functions are obtained to study the steady state temperature distributions in human skin and subcutaneous tissues (SST). It is assumed that the skin is exposed to an air environment and heat transfer from the skin occurs by convection, radiation and evaporation. A mathematical model of the SST, accounting for heat conduction, perfusion of the capillary beds and metabolic heat productions of the dermis and subcutaneous tissues, has been solved to obtain interface temperatures for a wide range of environmental temperatures, rates of evaporation of sweat, wind speeds and relative humidities. The solutions provide inter-relationships between interface temperatures, thermal conductivities, metabolic heat production, blood perfusion, thicknesses of various layers of SST and ambient temperature.     

Kinetics of heat processes in human muscle]

Measurements of deep temperature in muscle are conducted by means of microwave radiothermometer which allow one to separate contributions of different intramuscle processes: that of the contractile system, bloodflow, heat production due to metabolic processes during muscle work. The efficiency coefficient of the contractile system is not less than 33%, bloodflow and metabolism induce equal temperature increase. A mathematical model is proposed to calculate from noninvasive experimental data the blood flow dynamics during and after different muscle loads.     

Estimation of surface heat flux and temperature distributions in a multilayer tissue based on the hyperbolic model of heat conduction

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to solve the inverse hyperbolic heat conduction problem in estimating the unknown time-dependent surface heat flux in a skin tissue, which is stratified into epidermis, dermis, and subcutaneous layers, from the temperature measurements taken within the medium. Subsequently, the temperature distributions in the tissue can be calculated as well. The concept of finite heat propagation velocity is applied to the modeling of the bioheat transfer problem. The inverse solutions will be justified based on the numerical experiments in which two different heat flux distributions are to be determined. The temperature data obtained from the direct problem are used to simulate the temperature measurements. The influence of measurement errors on the precision of the estimated results is also investigated. Results show that an excellent estimation on the time-dependent surface heat flux can be obtained for the test cases considered in this study.     

Heat Transfer Analysis for Stationary Boundary Layer Slip Flow of a Power-Law Fluid in a Darcy Porous Medium with Plate Suction/Injection

In this paper, we investigate the slip effects on the boundary layer flow and heat transfer characteristics of a power-law fluid past a porous flat plate embedded in the Darcy type porous medium. The nonlinear coupled system of partial differential equations governing the flow and heat transfer of a power-law fluid is transformed into a system of nonlinear coupled ordinary differential equations by applying a suitable similarity transformation. The resulting system of ordinary differential equations is solved numerically using Matlab bvp4c solver. Numerical results are presented in the form of graphs and the effects of the power-law index, velocity and thermal slip parameters, permeability parameter, suction/injection parameter on the velocity and temperature profiles are examined.     

Blood flow: Theory,effective viscosity and effects of particle distribution

A study is made of blood flow by assuming that the blood constitutes a suspension of cells in plasma instead of a simple homogeneous fluid. A macroscopic theory governing the motion of plasma in a plasma-cell system is derived from the local volume averaging method for a system without mass transfer between the phases, and its characteristic length is much larger than the size of the cells. The equations governing the motion of the local averaged fluid quantities include one additional term in the equation of motion and two additional terms in the energy equation. These terms represent, respectively, the force exerted upon the fluid by the particles, and the rate of heat transfer and work kone upon the fluid by the particles. The theory is applied to obtain the effective viscosity as the explicit function of the volume concentration of the cells by assuming that the cells behave like rigid spherical particles with slip-collision, and the plasma is an compressible Newtonian fluid. Comparison with existing experimental results shows a good agreement. The theory is also used to obtain the effects of cell distribution upon the overall effective viscosity in a circular tube. The quantitative result shows that there is a decrease in overall effective viscosity as the concentration of cells increases toward the center of the tube, and the overall effective viscosity is smaller than the flow with evenly distributed cells.     

Structure of the brain and eye heater tissue in marlins, sailfish, and spearfishes

Marlins, sailfish, and spearfishes have a heat-producing tissue beneath the brain and adjacent to the eyes. This tissue warms the brain and eyes while the rest of the body remains at water temperature. The heater tissue is derived from the superior rectus eye muscle. Only a portion of this eye muscle contains normal skeletal muscle tissue; the rest consists of the modified muscle tissue that is associated with heat production. The heat-producing portion is supplied with blood through a countercurrent heat exchanger that originates from the carotid artery. The vascular rate prevents the heat being produced by the tissue from being dissipated at the gill. An unusual circulatory supply to the eyes and brain is associated with the presence of the heater tissue in these fishes.     

Wavelet decomposition of transmitted ultrasound wave through a 1-D muscle-bone system

In the attempt for using ultrasound as a diagnostic device for osteoporosis, several authors have described the result of the in vitro experiment in which ultrasound is passed through a cancellous bone specimen placed in a water tank. However, in the in vivo setting, a patient's cancellous bone is surrounded by cortical and muscle layers. This paper considers in the one-dimensional case (1) what effect the cortical bone segments surrounding the cancellous segment would have on the received signal and (2) what the received signal would be when a source and receiver are placed on opposite sides of a structure consisting of a cancellous segment surrounded by cortical and muscle layers. Mathematically this is accomplished by representing the received signal as a sum of wavelets which go through different reflection-transmission histories at the muscle-cortical bone and cortical-cancellous bone interfaces. The muscle and cortical bone are modeled as elastic materials and the cancellous bone as a poroelastic material described by the Biot-Johnson-Koplik-Dashen model. The approach presented here permits the assessment of which possible paths of transmission and reflection through the cortical-cancellous or muscle-cortical-cancellous complex will result in significant contributions to the received waveform. This piece of information can be useful for solving the inverse problem of non-destructive assessment of material properties of bone. Our methodology can be generalized to three-dimensional parallelly layered structure by first applying Fourier transform in the directions perpendicular to the transverse direction.     

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.     

Swimming muscle helps warm the brain of lamnid sharks

Summary Lamnid sharks are known to have warm red muscle and warm brains. We describe a large vein in lamnid sharks that provides a route for transfer of warm blood from the red muscle to the central nervous system. This red muscle vein runs longitudinally in the red muscle and is valved to direct blood flow anteriorly. It joins the myelonal vein in the neural canal, thus providing a route for blood flow from the red muscle to the brain. Temperature profiles along the neural canal of freshly caught mako sharks show that warm blood enters the myelonal vein from the red muscle vein. Experiments with heat generation by model brains indicate that the metabolic heat produced by the brain is probably not sufficient to cause the temperature elevations observed. Metabolic heat imported from the red swimming muscle may be a valuable addition to the heat budget of the head.     

Hydromagnetic Flow and Heat Transfer over a Porous Oscillating Stretching Surface in a Viscoelastic Fluid with Porous Medium

An analysis is carried out to study the heat transfer in unsteady two-dimensional boundary layer flow of a magnetohydrodynamics (MHD) second grade fluid over a porous oscillating stretching surface embedded in porous medium. The flow is induced due to infinite elastic sheet which is stretched periodically. With the help of dimensionless variables, the governing flow equations are reduced to a system of non-linear partial differential equations. This system has been solved numerically using the finite difference scheme, in which a coordinate transformation is used to transform the semi-infinite physical space to a bounded computational domain. The influence of the involved parameters on the flow, the temperature distribution, the skin-friction coefficient and the local Nusselt number is shown and discussed in detail. The study reveals that an oscillatory sheet embedded in a fluid-saturated porous medium generates oscillatory motion in the fluid. The amplitude and phase of oscillations depends on the rheology of the fluid as well as on the other parameters coming through imposed boundary conditions, inclusion of body force term and permeability of the porous medium. It is found that amplitude of flow velocity increases with increasing viscoelastic and mass suction/injection parameters. However, it decreases with increasing the strength of the applied magnetic field. Moreover, the temperature of fluid is a decreasing function of viscoelastic parameter, mass suction/injection parameter and Prandtl number.     

Penetration of external thermal perturbations into homeothermic organisms, part I (author's transl)

The general importance of the mean surface curvature for heat conduction problems is explained and a special symmetry with constant mean curvature on the isothermal surfaces is defined. The applicability for the body shapes of homeothermic organisms is demonstrated and the partial differential equation of heat conduction for this case is derived. The definition: heat release = real heat production + convective pseudoproduction eliminates the term of convective heat transfer through the blood stream and allows the reduction to a mere heat conduction problem. Formulas for the heat loss to the environment and for steady state temperature profiles are given. In case of sudden change of heat loss the partial differential equation is solved and a formula is derived, using dimensionless coordinates of time and distance. The mean surface curvature has strongest influence to the interior temperature field. The solution shows clearly the importance of thermal inertia of the homeothermic organism, for the external temperature wave penetrates into the body with a long phase displacement in time.     

Temperature regulation of marine mammals

A mathematical model of heat loss from an aquatic animal to the surrounding water is presented. Heat is generated in metabolically active tissues and distributed by circulating blood and by conduction. The time dependent radial temperature profile of the animal is numerically solved from heat transfer equations by a computer. The model is applied to large whales, porpoises, and seals. For the whales, blood circulation to the dermal layer below appendage and body skin surfaces proved to be essential for sufficient heat dissipation. When decreasing the blood flow below a certain value (dependent on sea temperature and whale activity) the large whales would overheat. Blubber thickness was found to be of minor importance in whale thermoregulation, because the blubber coat can be bypassed by blood circulation. On the other hand, it is in general not possible for small porpoises and seals to stay warm in the coldest waters using normal mammalian resting metabolic rates, even if the peripheral circulation is shut off (or artery-vein heat exchangers used). Heat loss can be reduced if the outermost tissue layers are allowed to cool. This is achieved by minimizing convective radial heat flow via the circulation. (For large whales even minute radial blood flow raises the muscle temperatures to the core temperature level.) Seasonal acclimatization of harbour seals is explained by changes in their effective insulation thickness. Differences in whale activity induce changes in the temperature profile mainly within the first few centimeters from the skin surface. These superficial temperatures, if known, could be used to estimate whale metabolic rates. Since they drop close to the sea water temperature within minutes after whale death, the measurements should be done of live whales.     

Evaluation of photobioreactor heat balance for predicting changes in culture medium temperature due to light irradiation

Microalgal photosynthesis requires appropriate culture medium temperatures to achieve high photosynthetic performance and to maintain production of a high-quality biomass product. Enclosed systems, such as our conical, helical tubular photobioreactor (HTP), can accomplish high photosynthetic efficiency and the small amount of culture medium used by these systems means that the culture medium temperature may be effectively controlled. On the other hand, because a high ratio of surface area to culture medium volume leads to rapid heating under the illumination condition and substantial heat loss at night, maintaining a suitable culture medium temperature is necessary to achieve efficient, commercially practical biomass production. In order to predict changes in the culture medium temperature caused by changes in solar irradiance and ambient temperature, it is necessary to understand the heat balance within the photobioreactor. We therefore investigated the heat balance in three major parts (photostage, degasser, and helical heat exchanger) of our conical HTP, analyzed the time-dependent changes in medium temperature at various room temperatures and radiant energy inputs, and predicted changes in the culture medium temperature based on the characteristics of heat transfer among the three parts. Using this model, the predicted changes in culture medium temperature were very similar to the changes observed experimentally in the laboratory and under field conditions. This means that by calculating the time-dependent changes in the culture medium temperature, based on measurements of solar energy input and ambient temperature, we should be able to estimate the energy required to maintain the culture medium temperature within a range where photosynthetic performance of microalgae is high.