Abstract: Basal metabolic rate (BMR) is widely used and an accepted measure of energy expenditure. Its principal determinant is body mass. However, this parameter is also correlated with a variety of other factors. The objective of this study is to measure BMR and compare it with the values obtained from predictive equations in adults classified according to their body mass index (BMI) values. 276 adults were included into the scope of this study. Their age, height and weight values were recorded. Five groups were designed based on their BMI values. First group (n = 85) was composed of individuals with BMI values varying between 18.5 and 24.9 kg/m2. Those with BMI values varying from 25.0 to 29.9 kg/m2 constituted Group 2 (n = 90). Individuals with 30.0-34.9 kg/m2, 35.0-39.9 kg/m2, > 40.0 kg/m2 were included in Group 3 (n = 53), 4 (n = 28) and 5 (n = 20), respectively. The most commonly used equations to be compared with the measured BMR values were selected. For this purpose, the values were calculated by the use of four equations to predict BMR values, by name, introduced by Food and Agriculture Organization (FAO)/World Health Organization (WHO)/United Nations University (UNU), Harris and Benedict, Owen and Mifflin. Descriptive statistics, ANOVA, post-Hoc Tukey and Pearson’s correlation tests were performed by a statistical program designed for Windows (SPSS, version 16.0). p values smaller than 0.05 were accepted as statistically significant. Mean ± SD of groups 1, 2, 3, 4 and 5 for measured BMR in kcal were 1440.3 ± 210.0, 1618.8 ± 268.6, 1741.1 ± 345.2, 1853.1 ± 351.2 and 2028.0 ± 412.1, respectively. Upon evaluation of the comparison of means among groups, differences were highly significant between Group 1 and each of the remaining four groups. The values were increasing from Group 2 to Group 5. However, differences between Group 2 and Group 3, Group 3 and Group 4, Group 4 and Group 5 were not statistically significant. These insignificances were lost in predictive equations proposed by Harris and Benedict, FAO/WHO/UNU and Owen. For Mifflin, the insignificance was limited only to Group 4 and Group 5. Upon evaluation of the correlations of measured BMR and the estimated values computed from prediction equations, the lowest correlations between measured BMR and estimated BMR values were observed among the individuals within normal BMI range. The highest correlations were detected in individuals with BMI values varying between 30.0 and 34.9 kg/m2. Correlations between measured BMR values and BMR values calculated by FAO/WHO/UNU as well as Owen were the same and the highest. In all groups, the highest correlations were observed between BMR values calculated from Mifflin and Harris and Benedict equations using age as an additional parameter. In conclusion, the unique resemblance of the FAO/WHO/UNU and Owen equations were pointed out. However, mean values obtained from FAO/WHO/UNU were much closer to the measured BMR values. Besides, the highest correlations were found between BMR calculated from FAO/WHO/UNU and measured BMR. These findings suggested that FAO/WHO/UNU was the most reliable equation, which may be used in conditions when the measured BMR values are not available.
Abstract: The biochemical industry is one of the most important modern industries. Biochemical reactors are crucial devices of the biochemical industry. The essential bioprocess carried out in bioreactors is the fermentation process. A thorough insight into the fermentation process and the knowledge how to control it are essential for effective use of bioreactors to produce high quality and quantitatively enough products. The development of the control system starts with the determination of a mathematical model that describes the steady state and dynamic properties of the controlled plant satisfactorily, and is suitable for the development of the control system. The paper analyses the fermentation process in bioreactors thoroughly, using existing mathematical models. Most existing mathematical models do not allow the design of a control system for controlling the fermentation process in batch bioreactors. Due to this, a mathematical model was developed and presented that allows the development of a control system for batch bioreactors. Based on the developed mathematical model, a control system was designed to ensure optimal response of the biochemical quantities in the fermentation process. Due to the time-varying and non-linear nature of the controlled plant, the conventional control system with a proportional-integral-differential controller with constant parameters does not provide the desired transient response. The improved adaptive control system was proposed to improve the dynamics of the fermentation. The use of the adaptive control is suggested because the parameters’ variations of the fermentation process are very slow. The developed control system was tested to produce dairy products in the laboratory bioreactor. A carbon dioxide concentration was chosen as the controlled variable. The carbon dioxide concentration correlates well with the other, for the quality of the fermentation process in significant quantities. The level of the carbon dioxide concentration gives important information about the fermentation process. The obtained results showed that the designed control system provides minimum error between reference and actual values of carbon dioxide concentration during a transient response and in a steady state. The recommended control system makes reference signal tracking much more efficient than the currently used conventional control systems which are based on linear control theory. The proposed control system represents a very effective solution for the improvement of the milk fermentation process.
Abstract: This paper presents wavelet based classification of various heart diseases. Electrocardiogram signals of different heart patients have been studied. Statistical natures of electrocardiogram signals for different heart diseases have been compared with the statistical nature of electrocardiograms for normal persons. Under this study four different heart diseases have been considered as follows: Myocardial Ischemia (MI), Congestive Heart Failure (CHF), Arrhythmia and Sleep Apnea. Statistical nature of electrocardiograms for each case has been considered in terms of kurtosis values of two types of wavelet coefficients: approximate and detail. Nine wavelet decomposition levels have been considered in each case. Kurtosis corresponding to both approximate and detail coefficients has been considered for decomposition level one to decomposition level nine. Based on significant difference, few decomposition levels have been chosen and then used for classification.
Abstract: A numerical approach of the effectiveness of numerous
parameters on magnetohydrodynamic (MHD) natural convection
heat and mass transfer problem of a dusty micropolar fluid in
a non-Darcy porous regime is prepared in the current paper.
In addition, a convective boundary condition is scrutinized into
the micropolar dusty fluid model. The governing boundary layer
equations are converted utilizing similarity transformations to a
system of dimensionless equations to be convenient for numerical
treatment. The resulting equations for fluid phase and dust phases
of momentum, angular momentum, energy, and concentration with
the appropriate boundary conditions are solved numerically applying
the Runge-Kutta method of fourth-order. In accordance with the
numerical study, it is obtained that the magnitude of the velocity
of both fluid phase and particle phase reduces with an increasing
magnetic parameter, the mass concentration of the dust particles, and
Forchheimer number. While rises due to an increment in convective
parameter and Darcy number. Also, the results refer that high values
of the magnetic parameter, convective parameter, and Forchheimer
number support the temperature distributions. However, deterioration
occurs as the mass concentration of the dust particles and Darcy
number increases. The angular velocity behavior is described by
progress when studying the effect of the magnetic parameter and
microrotation parameter.
Abstract: The aim of this study is to assess the influence of plastic fines content on sand-clay mixtures on maximum shear modulus and liquefaction resistance using a series of resonant column tests. A high plasticity clay called bentonite was added to 161 Firoozkooh sand at the percentages of 10, 15, 20, 25, 30 and 35 by dry weight. The resonant column tests were performed on the remolded specimens at constant confining pressure of 100 KPa and then the values of Gmax and liquefaction resistance were investigated. The maximum shear modulus and cyclic resistance ratio (CRR) are examined in terms of fines content. Based on the results, the maximum shear modulus and liquefaction resistance tend to decrease within the increment of fine contents.
Abstract: The main objective of this research is to optimize the surface roughness of a milling operation on AISI 1018 steel using live tooling on a HAAS ST-20 lathe. In this study, Taguchi analysis is used to optimize the milling process by investigating the effect of different machining parameters on surface roughness. The L9 orthogonal array is designed with four controllable factors with three different levels each and an uncontrollable factor, resulting in 18 experimental runs. The optimal parameters determined from Taguchi analysis were feed rate – 76.2 mm/min, spindle speed 1150 rpm, depth of cut – 0.762 mm and 2-flute TiN coated high-speed steel as tool material. The process capability Cp and process capability index Cpk values were improved from 0.62 and -0.44 to 1.39 and 1.24 respectively. The average surface roughness values from the confirmation runs were 1.30 µ, decreasing the defect rate from 87.72% to 0.01%. The purpose of this study is to efficiently utilize the Taguchi design to optimize the surface roughness in a milling operation using live tooling.
Abstract: Loose soils normally are of weak bearing capacity due to their structural nature. Being exposed to heavy traffic loads, they would fail in most cases. To tackle the aforementioned issue, geotechnical engineers have come up with different approaches; one of which is making use of geosynthetic-reinforced soil-aggregate systems. As these polymeric reinforcements have highlighted economic and environmentally-friendly features, they have become widespread in practice during the last decades. The present research investigates the efficiency of four different types of these reinforcements in increasing the bearing capacity of two-layered soil sections using a series California Bearing Ratio (CBR) test. The studied sections are comprised of a 10 cm-thick layer of no. 161 Firouzkooh sand (weak subgrade) and a 10 cm-thick layer of compacted aggregate materials (base course) classified as SP and GW according to the United Soil Classification System (USCS), respectively. The aggregate layer was compacted to the relative density (Dr) of 95% at the optimum water content (Wopt) of 6.5%. The applied reinforcements were including two kinds of geocomposites (type A and B), a geotextile, and a geogrid that were embedded at the interface of the lower and the upper layers of the soil-aggregate system. As the standard CBR mold was not appropriate in height for this study, the mold used for soaked CBR tests were utilized. To make a comparison between the results of stress-settlement behavior in the studied specimens, CBR values pertinent to the penetrations of 2.5 mm and 5 mm were considered. The obtained results demonstrated 21% and 24.5% increments in the amount of CBR value in the presence of geocomposite type A and geogrid, respectively. On the other hand, the effect of both geotextile and geocomposite type B on CBR values was generally insignificant in this research.
Abstract: Emotional Association (EA) Theory deals with the psychological attachment of the employees to their employer as a focal way of awakening employees’ productivity, innovativeness, and creativity towards achieving a common cause within an organization. The objectives of this paper include: to comprehend the forms of motivation at workstation as provided by the Emotion Association Theory; to improve access to the skills relevant for a good working environment; to raise new skills through knowing the power to influence employees; to improve communication skills as well as researching current leaders and their leadership skills. The paper makes use of descriptive and intervention by examining the effect of motivation on employees. The method makes use of psychological EA theory that analyses the 3E leadership model to impact the ability to adopt the organization’s policy and employee productivity. In this case, the method will assess the workplace culture by assessing personal values and qualities that make master manager in organizations. In addition, the method will apply the theory to support the positive work engagement and its successful implementation to effectively influence employee productivity. The findings of this research showcase the significance motivating employees to increase their productivity as provided by the theory. Nonetheless, it improves sense of belonging among workers in a firm since it is employee-oriented. In addition, it works upon unification of workers within a workplace through mutual respect and empathy which promotes competence and policy implementation. Therefore, emotionally related qualities ignite motivation in workers.
Abstract: Moraceae family has immense phytochemical constituents and significant pharmacological properties, hence have great medicinal values. The aim of this study was to screen and quantify phytochemicals as well as the antioxidant activities of the leaf and stem bark extracts and fractions (crude ethanol extracts, n-hexane, ethyl acetate and aqueous ethanol fractions) of Ficus sagittifolia. Leaf and stem bark of F. sagittifolia were extracted by maceration method using ethanol to give ethanol crude extract. The ethanol crude extract was partitioned by n-hexane and ethyl-acetate to give their respective fractions. All the extracts were screened for their phytochemicals using standard methods. The total phenolic, flavonoid, tannin, saponin contents and antioxidant activity were determined by spectrophotometric method while the alkaloid content was evaluated by titrimetric method. The amount of total phenolic in extracts and fractions were estimated in comparison to gallic acid, whereas total flavonoids, tannins and saponins were estimated corresponding to quercetin, tannic acid and saponin respectively. 2, 2-diphenylpicryl hydrazyl radical (DPPH)* and phosphomolybdate methods were used to evaluate the antioxidant activities of leaf and stem bark of F. sagittifolia. Phytochemical screening revealed the presence of flavonoids, saponins, terpenoids/steroids, alkaloids for both extracts of leaf and stem bark of F. sagittifolia. The phenolic content of F. sagittifolia was most abundant in leaf ethanol crude extract as 3.53 ± 0.03 mg/g equivalent of gallic acid. Total flavonoids and tannins content were highest in stem bark aqueous ethanol fraction of F. sagittifolia estimated as 3.41 ± 0.08 mg/g equivalent of quercetin and 1.52 ± 0.05 mg/g equivalent of tannic acid respectively. The hexane leaf fraction of F. sagittifolia had the utmost saponin and alkaloid content as 5.10 ± 0.48 mg/g equivalent of saponins and 0.171 ± 0.39 g of alkaloids. Leaf aqueous ethanol fraction of F. sagittifolia showed high antioxidant activity (IC50 value of 63.092 µg/mL) and stem ethanol crude extract (227.43 ± 0.78 mg/g equivalent of ascorbic acid) for DPPH and phosphomolybdate method respectively and the least active was found to be the stem hexane fraction using both methods (313.32 µg/mL; 16.21 ± 1.30 mg/g equivalent of ascorbic acid). The presence of these phytochemicals in the leaf and stem bark of F. sagittifolia are responsible for their therapeutic importance as well as the ability to scavenge free radicals in living systems.
Abstract: Inelastic deformation of the brace in Special Concentrically Braced Frame (SCBF) creates inelastic damages on gusset plate connections such as buckling at edges. In this study, to improve the seismic performance of SCBFs connections, an analytical study was undertaken. To improve the gusset plate connection, this study proposes using edge’s stiffeners in both sides of gusset plate. For this purpose, in order to examine edge’s stiffeners effect on gusset plate connections, two groups of modeling with and without considering edge’s stiffener and different types of braces were modeled using ABAQUS software. The results show that considering the edge’s stiffener reduces the equivalent plastic strain values at a connection region of gusset plate with beam and column, which can improve the seismic performance of gusset plate. Furthermore, considering the edge’s stiffeners significantly decreases the strain concentration at regions where gusset plates have been connected to beam and column. Moreover, considering 2tpl distance causes reduction in the plastic strain.
Abstract: Zagros mountain range is a very important precipitation zone in Iran as it receives high average annual precipitation compared to other parts of this country. Although this region is important precipitation zone in semi-arid an arid country like Iran, accurate method to study water resources in this region has not been applied yet. In this study, stable isotope δ18O content of precipitation and groundwater resources showed spatial variations across Zagros region as southern parts of Zagros region showed more enriched isotope values compared to the northern parts. This is normal as southern Zagros region is much drier with higher air temperature and evaporation compared to northern parts. In addition, the spatial variations of stable isotope δ18O in precipitation in Zagros region have been simulated by the models which consider the altitude and latitude variations as input to simulate δ18O in precipitation.
Abstract: The principal objective of this study is the evaluation of the seismic performance of reinforced concrete frame structures, taking into account of the behavior laws, reflecting the real behavior of materials, using CASTEM2000 software. A finite element model used is based in modified Takeda model with Timoshenko elements for columns and beams. This model is validated on a Vecchio experimental reinforced concrete (RC) frame model. Then, a study focused on the behavior of a RC frame with three-level and three-story in order to visualize the positioning the plastic hinge (plastic rotation), determined from the curvature distribution along the elements. The results obtained show that the beams of the 1st and 2nd level developed a very large plastic rotations, or these rotations exceed the values corresponding to CP (Collapse prevention with cp qCP = 0.02 rad), against those developed at the 3rd level, are between IO and LS (Immediate occupancy and life Safety with qIO = 0.005 rad and rad qLS = 0.01 respectively), so the beams of first and second levels submit a very significant damage.
Abstract: The process of modification of ed-20 epoxy resin synthesized by vinyl-containing compounds is considered. It is shown that the introduction of vinyl-containing compounds into the composition based on epoxy resin ED-20 allows adjusting the technological and operational characteristics of the binder. For improvement of the properties of epoxy resin, following modifiers were selected: polyvinylformalethyl, polyvinyl butyral and composition of linear and aromatic amines (Аramine) as a hardener. Now the big range of hardeners of epoxy resins exists that allows varying technological properties of compositions, and also thermophysical and strength indicators. The nature of the aramin type hardener has a significant impact on the spatial parameters of the mesh, glass transition temperature, and strength characteristics. Epoxy composite materials based on ED-20 modified with polyvinyl butyral were obtained and investigated. It is shown that the composition of resins based on derivatives of polyvinyl butyral and ED-20 allows obtaining composite materials with a higher complex of deformation-strength, adhesion and thermal properties, better water resistance, frost resistance, chemical resistance, and impact strength. The magnitude of the effect depends on the chemical structure, temperature and curing time. In the area of concentrations, where the effect of composite synergy is appearing, the values of strength and stiffness significantly exceed the similar parameters of the individual components of the mixture. The polymer-polymer compositions form their class of materials with diverse specific properties that ensure their competitive application. Coatings with high performance under cyclic loading have been obtained based on epoxy oligomers modified with vinyl-containing compounds.
Abstract: Introduction: Some parameters should be considered to investigate the chronic effects of radiation absorption in radiation workers. Trace elements are parameters which small changes in them can cause significant effects on live systems. The role of trace element concentration in human health is significant. These elements play an important role in the developing and functioning of the immune system, cellular respiration, and oxidation processes. Considering the importance and necessity of this issue and few studies, measurements of concentration changes of these elements due to the absorbed dose are important. Purpose: This study aimed to determine the biological effects of occupational dose absorption on plasma and erythrocyte concentration of Zn and Cu in the radiology staff of Tehran Oil Hospital. Material and methods: In this analytical-comparative study, 72 people have entered. 36 people (18 males and 18 females) were selected as radiology staff in the diagnostic and therapeutic departments of Tehran Oil Hospital. And 36 people (18 males and 18 females) were selected as general section staff in the same hospital as a control group. Radiology and control groups’ age and sex were matched. 10 ml of venous blood was taken from all people. An atomic absorption spectrometer was used to obtain zinc and copper plasma concentrations. Levine test was used to compare these results validity. Results: The mean concentrations of copper and zinc were measured as 0.951 and 0.754 mg/L in the plasma phase and 3.2 and 0.401 mg/L in the RBC phase for the radiology group. Copper and zinc average concentrations, respectively 0.976 and 0.813 mg/L in the plasma phase and 2.906 and 0.476 mg/L in the RBC phase, were measured for the control group. These elements Concentrations in the plasma phase were significantly different from that of the control group, but the concentrations in the red blood cell phase did not show a significant difference compared to the control group. In comparison, a separate comparison between men and women in the experimental and control groups showed a significant difference in the values of the elements mentioned. With a significant increase in samples, a better justification than the available statistical results can be extracted. Conclusions: Within this study results, chronic occupational probabilistic absorption destructive effects (even within the permitted range) on blood trace element concentration have been confirmed.
Abstract: This paper uses the analytic hierarchy process to study the execution effect of the minimum purchase price of grain in different regions and various grain crops. Firstly, for different regions, five indicators including grain yield, grain sown area, gross agricultural production, grain consumption price index, and disposable income of rural residents were selected to construct an evaluation index system. We collect data of six provinces including Hebei Province, Heilongjiang Province and Shandong Province from 2006 to 2017. Then, the judgment matrix is constructed, and the hierarchical single ordering and consistency test are carried out to determine the scoring standard for the minimum purchase price of grain. The ranking of the execution effect from high to low is: Heilongjiang Province, Shandong Province, Hebei Province, Guizhou Province, Shaanxi Province, and Guangdong Province. Secondly, taking Shandong Province as an example, we collect the relevant data of sown area and yield of cereals, beans, potatoes and other crops from 2006 to 2017. The weight of area and yield index is determined by expert scoring method. And the average sown area and yield of cereals, beans and potatoes in 2006-2017 were calculated, respectively. On this basis, according to the sum of products of weights and mean values, the execution effects of different grain crops are determined. It turns out that among the cereals, the minimum purchase price had the best execution effect on paddy, followed by wheat and finally maize. Moreover, among major categories of crops, cereals perform best, followed by beans and finally potatoes. Lastly, countermeasures are proposed for different regions, various categories of crops, and different crops of the same category.
Abstract: This paper presents an approach for easy creation and
classification of institutional risk profiles supporting endangerment
analysis of file formats. The main contribution of this work is the
employment of data mining techniques to support set up of the most
important risk factors. Subsequently, risk profiles employ risk factors
classifier and associated configurations to support digital preservation
experts with a semi-automatic estimation of endangerment group
for file format risk profiles. Our goal is to make use of an expert
knowledge base, accuired through a digital preservation survey
in order to detect preservation risks for a particular institution.
Another contribution is support for visualisation of risk factors for
a requried dimension for analysis. Using the naive Bayes method,
the decision support system recommends to an expert the matching
risk profile group for the previously selected institutional risk profile.
The proposed methods improve the visibility of risk factor values
and the quality of a digital preservation process. The presented
approach is designed to facilitate decision making for the preservation
of digital content in libraries and archives using domain expert
knowledge and values of file format risk profiles. To facilitate
decision-making, the aggregated information about the risk factors
is presented as a multidimensional vector. The goal is to visualise
particular dimensions of this vector for analysis by an expert and
to define its profile group. The sample risk profile calculation and
the visualisation of some risk factor dimensions is presented in the
evaluation section.
Abstract: Comparative research has been conducted to allow us to determine the content of macro and microelements in the vegetative and reproductive organs of grass pea and the quality of grass pea seeds, as well as to identify the possibility of grass pea growth on soils contaminated by heavy metals. The experiment was conducted on an agricultural field subjected to contamination from the Non-Ferrous-Metal Works (MFMW) near Plovdiv, Bulgaria. The experimental plots were situated at different distances of 0.5 km and 8 km, respectively, from the source of pollution. On reaching commercial ripeness the grass pea plants were gathered. The composition of the macro and microelements in plant materials (roots, stems, leaves, seeds), and the dry matter content, sugars, proteins, fats and ash contained in the grass pea seeds were determined. Translocation factors (TF) and bioaccumulation factor (BCF) were also determined. The quantitative measurements were carried out through inductively-coupled plasma (ICP). The grass pea plant can successfully be grown on soils contaminated by heavy metals. Soil pollution with heavy metals does not affect the quality of the grass pea seeds. The seeds of the grass pea contain significant amounts of nutrients (K, P, Cu, Fe Mn, Zn) and protein (23.18-29.54%). The distribution of heavy metals in the organs of the grass pea has a selective character, which reduces in the following order: leaves > roots > stems > seeds. BCF and TF values were greater than one suggesting efficient accumulation in the above ground parts of grass pea plant. Grass pea is a plant that is tolerant to heavy metals and can be referred to the accumulator plants. The results provide valuable information about the chemical and nutritional composition of the seeds of the grass pea grown on contaminated soils in Bulgaria. The high content of macro and microelements and the low concentrations of toxic elements in the grass pea grown in contaminated soil make it possible to use the seeds of the grass pea as animal feed.
Abstract: This study aims to examine the association between disclosure of social responsibility and tax aggressiveness in developing countries, namely Thailand. This is due to the increasing trend of disclosure of social responsibility in developing countries, even though this disclosure of information is still voluntary. On the other hand, developing countries have low taxation rate and investor protection infrastructures that allow the disclosure of social responsibility to be used opportunistically as a tool to fool the attainment of interests. This study also examines the role of assurance on the association between corporate social responsibility disclosure and tax aggressiveness. The assurance aims to provide confidence that the disclosure of social responsibility by the company is valid. This research builds an index to measure the disclosure of social responsibility based on the rules issued by the innovative Global Reporting. The results of the study are based on a sample of publicly traded companies in Thailand, which showed a positive association between disclosure of corporate social responsibility and tax aggressiveness, but it was further discovered that these results were mitigated by the existence of assurance against disclosure of corporate social responsibility. The results of this study indicate that the disclosure of corporate social responsibility can show that the company cares about the issue of social responsibility but does not automatically make the company as one that holds ethical values in its business practices.
Abstract: The synergistic impact and optimization of gas flow rate, concentration of CO2, and light intensity on CO2 biofixation rate were investigated using wastewater as a medium to cultivate Chlorella vulgaris under different conditions (gas flow rate 1-8 L/min), CO2 concentration (0.03-7%), and light intensity (150-400 µmol/m2.s)). Response Surface Methodology and Box-Behnken experimental Design were applied to find optimum values for gas flow rate, CO2 concentration, and light intensity. The optimum values of the three independent variables (gas flow rate, concentration of CO2, and light intensity) and desirability were 7.5 L/min, 3.5%, and 400 µmol/m2.s, and 0.904, respectively. The highest amount of biomass produced and CO2 biofixation rate at optimum conditions were 5.7 g/L, 1.23 gL-1d-1, respectively. The synergistic effect between gas flow rate and concentration of CO2, and between gas flow rate and light intensity was significant on the three responses, while the effect between CO2 concentration and light intensity was less significant on CO2 biofixation rate. The results of this study could be highly helpful when using microalgae for CO2 biofixation in wastewater treatment.
Abstract: In this paper, one dimensional advection diffusion
model is analyzed using finite difference method based on
Crank-Nicolson scheme. A practical problem of filter cake washing
of chemical engineering is analyzed. The model is converted into
dimensionless form. For the grid Ω × ω = [0, 1] × [0, T], the
Crank-Nicolson spatial derivative scheme is used in space domain
and forward difference scheme is used in time domain. The scheme is
found to be unconditionally convergent, stable, first order accurate in
time and second order accurate in space domain. For a test problem,
numerical results are compared with the analytical ones for different
values of parameter.