Search results for: radial distribution functions

Authors: Maryamosadat Ghasemi, Reza Amrollahi

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Plasma equilibrium geometry has a great influence on the confinement and magnetohydrodynamic stability in tokamaks. The poloidal field (PF) system of a tokamak should be able to support this plasma equilibrium geometry. In this work the prepared numerical code based on radial basis functions are presented and used to solve the Grad–Shafranov (GS) equation for the axisymmetric equilibrium of tokamak plasma. The radial basis functions (RBFs) which is a kind of numerical meshfree method (MFM) for solving partial differential equations (PDEs) has appeared in the last decade and is developing significantly in the last few years. This technique is applied in this study to obtain the equilibrium configuration for Alborz Tokamak. The behavior of numerical solution convergences show the validation of this calculations.

Keywords: equilibrium, grad–shafranov, radial basis functions, Alborz Tokamak

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Authors: Nazish Iftikhar, Adil Jhangeer, Tayyaba Naz

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The universe is expanding at an accelerated rate. Symmetries are useful in understanding universe’s behavior. Emmy Noether reported the relation between symmetries and conservation laws. These symmetries are known as Noether symmetries which correspond to a conserved quantity. In differential equations, conservation laws play an important role. Noether symmetries are helpful in modified theories of gravity. Time independent plane symmetric spacetime was classified by Noether`s theorem. By using Noether`s theorem, set of linear partial differential equations was obtained having A(r), B(r) and F(r) as unknown radial functions. The Lagrangian corresponding to considered spacetime in the Noether equation was used to get Noether operators. Different possibilities of radial functions were considered. Firstly, all functions were same. All the functions were considered as non-zero constant, linear, reciprocal and exponential respectively. Secondly, two functions were proportional to each other keeping third function different. Second case has four subcases in which four different relationships between A(r), B(r) and F(r) were discussed. In all cases, we obtained nontrivial Noether operators including gauge term. Conserved quantities for each Noether operators were also presented.

Keywords: Noether gauge symmetries, radial function, Noether operator, conserved quantities

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Authors: Elyas Shivanian

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In this paper, the spectral meshless radial point interpolation (SMRPI) technique is applied to the Cauchy problems of two-dimensional elliptic PDEs in doubly connected domains. It is obtained the unknown data on the inner boundary of the domain while overspecified boundary data are imposed on the outer boundary of the domain by using the SMRPI. Shape functions, which are constructed through point interpolation method using the radial basis functions, help us to treat problem locally with the aim of high order convergence rate. In this way, localization in SMRPI can reduce the ill-conditioning for Cauchy problem. Furthermore, we improve previous results and it is revealed the SMRPI is more accurate and stable by adding strong perturbations.

Keywords: cauchy problem, doubly connected domain, radial basis function, shape function

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Authors: Azim Khodadadi, Sahar Sadaat Vakili, Ebrahim Babaei

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This study presents a numerical method to optimize the failure rate and repair time of a typical radial distribution system. Failure rate and repair time are effective parameters in customer and energy based indices of reliability. Decrease of these parameters improves reliability indices. Thus, system stability will be boost. The penalty functions indirectly reflect the cost of investment which spent to improve these indices. Constraints on customer and energy based indices, i.e. SAIFI, SAIDI, CAIDI and AENS have been considered by using a new method which reduces optimization algorithm controlling parameters. Imperialist Competitive Algorithm (ICA) used as main optimization technique and particle swarm optimization (PSO), simulated annealing (SA) and differential evolution (DE) has been applied for further investigation. These algorithms have been implemented on a test system by MATLAB. Obtained results have been compared with each other. The optimized values of repair time and failure rate are much lower than current values which this achievement reduced investment cost and also ICA gives better answer than the other used algorithms.

Keywords: imperialist competitive algorithm, failure rate, repair time, radial distribution network

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Authors: Atabak Faramarzpour, Mohsen Mohammadian

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In this article, we introduce the stability of power system voltage and state DG power plants placement and its effect on improving voltage security margin in radial distribution networks. For this purpose, first, important definitions in voltage stability area such as small and big voltage disturbances, instability, and voltage collapse, and voltage security definitions are stated. Then, according to voltage collapse time, voltage stability is classified and each one's characteristics are stated.

Keywords: DG power plants, evaluation, voltage security, radial distribution networks

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Authors: Mohammed Habchi, Sidi Mohammed Mesli, Rafik Benallal, Mohammed Kotbi

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On the basis of four partial correlation functions and some geometric constraints obtained from neutron scattering experiments, a Reverse Monte Carlo (RMC) simulation has been performed in the study of the aqueous electrolyte LiCl6H2O at the glassy state. The obtained 3-dimensional model allows computing pair radial and orientational distribution functions in order to explore the structural features of the system. Unrealistic features appeared in some coordination peaks. To remedy to this, we use the Hybrid Reverse Monte Carlo (HRMC), incorporating an additional energy constraint in addition to the usual constraints derived from experiments. The energy of the system is calculated using an Environment Dependence Interaction Potential (EDIP). Ions effects is studied by comparing correlations between water molecules in the solution and in pure water at room temperature Our results show a good agreement between experimental and computed partial distribution functions (PDFs) as well as a significant improvement in orientational distribution curves.

Keywords: LiCl6H2O, glassy state, RMC, HRMC

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Authors: Xiaolai Zhang, Haitao Zhang, Qiwen Sun, Weixin Qian, Weiyong Ying

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High temperature Fischer-Tropsch synthesis process use fixed fluidized bed as a reactor. In order to understand the flow behavior in the fluidized bed better, the research of how the radial velocity affect the entire flow field is necessary. Laser Doppler Velocimetry (LDV) was used to study the radial velocity distribution along the diameter direction of the cross-section of the particle in a fixed fluidized bed. The velocity in the cross-section is fluctuating within a small range. The direction of the speed is a random phenomenon. In addition to r/R is 1, the axial velocity are more than 6 times of the radial velocity, the radial velocity has little impact on the axial velocity in a fixed fluidized bed.

Keywords: Fischer-Tropsch synthesis, Fixed fluidized bed, LDV, Velocity

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Authors: Hebert Montegranario, Mauricio Londoño

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Solutions of Helmholtz equation are essential in seismic imaging methods like full wave inversion, which needs to solve many times the wave equation. Traditional methods like Finite Element Method (FEM) or Finite Differences (FD) have sparse matrices but may suffer the so called pollution effect in the numerical solutions of Helmholtz equation for large values of the wave number. On the other side, global radial basis functions have a better accuracy but produce full matrices that become unstable. In this research we combine the virtues of both approaches to find numerical solutions of Helmholtz equation, by applying a meshless method that produce sparse matrices by local radial basis functions. We solve the equation with absorbing boundary conditions of the kind Clayton-Enquist and PML (Perfect Matched Layers) and compared with results in standard literature, showing a promising performance by tackling both the pollution effect and matrix instability.

Keywords: Helmholtz equation, meshless methods, seismic imaging, wavefield inversion

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Authors: A. Amiri Delouei

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In the current study, two-dimensional unsteady heat conduction in a functionally graded cylinder is studied analytically. The temperature distribution is in radial and longitudinal directions. Heat conduction coefficients are considered a power function of radius both in radial and longitudinal directions. The proposed solution can exactly satisfy the boundary conditions. Analytical unsteady temperature distribution for different parameters of functionally graded cylinder is investigated. The achieved exact solution is useful for thermal stress analysis of functionally graded cylinders. Regarding the analytical approach, this solution can be used to understand the concepts of heat conduction in functionally graded materials.

Keywords: functionally graded materials, unsteady heat conduction, cylinder, temperature distribution

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Authors: Sumit Banerjee, Chandan Kumar Chanda

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The paper presents allocation of active power losses and energy losses to consumers connected to radial distribution networks in a deregulated environment for loads of composite types. A detailed comparison among four algorithms, namely quadratic loss allocation, proportional loss allocation, pro rata loss allocation and exact loss allocation methods are presented. Quadratic and proportional loss allocations are based on identifying the active and reactive components of current in each branch and the losses are allocated to each consumer, pro rata loss allocation method is based on the load demand of each consumer and exact loss allocation method is based on the actual contribution of active power loss by each consumer. The effectiveness of the proposed comparison among four algorithms for composite load is demonstrated through an example.

Keywords: composite type, deregulation, loss allocation, radial distribution networks

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Authors: Abdurrahim Dal, Tuncay Karaçay

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Dynamics of a rotor supported by air bearings is strongly depends on the pressure distribution between the rotor and the bearing. In this study, internal pressure in air bearings is numerical and experimental analyzed for different radial clearances. Firstly the pressure distribution between rotor and bearing is modeled using Reynold's equation and this model is solved numerically. The rotor-bearing system is also modeled in four degree of freedom and it is simulated for different radial clearances. Then, in order to validate numerical results, a test rig is designed and the rotor bearing system is run under the same operational conditions. Pressure signals of left and right bearings are recorded. Internal pressure variations are compared for numerical and experimental results for different radial clearances.

Keywords: air bearing, internal pressure, Reynold’s equation, rotor

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Authors: Philip Symonds, Jon Taylor, Zaid Chalabi, Michael Davies

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With the world climate projected to warm and major cities in developing countries becoming increasingly populated and polluted, governments are tasked with the problem of overheating and air quality in residential buildings. This paper presents the development of an adaptable model of these risks. Simulations are performed using the EnergyPlus building physics software. An accurate metamodel is formed by randomly sampling building input parameters and training on the outputs of EnergyPlus simulations. Metamodels are used to vastly reduce the amount of computation time required when performing optimisation and sensitivity analyses. Neural Networks (NNs) are compared to a Radial Basis Function (RBF) algorithm when forming a metamodel. These techniques were implemented using the PyBrain and scikit-learn python libraries, respectively. NNs are shown to perform around 15% better than RBFs when estimating overheating and air pollution metrics modelled by EnergyPlus.

Keywords: neural networks, radial basis functions, metamodelling, python machine learning libraries

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Authors: A. Suparmi, C. Cari, M. Yunianto, B. N. Pratiwi

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D-dimensional Dirac equations of q-deformed shape invariant potentials were solved using supersymmetric quantum mechanics (SUSY QM) in the case of exact spin symmetry. The D dimensional radial Dirac equation for shape invariant potential reduces to one-dimensional Schrodinger type equation by an appropriate variable and parameter change. The relativistic energy spectra were analyzed by using SUSY QM and shape invariant properties from radial D dimensional Dirac equation that have reduced to one dimensional Schrodinger type equation. The SUSY operator was used to generate the D dimensional relativistic radial wave functions, the relativistic energy equation reduced to the non-relativistic energy in the non-relativistic limit.

Keywords: D-dimensional dirac equation, non-central potential, SUSY QM, radial wave function

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Authors: Hela Krir, Abdelhak Ayadi, Chedly Bradaii

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The influence of both intrinsic factors, elastic energy and memory effect, and radial flow on the appearance and the evolution of the extrudate swelling are investigated in the present work. The experiments have been performed with linear polydimethylsiloxane (PDMS) via a capillary rheometer in which a convergent radial flow was created upstream the contraction. The correspondence between the effects of radial flow, entry elastic stored energy and memory effect is discussed. In particular, as the influence of the considered radial flow, extrudate photographs showed that when the gap ratio is reduced, the extrudate swell is lessened than what it is when radial flow geometry is not installed. Moreover, with a narrower gap, the polymer stores less energy during its passage through the die which implies a lower extrudate swelling at the outlet of the die. Results previously mentioned may be related both to shear and elongational components of radial flow.

Keywords: elastic energy, extrudate swell, memory effect, radial flow

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Authors: Mohammed Alenezy

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The function of cardiac motion can be used as an indicator of the heart abnormality by evaluating longitudinal, circumferential, and Radial Strain of the left ventricle. In this paper, the Radial Strain and SR is studied using tagged MRI (tMRI) data during the cardiac cycle on the mid-ventricle level of the left ventricle. Materials and methods: The short-axis view of the left ventricle of five healthy human (three males and two females) and four healthy male rats were imaged using tagged magnetic resonance imaging (tMRI) technique covering the whole cardiac cycle on the mid-ventricle level. Images were processed using Image J software to calculate the left ventricle wall Radial Strain and radial SR. The left ventricle Radial Strain and radial SR were calculated at the mid-ventricular level during the cardiac cycle. The peak Radial Strain for the human and rat heart was 40.7±1.44, and 46.8±0.68 respectively, and it occurs at 40% of the cardiac cycle for both human and rat heart. The peak diastolic and systolic radial SR for human heart was -1.78 s-1 ± 0.02 s-1 and 1.10±0.08 s-1 respectively, while for rat heart it was -5.16± 0.23s-1 and 4.25±0.02 s-1 respectively. Conclusion: This results show the ability of the tMRI data to characterize the cardiac motion during the cardiac cycle including diastolic and systolic phases which can be used as an indicator of the cardiac dysfunction by estimating the left ventricle Radial Strain and radial SR at different locations of the cardiac tissue. This study approves the validity of the tagged MRI data to describe accurately the cardiac radial motion.

Keywords: left ventricle, radial strain, tagged MRI, cardiac cycle

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Authors: Mahmoud Samkan

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Dispersed Generation (DG) is a promising solution to many power system problems such as voltage regulation and power loss. This paper proposes a heuristic two-step method to optimize the location and size of DG for reducing active power losses and, therefore, improve the voltage profile in radial distribution networks. In addition to a DG placed at the system load gravity center, this method consists in assigning a DG to each lateral of the network. After having determined the central DG placement, the location and size of each lateral DG are predetermined in the first step. The results are then refined in the second step. This method is tested for 33-bus system for 100% DG penetration. The results obtained are compared with those of other methods found in the literature.

Keywords: optimal location, optimal size, dispersed generation (DG), radial distribution networks, reducing losses

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Authors: Darren Camilleri, Robert Rolston

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Rotor radial vents make use of the pumping effect to increase airflow through the active material thus reduce hotspot temperatures. The effect of rotor radial pumping in synchronous machines has been studied previously. This paper presents the findings of previous studies and builds upon their theories using a parametric numerical approach to investigate the rotor radial pumping effect. The pressure head generated by the poles and radial vent flow-rate were identified as important factors in maximizing the benefits of the pumping effect. The use of Minitab and ANSYS Workbench to investigate the key performance characteristics of radial pumping through a Design of Experiments (DOE) was described. CFD results were compared with theoretical calculations. A correlation for each response variable was derived through a statistical analysis. Findings confirmed the strong dependence of radial vent length on vent pressure head, and radial vent cross-sectional area was proved to be significant in maximising radial vent flow rate.

Keywords: CFD, cooling, electrical machines, regression analysis

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Authors: Sani M. Lawal, Idris Musa, Aliyu D. Usman

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The Pareto approach of optimal solutions in a search space that evolved in multi-objective optimization problems is adopted in this paper, which stands for a set of solutions in the search space. This paper aims at presenting an optimal placement of Distributed Generation (DG) in radial distribution networks with an optimal size for minimization of power loss and voltage deviation as well as maximizing voltage profile of the networks. And these problems are formulated using particle swarm optimization (PSO) as a constraint nonlinear optimization problem with both locations and sizes of DG being continuous. The objective functions adopted are the total active power loss function and voltage deviation function. The multiple nature of the problem, made it necessary to form a multi-objective function in search of the solution that consists of both the DG location and size. The proposed PSO algorithm is used to determine optimal placement and size of DG in a distribution network. The output indicates that PSO algorithm technique shows an edge over other types of search methods due to its effectiveness and computational efficiency. The proposed method is tested on the standard IEEE 34-bus and validated with 33-bus test systems distribution networks. Results indicate that the sizing and location of DG are system dependent and should be optimally selected before installing the distributed generators in the system and also an improvement in the voltage profile and power loss reduction have been achieved.

Keywords: distributed generation, pareto, particle swarm optimization, power loss, voltage deviation

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Authors: Serge Provost, Abdous Saboor

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A q-analogue of the generalized extreme value distribution which includes the Gumbel distribution is introduced. The additional parameter q allows for increased modeling flexibility. The resulting distribution can have a finite, semi-infinite or infinite support. It can also produce several types of hazard rate functions. The model parameters are determined by making use of the method of maximum likelihood. It will be shown that it compares favourably to three related distributions in connection with the modeling of a certain hydrological data set.

Keywords: extreme value theory, generalized extreme value distribution, goodness-of-fit statistics, Gumbel distribution

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Authors: Abhishek Kumar Gupta

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Atomistic Molecular Dynamics (MD) Simulations have been performed to study the effect of monovalent salt i.e. NaCl concentration (Cs) and chain degree of neutralization (f) on the structure and dynamics of anionic poly(methacrylic acid) (PMA) in dilute aqueous solutions. In the present study, the attention is to unveil the conformational structure, hydrogen-bonding, local polyion-counterion structure, h-bond dynamics, chain dynamics and thermodynamic enthalpy of solvation of a-PMA in dilute aqueous solutions as a function of salt concentration, Cs and f. The results have revealed that at low salt concentration, the conformational radius of gyration (Rg) increases and then decreases reaching a maximum in agreement with the reported light scattering experimental results. The Rg at f = 1 shows a continual decrease and acquire a plateau value at higher salt concentration in agreement with results obtained by light scattering experiments. The radial distribution functions between PMA, salt and water atoms has been computed with respect to atom and centre-of-mass to understand the intermolecular structure in detail. The results pertaining to PMA chain conformations and hydrogen bond autocorrelation function showcasing the h-bond dynamics will be presented. The results pertaining to chain dynamics will be presented. The results pertaining to counterion condensation on the PMA chain shows greater condensation of Na+ ions on to the carboxylate ions with increase in salt concentration. Moreover, the solvation enthalpy of the system as a function of salt concentration will be presented.

Keywords: conformations, molecular dynamics simulations, NaCl concentration, radial distribution functions

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Authors: Edward J. Kansa, Pavel Holoborodko

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Continuously differentiable radial basis functions (RBFs) are meshfree, converge faster as the dimensionality increases, and is theoretically spectrally convergent. When implemented on current single and double precision computers, such RBFs can suffer from ill-conditioning because the systems of equations needed to be solved to find the expansion coefficients are full. However, the Advanpix extended precision software package allows computer mathematics to resemble asymptotically ideal Platonic mathematics. Additionally, full systems with extended precision execute faster graphical processors units and field-programmable gate arrays because no branching is needed. Sparse equation systems are fast for iterative solvers in a very limited number of cases.

Keywords: partial differential equations, Meshfree radial basis functions, , no restrictions on spatial dimensions, Extended arithmetic precision.

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Authors: Sidi Mohamed Mesli, Mohamed Habchi, Arslane Boudghene Stambouli, Rafik Benallal

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The BaMnMF7 (M=Fe,V, transition metal fluoride glass, assuming isomorphous replacement) have been structurally studied through the simultaneous simulation of their neutron diffraction patterns by reverse Monte Carlo (RMC) and by the Hybrid Reverse Monte Carlo (HRMC) analysis. This last is applied to remedy the problem of the artificial satellite peaks that appear in the partial pair distribution functions (PDFs) by the RMC simulation. The HRMC simulation is an extension of the RMC algorithm, which introduces an energy penalty term (potential) in acceptance criteria. The idea of this work is to apply the Buckingham potential at the title glass by ignoring the van der Waals terms, in order to make a fit of the partial pair distribution functions and give the most possible realistic features. When displaying the partial PDFs, we suggest that the Buckingham potential is useful to describe average correlations especially in similar interactions.

Keywords: fluoride glasses, RMC simulation, hybrid RMC simulation, Buckingham potential, partial pair distribution functions

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Authors: Anasuya Ghosh, Subhramoy Chaudhury

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During routine cadaveric dissection at gross anatomy lab of our institution, a radial artery was found with unusual origin and superficial course. Normally the radial artery takes its origin as one of the terminal branches of brachial artery at the level of the neck of radius. It usually lies along the lateral border of fore arm deep to the brachioradialis muscle. While dissecting a 72-year-old Caucasian female cadaver, it was found that the right sided radial artery originated from the upper part of brachial artery of arm, 2 cm below the lower border of teres major muscle, from the lateral aspect of brachial artery. Then the radial artery superficially crossed the brachial artery and median nerve from lateral to medial direction and rested superficially at the cubital fossa. Embryologically, it can be explained as a failure of disappearance, or abnormal persistence of some insignificant embryonic vessels may give rise to this kind of vascular anomalies. As radial artery is one of the most important upper limb arteries, its variation and related complications are clinically significant. This unusual origin and course of radial artery should be kept in mind by all healthcare providers including surgeons and radiologists during routine venipuncture, orthopedic and plastic surgeries of arm, coronary angiographic procedures in radial approach etc. to prevent unwanted complications.

Keywords: brachial artery anomalies, brachio-radial artery, high origin radial artery, superficial radial artery

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Authors: J. S. Savier

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Real power is the component power which is converted into useful energy whereas reactive power is the component of power which cannot be converted to useful energy but it is required for the magnetization of various electrical machineries. If the reactive power is compensated at the consumer end, the need for reactive power flow from generators to the load can be avoided and hence the overall power loss can be reduced. In this scenario, this paper presents a succinct method called JSS method for allocation of reactive power losses to consumers connected to radial distribution networks in a deregulated environment. The proposed method has the advantage that no assumptions are made while deriving the reactive power loss allocation method.

Keywords: deregulation, reactive power loss allocation, radial distribution systems, succinct method

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Authors: Aicha Rima Cheniti, Hatem Besbes, Joseph Haggege, Christophe Sintes

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In this paper, we consider a drift flux mixture model of the blood flow. The mixture consists of gas phase which is carbon dioxide and liquid phase which is an aqueous carbon dioxide solution. This model was used to determine the distributions of the mixture velocity, the mixture pressure, and the carbon dioxide pressure. These theoretical data are used to determine a measurement method of mean gas pressure through the determination of radial velocity distribution. This method can be applicable in experimental domain.

Keywords: mean carbon dioxide pressure, mean mixture pressure, mixture velocity, radial velocity

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Authors: Nattachote Rugthaicharoencheep

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This paper presents a feeder reconfiguration problem in distribution systems. The objective is to minimize the system power loss and to improve bus voltage profile. The optimization problem is subjected to system constraints consisting of load-point voltage limits, radial configuration format, no load-point interruption, and feeder capability limits. A method based on genetic algorithm, a search algorithm based on the mechanics of natural selection and natural genetics, is proposed to determine the optimal pattern of configuration. The developed methodology is demonstrated by a 33-bus radial distribution system with distributed generations and feeder capacitors. The study results show that the optimal on/off patterns of the switches can be identified to give the minimum power loss while respecting all the constraints.

Keywords: network reconfiguration, distributed generation capacitor placement, loss reduction, genetic algorithm

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Authors: A. Ejah Umraeni Salam, M. Tola, M. Selintung, F. Maricar

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Clean water is an essential and fundamental human need. Therefore, its supply must be assured by maintaining the quality, quantity and water pressure. However the fact is, on its distribution system, leakage happens and becomes a common world issue. One of the technical causes of the leakage is a leaking pipe. The purpose of the research is how to use the Radial Basis Function Neural (RBFNN) model to detect the location and the magnitude of the pipeline leakage rapidly and efficiently. In this study the RBFNN are trained and tested on data from EPANET hydraulic modeling system. Method of Radial Basis Function Neural Network is proved capable to detect location and magnitude of pipeline leakage with of the accuracy of the prediction results based on the value of RMSE (Root Meant Square Error), comparison prediction and actual measurement approaches 0.000049 for the whole pipeline system.

Keywords: radial basis function neural network, leakage pipeline, EPANET, RMSE

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Authors: Zakir Husain, Neem Sagar, Neeraj Gupta

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Due to the increased penetration of renewable energy resources in the distribution system, the system is no longer passive in nature. In this paper, a steady state analysis of the distribution system has been done with the inclusion of wind generation. The modeling of wind turbine generator system and wind generator has been made to obtain the average active and the reactive power injection into the system. The study has been conducted on a IEEE-33 bus system with two wind generators. The present research work is useful not only to utilities but also to customers.

Keywords: distributed generation, distribution network, radial network, wind turbine generating system

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Authors: Md. Rashidul Hasan, Atikur Rahman Baizid

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The Bayesian estimation approach is a non-classical estimation technique in statistical inference and is very useful in real world situation. The aim of this paper is to study the Bayes estimators of the parameter of exponential distribution under different loss functions and then compared among them as well as with the classical estimator named maximum likelihood estimator (MLE). In our real life, we always try to minimize the loss and we also want to gather some prior information (distribution) about the problem to solve it accurately. Here the gamma prior is used as the prior distribution of exponential distribution for finding the Bayes estimator. In our study, we also used different symmetric and asymmetric loss functions such as squared error loss function, quadratic loss function, modified linear exponential (MLINEX) loss function and non-linear exponential (NLINEX) loss function. Finally, mean square error (MSE) of the estimators are obtained and then presented graphically.

Keywords: Bayes estimator, maximum likelihood estimator (MLE), modified linear exponential (MLINEX) loss function, Squared Error (SE) loss function, non-linear exponential (NLINEX) loss function

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Authors: Taha Zakaraia Abdel Wahid

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The behavior of the unsteady non-equilibrium distribution function for a dilute gas under the effect of non-linear thermal radiation field is presented. For the best of our knowledge this is done for the first time at all. The distinction and comparisons between the unsteady perturbed and the unsteady equilibrium velocity distribution functions are illustrated. The equilibrium time for the dilute gas is determined for the first time. The non-equilibrium thermodynamic properties of the system (gas+the heated plate) are investigated. The results are applied to the Argon gas, for various values of radiation field intensity. 3D-Graphics illustrating the calculated variables are drawn to predict their behavior. The results are discussed.

Keywords: dilute gas, radiation field, exact solutions, travelling wave method, unsteady BGK model, irreversible thermodynamics, unsteady non-equilibrium distribution functions

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