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In this paper, the analytical solution is obtained for temperature distribution, efficiency, effectiveness and thermal stresses in convective fin of a rectangular profile with thermosensitive conductivity by implementing Homotopy Perturbation Method (HPM). This method is one of the effective tool to solve the fractional order non-linear diffussion equation with thermosensitive conductivity. The results obtained are illustrated graphically for better understanding of the effect of fractional parameter on fin effeciency and effectiveness with respect to thermogeometric fin parameter.

We successfully extend a multiscale simulation (MSS) method to nonisothermal well-entangled polymer melt flows between two coaxial cylinders. In the multiscale simulation, the macroscopic flow system is connected to a number of microscopic systems through the velocity gradient tensor, stress tensor and temperature. At the macroscopic level, in addition to the momentum balance equation, we consider the energy balance equation, where heat generation plays an important role not only in the temperature distribution but also in the flow profile. At the microscopic level, a dual slip-link model is employed for well-entangled polymers. To incorporate the temperature effect into the microscopic systems, we used the time-temperature superposition rule for the slip-link model, in which the temperature dependence of the parameters is not known; on the other hand, the way to take into account the temperature effect in the macroscopic equations has been well established. We find that the extended multiscale simulation method is quite effective in revealing the relation between nonisothermal polymeric flows for both steady and transient cases and the microscopic states of polymer chains expressed by primitive paths and slip-links. It is also found that the temperature-dependent reptation-time-based Weissenberg number is a suitable measure for understanding the extent of the polymer chain deformation in the range of the shear rate used in this study., Comment: 15 pages, 12 figures

In this paper, the performance of a PVT (photovoltaic thermal) air collector with V-groove absorber in the air channel is theoretically and experimentally examined under different climate conditions of Ghaziabad city, India, in summer, June 2019. A low power brushless DC fan is fixed at the input of the air-channel to ensure the circulation of air through the V-groove. The energy balance equation is developed with the matrix-inversion method to estimate the PV (photovoltaic) cell and air output temperatures. The theoretical results obtained using mathematical modeling has been compared with that of the real-time experimental results. The electrical, thermal, and overall efficiencies for the theoretical and experimental studies are found in the range of 10.39–10.26%, 41.78–41.57%, and 52.17–51.81%, respectively. It has been observed that the theoretical results are coherent with experimental results for the proposed model achieving an accuracy of 98.98%, 99.43%, and 99.31% for electrical, thermal, and overall efficiencies, respectively.

A continuum model is proposed and a system of equations is constructed to describe the processes of destruction of a solid. In the framework of the model, a decaying solid is considered as a heterogeneous medium consisting of two phases—solid and gaseous. Based on the analysis of the energy balance equation, in which its surface component is taken into account, the regularities of the onset of individual stages of the development of the process of destruction of a solid are studied. A description of each of the stages is given, the conditions are investigated, and criteria are formulated under which their implementation is possible.

Different from the rigid separation of biological tissue by scalpel, medical waterjet technology utilizes the impact kinetic energy of high-speed waterjet to instantly destroy the surface of biological tissue to achieve better clinical separation effect. Since the gelatin samples are transparent biomaterials, they were taken as the only substitute for soft tissue in experimental studies and observation in the current studies of medical waterjet separation technology, but the mechanical behavioural difference between the two has not been reported. To verify the adaptability of gelatin as a substitute of soft tissue under the impact of high-speed waterjet. Firstly, the dynamic process of impact was described through the energy balance equation. Then, based on the principle of altering a single variable, the difference of damage depth between 8 wt. %, 10 wt. %, and 12 wt. % gelatin samples and porcine liver tissue under various impact pressure, impact distance, and waterjet speed of motion (as opposed to flow velocity) was compared. The results show that the gelatin sample replicates the damage behaviour of porcine liver samples under the specific waterjet impact conditions, and the direction of the waterjet hydraulic power optimisation of the two materials is also consistent: however, due to the different sampling sites and anisotropy of porcine liver samples, the mechanical response of soft tissue under high-speed waterjet impact cannot be fully expressed by gelatin samples. The experimental results can provide support for the further study of medical waterjet separation technology.

The converted Solar energy as electrical and thermal energy was named photovoltaic thermal (PVT). The aim of this study is to the analysis of different length and depth channel effect of photovoltaic thermal with ∇-groove collector by a mathematical model. The matrix inversion was used to analyze the energy balance equation. Simulation results were conducted below the solar intensity of 800 W/m2 and mass flow rate between 0.0069 kg/s and 0.0491 kg/s. Electrical and thermal efficiency was done to assess the effect of different length and channel depth of PVT system with ∇-groove collector. The effect of different length and depth of ∇-groove collector for electrical and thermal performance is caused by changed mass flow rate. The effect Increasing of the mass flow rate of collector increased the thermal and electrical performance of the ∇-groove collector.

To reveal distribution of slab thermal efficiency (STE) and its bottlenecks, a slab region thermal efficiency (SRTE) model and an STE model were established based on the energy apportionment model of a reheating furnace in this paper. The bottleneck index of the slab thermal efficiency (BISTE), which could be used to assess the influence of SRTE on STE in a particular region, was proposed. First, the regional energy balance equation was listed based on reheating furnace region division. Next, the SRTE and STE models were established. Second, the bottleneck of slab thermal efficiency (BSTE) was achieved through a partial correlation analysis (PCA) of billet samples, which were obtained according to the difference between billet loading temperature and its residence time in the reheating furnace. Next, the BISTE was advanced to accurately determine the BSTE. Finally, several suggestions or measures, that could improve SRTE, were proposed. The case study has demonstrated the validation of these models, and the BISTE was 42% (Preheating), 19% (Heating II), 18% (Soaking), 11% (Heating I) and 10% (Preheating & Heating), respectively. Therefore, the preheating zone is the key region used to improve STE.

Here, the authors present a theoretical and experimental study for the hybrid solar collector system photovoltaic thermal (PVT) compared to the conventional thermal collector CTH and the photovoltaic panel PV using a mathematical model that is developed in order to predict the performance of the system. The model is based on the equations of the energy balances of each system to see these thermal and electrical performances. The system studied consists of a PV panel welded above the outside face of a thermal system in order to cool the PV cells and increase their electrical efficiency. The results of the experimental study were compared with the theoretical data and the model was validated.

The operating temperature of photovoltaic (PV) modules affects the photovoltaic conversion process. The operating temperature depends on various environmental conditions and on material-dependent properties of the PV modules. Many expressions for the operating temperature have been proposed in the literatures, some are simplified working Equation as NOCT (Nominal Operating Cell Temperature), and other are more complex, being based on a combination of the energy balance Equation and NOCT. The present study offers a new approach (model) for determining the PV module temperature based on the energy balance Equation and on the solar spectrum irradiance. While using the new model, the operating temperature has been determined for four module technologies: c-Si, a-Si/ &mu, c-Si, CdTe, and CIGS and it shows that the operating temperatures for the different cell types are close to the manufacturers&rsquo, NOCT data-sheet temperatures. For c-Si technology, for example, the simulation resulted in 43.2&deg, and 46&deg, for the spectrum and NOCT models, respectively. The proposed new model offers a new approach for determining the operating temperature of PV modules.

Based on the energy balance equation of semitransparent PV module, an improved analytical expression for solar cell electrical efficiency (ηc) and solar cell temperature (Tc) has been derived. Numerical computations have been carried out for New Delhi climatic condition for all weather conditions. It has been observed that there is an increase of 0.97% in the electrical efficiency of solar cell for New Delhi climatic condition in comparison with the results of the previous proposed model.

Bonding of air plasma oxidized polydimethylsiloxane (PDMS) strips is evaluated in this paper by peel testing. Two PDMS–PDMS strips, after being treated with air plasma, were brought together for bonding into a specimen, which was subsequently subjected to peeling until breaking apart. The maximum load applied in each peel test was used to indicate the bonding strength. Among the 68 specimens tested, 40 experienced a maximum load in the range of 0.1–0.2 N mm−1. Seventy-six percent of the specimens under peel testing failed at the cohesive mode, meaning that the air plasma-based bonding can be strong enough to retain its integrity after peeling. Correlation between the maximum load and failure modes suggests that strong bonding can be achieved with a higher plasma power for 50–60 seconds of treatment in air plasma. Based on the Kendall energy balance equation, we suggest that the higher the maximum load per unit width applied in the peel test, the larger the adhesion energy in the bonding interface.

A model for predicting the variation of flammability limits by the initial temperature was derived from the energy balance equation. All parameters of this proposed model can be sourced from the literature and do not need to be regressed by any experimental data. The proposed model was validated using 20 sets of experimental data consisting of 11 compounds, including alkanes, alkenes, alcohols, a ketone, an ester and inorganic fuels. Some samples were measured experimentally and other sample data were adopted from the literature. Overall, the proposed model predicted the temperature variation data of the flammability limits well when based on the adiabatic assumption. Application of this model is not restricted to organic fuels, but also inorganic fuels, such as carbon monoxide and hydrogen.

With the development of IC manufacturing process, the device dimensions have been on the nanoscale, while the device performance, such as the electron velocity, mobility and thermal noise, is significantly affected by the hot carrier effect. This paper proposes an electron temperature model to accurately predict the hot carrier effect. The channel transverse electric field is firstly derived by using the channel electric potential equation, taking into account the boundary conditions of the electric field. Based on the electric field equation, the energy balance equation is solved involving the impact of the temperature gradient and then the electron temperature model is established. The impact of the electron temperature on the channel mobility and of temperature gradient on the electron velocity has also been investigated. The results show that when the device enters the nanoscale, the electron mobility is more susceptible to the influence of the electric field and the electron temperature, and the impact of the temperature gradient on the velocity becomes obviously greater. The electron temperature model proposed in this paper can be applied to the performance analysis and modeling of nanosized MOSFETs.

The friction as competitive process is considered from positions of energy balance equation. Friction surfaces joint work with using this equation is described. As the result of more full evolution of elementary tribosystem the unique nanostructure is formed and the basis of which is one mechanical (nano) quantum. Mechanical quantum represents the least structural form of solid material body in conditions of plastic deformation and under transition tribosystem across the limit activated state by development of selforganazing processes of tribosystem adaptation are formed. Mechanical quantum is dynamic oscillator of dissipative friction structure. Mechanical quantum can be examined as the elementary nanostructure of metal’s solid body. Calculations have shown the number of such mechanical “quanta” (subtribosystems) within the elementary tribosystem’s volume, which is close to the safe number of fatigue cycles. Their joint rotationary-oscillatory behavior in relation to each other has determined the dynamic dissipation energy effect. Calculative model for dynamic oscillator of friction dissipative structures is offered.

A passive thermal regulation technique with fins in conjunction with cotton wicks is developed in the present work for controlling the temperature of PV module during its operation. Experiments were conducted with the developed technique in the location of Tiruchirappalli (78.6°E and 10.8°N), Tamil Nadu, India with flat 25 Wp PV module and its viability was confirmed. The PV module temperature got reduced by 12 % while the electrical yield is increased by 14 % with the help of the developed cooling system. Basic energy balance equation applicable for PV module was used to evaluate the module temperatures and a fair agreement was obtained between the theoretical and experimental values for the cases of with cooling and without cooling.

In this paper, an analytical expression for characteristic equation of a partially covered photovoltaic thermal compound parabolic concentrator (PVT-CPC) water collector system similar to Hottel–Whillier–Bliss (HWB) equation of flat plate collector has been derived. The derivation is based on basic energy balance equation for each component of partially covered PVT-CPC water collector system. The analytical result of proposed partially covered PVT-CPC water collectors [case (i)] has been compared with [case (ii)]: fully covered PVT-CPC water collectors; [case (iii)]: conventional CPC water collectors and [case (iv)]: partially covered PVT water collectors. It is observed that (a) an overall exergy efficiency of partially covered PVT-CPC water collector (25%PV) system is maximum and (b) an instantaneous thermal efficiency of conventional CPC water collector system [case (iii)] is maximum as compared to other cases.

Summary A model to calculate arc temperature of air gaps discharge is presented in this article. Based on the energy balance equation, we obtained the mathematical method to evaluate the arc temperature. According to the model, arc temperature was calculated for two air gaps with different distance, respectively. The results showed that the peak arc temperature of 16.7 m air gap is 36 368°K, and the peak arc temperature of 10 m air gap is 34 277°K, which are in good agreement with the experiment results. The model built in this article can be used for lightning and switching impulse discharges in air gaps. Copyright © 2013 John Wiley & Sons, Ltd.

At the end of the primary recovery phase, enhanced oil recovery (EOR) process such as hot water flooding becomes more attractive to reduce the residual oil saturation and to increase the oil production. It is well known that during hot water injection, the heat transfers from the injected fluid to the reservoir matrix, and this transfer depends mostly on the rheological and thermal properties of the formation rock and fluids. Moreover, the injection time and fluid velocity play significant roles on the temperature distribution. Therefore, it is important to investigate the effects of fluid velocity on the temperature distribution during thermal operations. The temperature profile in a reservoir formation is an important indicator of various reservoir conditions, such as type of fluid encroachment, the state of water or gas influx, etc. This information is necessary for better reservoir management. Previous studies assumed constant fluid velocity throughout the reservoir to calculate the temperature variations. However, this work studies the temperature distributions of reservoir rock and fluid during thermal operations by employing the velocity profiles. The temperature distributions are estimated by coupling a proposed memory-based diffusivity model with energy balance equation. The variations of fluid velocity are produced by solving the memory-based diffusivity equation, and then the temperature distributions are estimated based on the fluid velocity profiles. The proposed energy balanced equation is solved by a newly developed numerical technique. This technique is used to couple the energy balance equation with the memory-based diffusivity model. The model equations are solved simultaneously together by Matlab programming language. The temperature profiles are analyzed for unequal rock and fluid temperatures throughout the reservoir. Results show that, coupling of the pressure model and temperature model can lead to more reasonable temperature distributions during thermal flooding and then to better design of such operations. In addition, it is found that temperature distributions are affected mainly by the pressure variations and the fluid velocity. The finding of this research will help to improve the performance/efficiency of thermal flooding operations.

Results of experimental determination of the energy balance in oxygen laser cutting of sheets 5–16 mm thick by a CO 2 laser in the operation regime of high-quality cutting with the minimum possible degree of surface roughness are presented. Oxygen is used as an assisting gas. For sheets 5, 10, and 16 mm thick, the energy power fluxes, which are involved into the energy balance equation, normalized to the unit thickness of the sheet are found to be independent of the latter and to have close values.

International audience; The establishment of energy balance equation is necessary to study the thermo-mechanical properties of unsaturated soils. To solve this equation, the determination of two fundamental parameters as volumetric specific parameter and thermal conductivity coefficient is essential. In this paper, the effective thermal conductivity coefficient of dry soil grain is analyzed for soils with different compositions, and the thermo-mechanical properties of porous media with water and gas are studied by considering the soil water retention curve (SWRC). Different methods, i.e. volumetric average method, self-consistent method, Hashin-Strikman method, are employed to calculate thermal conductivity coefficients, and a new method is proposed to determine the thermo-mechanical parameters. Comparison of the results obtained by different methods shows that the proposed method is in a good agreement with the experimental results and is suitable for describing the main properties of the thermomechanical behaviors of soils. The relationship between the SWRC and the seepage curve is further studied by the natural proportional rule. The characteristics of the SWRC, its differential coefficient and the seepage curve, are investigated by considering the physico-mechanical mechanism; the limit scopes of the indices of the SWRC and the seepage curve are also given.

Instantaneous acoustic heating in a weakly dispersive fluid flow is the subject of investigation. Splitting of energy balance equation yields in evolution equation for acoustic heating. The specific role of dispersion in this phenomenon is studied and discussed for two examples of weak dispersion mechanisms, relaxation and boundary layer.

In the fracture problems of hydrophilic elastic materials under coupling effects of heat conduction, moisture diffusion and mechanical deformation, the conventional J-integral is no longer path independent. The value of J is unequal to the energy release rate in hygrothermal coupling cases. In the present paper, we derived a general form of the energy release rate for hygrothermal fracture problems of the hydrophilic elastic materials on the basis of energy balance equation in cracked areas. By introducing the constitutive relations and the essential equations of irreversible thermodynamics, a specific expression of the energy release rate was obtained, and the expression can be reformmulated as path independent integrals, which is equivalent to the energy release rate of the fracture body. The path independence of the integrals is then verified numerically.

A critical thrust force at propagation of delamination zone due to drilling of an infinite FRP/metallic strip is obtained by the definition of energy release rate. The critical thrust force is derived in terms of the size of the delamination zone. The differences of the results by the previous and present methods are discussed.

Bulk maize cobs were stored in cribs in Barisal, Bangladesh in 1998 with an initial moisture content of 38% (db) and in 1999 with an initial moisture content of 40% (db) and dried to 16.10% and 18.32% respectively by natural air. The observed air temperature and grain temperature was found to be almost same. A mathematical model was developed to simulate the drying of maize in crib and the model consists of three sets of partial differential equations––mass balance equation, drying rate equation and energy balance equation. The equations were solved by numerical techniques with respect to time and positions, the width of crib being considered as a series of thin layers. The model was validated with the experimental data. Good agreement was found between the simulated temperature and moisture content both in 1998 and 1999.

Relying on the condition of dynamic matching of the process parameters in gas laser cutting, the dependence of the beam utilization factor on the cutting speed and the beam power has been determined. An energy balance equation has been derived for a wide range of cutting speed values.

The paper presents the method to identify the dissipative properties of the materials with a clear hysteresis loop under the quasi-static loads. Because of the fact that for low values of velocity, the resisting forces related to the speed are minimal, it is not possible to determine these forces as the functions of velocity in the quasi-static deformations. It results in the need to develop such methods for identification, which use the responses of the tested system to the cyclic loading with a high frequency. This paper presents such a method. Its application may be useful in the area of constructing the effective and modern ballistic shields.

This benchmark focuses on stress-induced heating in elastic solids. In the following, we briefly present governing equations relevant to this coupled thermal and mechanical processes.

The article presents the solution of heat balance equation system, describing heat exchange processes in ventilated envelopes, which was applied to derive formulas for the calculation of temperatures in the ventilated layers of the envelopes. The accurateness of the formulas was assessed by experimental research and analysis of the calculation results. During the process of heat exchange balance equation solution, the equations were simplified by introducing the following restriction into the derived formulas: they may only be applied for the ventilated envelopes with steel or similar coatings as their external layers, i.e. coatings having small heat capacity and minor difference between the external and internal surface temperatures. The derived formulas enable the calculation of the temperatures of the ventilated envelopes in the distance which does not exceed a half of the ventilated air gap length measuring from the air entrance into the gap. However, this restriction does not impede the estimation of the average thermal indicators of the ventilated envelopes.

This paper presents an analytical drain current model considering the impact ionization and parasitic BJT effects, an energy balance equation, and lattice thermal effect for short-channel fully-depleted ultrathin silicon-on-insulator NMOS devices. Supported by the experimental data, the analytical model shows a good prediction of the drain current characteristics. According to the model, in the saturation region at small V G , the impact ionization and parasitic BJT effects are important. At large V G , the lattice thermal effect is important.

A three-step method is proposed to relate engineering parameters of jet-grouting (grout elastic properties, injection velocity) to soilcrete column bearing capacity. 1. The soilcrete column diameter is determined from an energy balance equation. It is assumed that the grout kinematic energy is partially dissipated by friction and partially transformed into the work of the force required to expel the solid grains and pore water from the injected zone. The model has been calibrated with reference data found in the literature. 2. Soilcrete elastic properties are homogenized with a hollow sphere model. The column diameter determined in Step 1 defines the size of the Representative Elementary Volume (REV) considered. Soilcrete is modeled as a fictitious porous medium, in which soil grains are substituted by void pores, and grout constitutes the solid matrix. 3. Maximum settlements around the soilcrete column with the properties determined in Steps 1 & 2 are computed with a Finite Element program.

In this paper, the modeling of honeycomb double exposure solar still has been analyzed include four elements, such as the glass cover, honeycomb structure, water mass, and bottom absorber. The energy balance equation has been written for the still parameters. The computer program has been written for the analytical solutions of water, glass, and bottom absorber temperature. To validate the analytical results, experimental observations for one of the typical days in February 2012 have been taken. The correlation coefficients have been found and their r 2 values for water and bottom absorber are presented.

This paper reports a concise physical model considering energy transport and source resistance for deep submicron n-channel metal-oxide-semiconductor (NMOS) devices. As verified by the experimental data, the closed-form analytical model shows good accuracy in the IV characteristics.

The curing of epoxy-amine polymer has been modeled by the reaction of functional groups, and the mole balance of these is governed by a set of six nonlinear differential equations. In this work, we have first developed a complete analytical solution for isothermal curing. For nonisothermal curing, we have divided the domain of hydroxyl group concentration β into small increments Δβ and adopted our analytical results for this domain. In addition, we solved the energy balance equation analytically and obtained the temperature rise for Δβ. We have compared our results with those obtained from the Runge Kutta numerical solutions. We have shown that our semianalytical technique is about a thousand times more efficient and faster.

An efficient numerical method for the solution of hot‐carrier transport equations describing transient processes in submicrometer semiconductor devices is proposed. The calculations of transient processes in submicrometer MOS transistor were carried out and compared with the results obtained by conventional drift‐diffusion model.

The energy balance equation of the fast brittle fracture is extended in such a way that the fracture surface roughness effect is taken into account. Experimental results of Takahashi and Arakawa [1–3] are analyzed using the extended energy balance equation. It is found that our analysis qualitatively agrees with it in regard to the acceleration and deceleration of the crack propagation. The crack branching condition is also discussed.

This investigation examines the failure of circular plates subjected to impulsive velocities. Experiments are conducted on fully clamped circular mild steel plates subjected to a uniformly distributed impulse. The strain rate-sensitive plates exhibit mode I (large ductile deformation), modes II (tensile-tearing and deformation) and mode III (transverse shear) failure modes. An energy analysis is used on the test results which enables an energy balance equation relating input, deformation, tearing and disc energies to be formulated. The input and disc energies are obtained from experimental measurements; the deformation energy is predicted by making use of the final deformed height, a shape function and a rigid-plastic analysis. Good correlation is found and the experiments show good repeatability. The threshold velocities for the onset of failure modes II and III are given.

A method based on the energy balance equation for a cracked body is described for the determination of stress intensity factors and stress distribution in a crack plane from the COD measurements at several points at some distance from the crack tip. The efficiency of the approach proposed is supported by a number of examples.

Establish the concepts of conversion heat capacity and heat accumulation factor and derive out the unsteady state heat efficiency equation for solar water heating system.

A detailed formulation of energy balance equation is presented. The AlGaAs/GaAs QW results show that hot carrier effect can influence the I-V characteristics for devices with long relaxation lifetime at high injection level. Comparisons made with the available measured data support the modeling of QW p-i-n AlGaAs/GaAs photodiode structures.

Values calculated according to the energy balance equation of phenomenological thermomechanics have been compared with experimental data for Ne, Ar, Kr and Xe. The results obtained show that the internal energies of these substances can be subdivided into separate components rather accurately.

The paper aims to give an approximate evaluation of the ductility and strength demand so that a structure can resist strong earthquakes of an assigned intensity level. It is shown, by means of a suitable energy balance equation, that the aseismic capacity of structures depends on a special coupling of strength and ductility defined as aseismic toughness. A broad evaluation of the toughness ratios that can be achieved in reinforced concrete structures ends the paper.

First measurements of the charge-exchange ion temperature in the Heliotron-E device are described. The limiting temperatures calculated from a simple energy balance equation are presented and compared with the measured temperatures. In low-current plasma, the measured temperatures agree well with the thermal conduction limit based on neoclassical theory, which includes an effect of the electron-to-ion temperature ratio Te/Ti. In high-current plasma, however, the ion temperature is about one-third of the limiting temperature. This discrepancy may be due to anomalous heat and particle transport driven by the plasma current.

In this paper an anlytical model for the calculation of the pressure pulse in hexagonal ducts due to discharge of gas from a failed fuel pin is developed. The analysis yields the time history of the pressure pulse which can be used in the calculation of permanent deformation of the duct or in the assessment of the susceptibility of the duct to fracture. In this model the analysis is divided into two stages. In the first stage the gas expands as a spherical bubble, but the influence of duct wall is taken into account. At the end of the first stage the spherical shape of the bubble is assumed to be lost and the gas is assumed to expand axially as a column. The end conditions of stage 1 are the initial conditions for stage 2. The analysis involves solving the continuity and momentum equations for the liquid along with the energy balance equation for the gas. In the analysis the liquid is assumed to be incompressible.

A closed-circuit wind tunnel and an external microwave energy source formed the basis of an experimental technique to investigate relationships between climatic parameters and leaf temperatures. The results of these preliminary experiments are compared with theoretical results obtained by solving the energy balance equation for a single leaf. Time-temperature relationship of an attached bean leaf, exposed to microwave radiation, is compared with a mathematical model which is essentially derived from a knowledge of the cooling coefficient and the absorption factor. At high absorbed radiation and in darkness, stomatal opening of a real bean leaf may reduce its temperature between 2 to 5°C.