فهرست مطالب

International Journal of Engineering
Volume:32 Issue: 11, Nov 2019

  • TRANSACTIONS B: Applications
  • تاریخ انتشار: 1398/08/10
  • تعداد عناوین: 20
|
  • Khalilalrahman Dehvari, Mohammad Pazouki *, Azarmidokht Hosseinnia Pages 1506-1515
    Green nanotechnology with the goal of producing sustainable nanomaterials in an eco-friendly approach is becoming an increasing necessity for nanomanufacturing industries. In this regards, biosynthesis is well adopted as a viable method for producing benign nanoparticles for biomedical application. The present study aimed at optimization and study of the effects of external stimuli pH and gold ion concentration on the morphology of biosynthesized gold nanoparticles (GNPs) using Fusarium oxysporum. Based on the central composite design, the experimental method was developed at three levels of the operating parameters; the initial gold ion concentration, cell mass, and pH. The X-ray diffraction and transmission electron microscopy showed that the obtained GNPs were impurity-free while the size and shape of particles were a function of the pH and Au3+ concentration. Also, analysis of variance revealed that the cell mass and initial gold ion concentration have a significant effect on biosynthesis of GNPs. The optimal condition was found at the initial gold ion concentration of 550 µM, pH 3.5, and cell mass of 0.047 mg/mL with the obtained gold uptake of 98.29%. Pseudo-second order kinetics model best fitted the experimental results with the activation energy of 73.8 kJ indicating that complex chemisorption is the mechanism of gold biorecovery. Adsorption equilibrium followed Freundlich adsorption model and negative ΔG value at room temperature suggested that the GNPs can be synthesized at ambient temperature and atmosphere via an eco-friendly and economically viable process.
    Keywords: Gold Nanoparticles, Fusarium oxysporum, Biorecovery, optimization, Biosynthesis, Response Surface Methodology
  • Saad Mahmood Ali * Pages 1516-1526
    Centrifugal casting is one of the advanced casting branches widely used in the metallurgical industry in which the centrifugal force helps strengthen the workpiece material. The present work attempt to study the effect of the horizontal and vertical centrifugal casting parameters included the centrifugal mold rotation speeds and G-factors values on the quality of the product. The work has been completed with design and fabricated of a low cost horizontal and vertical centrifugal casting machine with the main accessories for producing a hypoeutectic aluminum silicone (AlSi) alloy (content 10 % Si) specimens. The experimental results were analyzed and improved by using the statistical computer program “Design Expert 11” and response surface methodology (RSM). The results showed that for vertical and horizontal casting processes, the finest surfaces quality was achieved when working at mold rotation speed from 520 to 690 and 950 to 1230 RPM, i.e., with an average value of the G-factor = 69 and 50, respectively. The proof stress values were increased with increasing the mold rotation speed up to (690 RPM) and (1230 RPM) or used the G- factor value of 87.99 and 60.96 gave an increase in proof stress by 6.7 and (20.62% for vertical and horizontal casting experiments compared with gravitational casting, respectively. The obtained tensile strengths values were improved by 38.6 and 45.41 %, compared with the gravitational casting, respectively; while the percentage elongations were reduced to 0.281and 0.291 %; which means decreased by 33.45 and 31.69 % for the vertical and horizontal centrifugal casting compared with the values obtained by gravitational casting experiments, respectively.
    Keywords: Horizontal, Vertical Centrifugal Casting Response Surface Methodology, Hypoeutectic AlSi Alloy, Design of experiments, G- factor, Mold Rotation Speed
  • Moslem M. Lakouraj, Amin Heydari, Mona Rouhi, Alireza G. Hosseinzadeh, Fatemeh N. Babaei, Ghasem Najafpour * Pages 1527-1533

    Natural gas is odorized by trace amount of mercaptans and organic sulfides to be recognized by individuals, in case of gas leakage. These materials may pollute the environment particularly in injection station at local gas plants. Therefore, removal of sulfur compounds from the remaining odorant in barrels is essential. To remove the residual portion of mercaptans and alkylsulfide mixtures different methods were utilized which among them extraction-distillation procedure was implemented in our project owing to environmentally safe and low cost process. Different solvents such as Methyl Ethyl Ketone (MEK), Ethyl acetate, Dichloromethane (DCM), Toluene and Kerosene were attempted for the efficient extraction which among them kerosene was the most desired and the best in terms of use and environmental friendly solvent. The results showed highly efficient method for the removal of odorants in which the regenerated mercaptan from the mercaptan contaminated barrels could be reused in injection step as well as the original odorant. The GC and 1H NMR analyses confirmed that the recovered organo-sulfur compounds, mainly composed of tertiary butyl mercaptan, which was desired for re-injection into natural gas stream as suitable odorants.

    Keywords: Extraction-Distillation, Mercaptan, Odorant, Organo-sulfur Compounds
  • Fariborz Nateghi *, Mohammad Hossein Ahmadi Pages 1534-1542

    Cement-based composite materials like Engineered Cementitious Composites (ECCs) are applicable in the strengthening of structures because of the high tensile strength and strain. Proper mix proportion, which has the best mechanical properties, is so essential in ECC design material to use in structural components. In this paper, after finding the best mix proportion based on uniaxial tensile strength and strain, the correlation between these parameters were calculated. Since material properties depend on the content ratios, six mixtures with different Fly Ash (FA) content were considered to find the best ECC mixture called Improved ECC (IECC). Also, The influence of local fine aggregates and FA on the tensile behavior of ECC was considered to introduce IECC which has the best tensile properties. To predict the mechanical properties of ECC based on experimental results, Artificial Neural Network (ANN) was used. Training and validation of the proposed model were carried out based on 36 experimental results to find the best results. Numerical analysis is utilized to find the best mix proportion of ECC in structural design. The results show that the effects of FA and fine aggregates are considerable. Also, The proposed ANN model predicts the tensile strength and strain of ECC with different FA ratios accurately. Furthermore, the model can estimate mechanical properties of ECC in previous experimental results.

    Keywords: Engineered Cementitious Composites Experimental Study, Artificial Neural Network, Local Admixtures, Mechanical properties
  • C Daniel *, G Hemalatha, L Sarala, D Tensing, S Sundar Manoharan Pages 1543-1547
    The present study focusses on the damping force control of shear mode magnetorheological (MR) damper for seismic mitigations. Therefore, the semi-active MR damper which can control the vibration is analyzed both experimentally and numerically. Carbonyl iron is used as the magnetic particle and Castrol Magnetec oil as carrier fluid throughout the study. MR damper is designed and fabricated, and its damping force was evaluated experimentally at 2.5 A- 10 V. Shear mode MR Damper is tested in universal testing machine using time history loading. The model was numerically analyzed using Newmark’s method for nonlinear system in MATLAB to control the three storey model building frame taken from the literature. The result indicates that 49.42% reduction in displacement at the second storey and 48.14% in the third storey, respectively. Maximum reduction was observed when damper was kept in the ground floor. The maximum force observed for the MR Damper is 0.777 kN.
    Keywords: Magnetorheological Damper, Magnetorheological Fluid, Mewmark’s Nonlinear method, time history analysis
  • Abbas Abdulmajeed, Jinan Laftah * Pages 1548-1558

    composite concrete-steel plate shear walls are the most critical resisting structural members that resist lateral and axial loads. This type of wall consisting of two steel faceplates presenting the outer skin, infill concrete and shear connectors which are used to provide the composite action of the steel faceplates with infill concrete in order to increase the strength and to reduce the local buckling of steel faceplates. The experimental investigation of composite concrete - steel plate shear walls under axial loads is presented in this research. The aim of this study is to evaluate the effect of concrete compressive strength and the thickness of the wall on the axial capacity, lateral displacement and axial shortening of the walls. The obtained results indicate that the increase in compressive strength of concrete enhances the ultimate axial load capacity of the wall and it should have an effect on crushing strength of the composite wall which can affect the failure loads of the composite walls. In addition, the concrete strength increased by enlarging the thickness of wall from 55mm to 70mm and this is because the concrete participation leads to large assistance to avoid relatively steel plate from premature buckling as well as, the concrete plays an important role in avoiding instability of steel plate. Thus, the failure load, lateral displacement at top and mid-height of the wall as well as the axial shortening at failure load increased by increasing the compressive strength and increasing the wall thickness of the wall. The failure of the composite walls was started by local buckling of the steel plates, cracking and crushing of the concrete infill in the top region of the composite wall.

    Keywords: Axial load, Composite Concrete-steel Plate Shear Walls, Failure mode, lateral displacement, Shortening
  • Hadi Valizadeh, Hedayat Veladi *, Mohammad Reza Sheidaii, Bahman Farahmand Pages 1559-1569

    An innovative type called "butterfly-shaped links steel plate shear wall (BLSPSW)" was proposed as a lateral load resisting system. In this novel system, by creating butterfly-shaped links in the four sides of the web plate, the lateral load resisting mechanism is not the development of a diagonal tension field on the web plate (similar to Conventional SPSWs), but the capacity of the system is determined by the shear strength of the links. Therefore, the geometric parameters of the link as initial design inputs affect predicting and controlling the stiffness and strength of the BLSPSW. Three experimental specimens were loaded to examine the behavior of the proposed system. The first one was the conventional steel plate shear wall (called SPSW-1), and two others prepared of the butterfly-shaped link steel plate shear wall (BLSPSW) with links that have been controlled by shear yield (SPSW-BL 80) and flexural yield (SPSW-BL 130). The experimental results showed that the stiffness and strength of the BLSPSW specimens can be controlled by the link geometry. Also, the BLSPSWs indicated desirable ductility up to 10 percent and high energy dissipation, even in small drifts compared to the SPSW-1. At last, the shear strength formulation of the butterfly fuses was used to determine the shear capacity of the BLSPSWs and compared with the experimental results.

    Keywords: Butterfly Link, Energy dissipation, Ductility, shear capacity, steel plate shear wall
  • D. Zhang *, Z. Zhang, T. Cheng, X. Zhao Pages 1570-1576
    This study investigated the vault settlement characteristics of an unsymmetrically loaded tunnel which was excavated by annular excavation via core rock support method. Response surface methodology (RSM) was employed to design the experiments, evaluate the results with the purpose of optimizing the value of design parameters for reducing the vault settlement. The parameters such as horizontal distance, step length, tunneling depth, width of core rock, strength of surrounding rocks and support strength were firstly examined, and a second-order polynomial regression equation was then derived to predict the responses of vault settlement. The percentage contribution, validity of model and effects of different parameters as well as their interactions were assessed by analysis of variance (ANOVA). In the order from high to low effect, these parameters are strength of surrounding rocks, support strength, horizontal distance, width of core rock, tunneling depth, and step length. The results indicated that the influence of uncontrollable factors (i.e. strength of surrounding rocks, tunneling depth, and horizontal distance) on the vault settlement can be reduced through the adjustment of controllable factors (i.e. Width of core rock, step length, and support strength). Moreover, the proposed method in this paper was validated with results of field test measurement and simulation calculation which verified its feasibility.
    Keywords: response surface method, Annular Excavation, Vault Settlement, Unsymmetrically Loaded Tunnel
  • Arvind Cholker *, Manzoor Tantray Pages 1577-1583
    Present paper investigated the strain and damage sensing property on concrete cubes embedded with carbon fibers. Concrete cubes of dimension 150 mm have been casted with different concentration of carbon fibers to study the strain and damage sensing property under cyclic loading that can be further used for health monitoring as non-destructive testing (NDT) approach. All the specimens were tested under cyclic loading within elastic region of the sample for three cycles of loading with a maximum load of 195kN for strain sensing test. During cyclic loading, fractional change in resistance (FCR) is calculated and co-relation with the stress is plotted. During strain sensing test, gauge factors (GF) were also calculated during loading and unloading on the samples. From obtained results, it is found that the concrete sample containing 1.5% of carbon fibers by weight of cement gives best co-relation between stress and FCR that can be further used for health monitoring purpose. Along with strain sensing property, damage sensing property and ultimate load carrying capacities of all the specimens are also reported in present paper with detailed explanation.
    Keywords: Carbon Fibers, Electrical Properties, Self-Compacting Concrete, Gauge Factor
  • Zhen XU *, Wei Jin, Ming Zheng Pages 1584-1590
    This study aims at quantifying the influence on the traversability of road network of road network caused by building collapse in earthquake. To this end, an analysis method on post-earthquake traversability of road network considering building collapse is proposed. First, the time-history analysis of seismic response based on the multi-degree of freedom (MDOF) model is performed for regional building groups, so that collapsed buildings could be determined. Subsequently, the impact ranges of collapsed buildings are calculated based on a probabilistic model of debris distributions. Finally, the analysis algorithm of the traversability of road network is designed based on the impact ranges, and therefore the solution to determining optimal rescue paths is also designed by using a geographic information system (GIS) platform. Taking a university campus as case study, the influences on the traversability of road network due to building collapse is analyzed in a virtual earthquake scenario. The results of case study indicate that building collapse alters the optimal rescue path, which has a significant influence on the post-earthquake emergency responses. This study can assess the influence on the post-earthquake traversability of road network due to building collapse, and help cities reasonably respond to the post-earthquake traffic.
    Keywords: Traversability, Building Collapse, Road Network, Seismic Demage, Geographic information system
  • Pegah Amirsoleimani, Alireza Panahi, Ehsan Darvishan, Gholamreza Ghodrati * Pages 1591-1609

    Due to low stiffness of braces after yielding, the structures with buckling-restrained braces (BRBs) experience high residual drifts during an earthquake, which can be intensified by aftershocks and causes considerable damages to structures. Also, due to poor distribution of stiffness, this problem is exacerbated for irregular structures. Recently, the yielding brace system (YBS) has been introduced; which is an alternative to BRBFs to solve this problem. YBS has a secondary stiffening part in its hysteresis behavior which can prevent excessive deformations. Therefore, structures with YBS are expected to show a better peroformance in seismic sequences compared to BRBs.  However, the seismic behavior of the YBS system in irregular structures has not been studied so far. On this basis, this paper investigates the seismic behavior of frames with BRB and YBS in regular and irregular structures under seismic sequences. Twenty four 4-, 8-, and 12-story frames with these two systems were designed and evaluated. First, a nonlinear dynamic analysis was conducted on the frames under mainshocks, and the maximum interstory drift and the residual interstory drift of the frames were compared. Then, using incremental dynamic analysis and fragility curves, the behavior of the frames under mainshocks was investigated. Afterwards, using incremental dynamic analysis and fragility curves, the behavior of the structures under mainshock-aftershock in three performance levels was aledso investigated. The results showed that YBS bracing, especially in low rise structures, leads to far lower maximum drifts and maximum residual drifts than BRB braces, which can reduce the probability of the occurrence of soft stories in structures.

    Keywords: Buckling-restrained brace, Yielding Brace System, Incremental Dynamic Analysis, Fragility curve
  • Hamid Afshang *, Farzad Tahami Pages 1610-1619
    Dynamic modeling and control of dc-dc series resonant converter (SRC) especially when operating in discontinuous conduction mode (DCM) is still a challenge in power electronics. Due to semiconductors switching, SRC is naturally represented as a switched linear system, a class of hybrid systems. Nevertheless, the hybrid nature of the SRC is commonly neglected and it is modeled as a purely continuous dynamics based on the sinusoidal approximation and averaging. However, an SRC may be purposely designed to operate in DCM so the sinusoidal approximation is no longer acceptable. Therefore, it is essential to analyze the stability using a more sophisticated model. This paper presents a novel hybrid control strategy for the output voltage regulation of the SRC operating in DCM. Neither sinusoidal nor averaging is used. The stability of the closed-loop system is systematically fulfilled by satisfying some linear matrix inequalities. The proposed hybrid control approach has simple hardware implementation which does not require fast sampling of the resonant tank waveforms and external voltage-controlled oscillator. A prototype of the SRC is constructed and the hybrid controller is realized on a TMS320F2812 DSP core. The effectiveness of the proposed method is verified by simulation and experimental results.
    Keywords: series resonant converter, Discontinuous Conduction Mode, Voltage Regulation, Hybrid control, Piecewise Affine System, Stability Analysis
  • Mohammad G. H. Alijani, Mohammad H. Neshati * Pages 1620-1626
    Using the sampled data of a desired pattern is a common technique in pattern synthesizing of array factor (AF) of antenna arrays. Based on the obtained data matrix, Least Square Method (LSM) is used to calculate the exciting coefficient of array elements. The most important parameter, which involves the accuracy and complexity of calculation, is the sampling rate of the desired pattern. Classical Least Square Method (CLSM) uses a linear combination of the samples, which provides low accuracy. In this paper, a new method is proposed by introducing a correction factor (CF) to increase the accuracy of the pattern estimation, while the design complexity is not increased basically. A normalized error between the desired and estimated pattern is considered and its variation versus CF is investigated.  It is shown that for an optimum value of correction factor, CFopt, the defined error is minimum. The proposed method is examined for a few well-known arrays and the obtained results are reported and compared with those of classical LSM. It is shown that the introduced method accurately estimates the required pattern of array factors of equally spaced linear arrays (EALAs).
    Keywords: antenna array, Least Square Method, Radiation Pattern, Pattern Synthesis
  • N. Nouri *, A. Entezari Pages 1627-1633
    Mobile cloud computing (MCC) is a new technology that has been developed to overcome the restrictions of smart mobile devices (e.g. battery, processing power, storage capacity, etc.) to send a part of the program (with complex computing) to the cloud server (CS). In this paper, we study a multi-cell with multi-input and multi-output (MIMO) system in which the cell-interior users request service for their processing from a common CS. Also, the problem of the optimum offloading is considered as an optimization problem with optimization parameters including communication resources (such as bandwidth, transmit power and backhaul link capacity) and computational resources (such as the capacity of cloud server) in the downlink network. The main goal is to minimize the total energy consumption by mobile users (MUs) for processing with the delay limitation for each use. This issue leads to a non-convex problem and to solve the problem, we use successive convex approximation (SCA) method. We finally show that the joint optimization of these parameters leads to reducing the energy consumption of the network with simulation examples.
    Keywords: Mobile Cloud Computing, Heteregeneous Network, Non-convex Function, Bandwidth Allocation, Convex Approximation
  • Alireza Fallah, Mohammad Ali Vahdatzad *, Ahmad Sadeghieh Pages 1634-1642

    The purpose of this article is to model and solve an integrated location, routing and inventory problem (LRIP) in cash-in-transit (CIT) sector. In real operation of cash transportation, to decrease total cost and to reduce risk of robbery of such high-value commodity. There must be substantial variation, making problem difficult to formulate. In this paper, to better fit real life applications and to make the problem more practical, a bi-objective multiple periods, capacitated facilities with time windows under uncertain demand (BO-PCLRIP-TW-FD) in the LRIP, motivated by the replenishment of automated teller machines, is proposed. Then, using the chance constrained fuzzy programming to deal with uncertain parameters, the comprehensive model is formulated as a crisp mixed-integer linear programming. At last, to validate the mathematical formulation and to solve the problem, the latest version of ε-constraint method (i.e., AUGMECON2) is used. The proposed solution approach is tested on a realistic instance in CIT sector. Numerical results demonstrate the suitability of the model and the formulation. The ability of the model to be useful references for security carriers in real-world cases.

    Keywords: Location-routing-inventory Problem, Cash in Transit, Multiple objectives optimization, Chance Constrained Fuzzy Programming, Augmented ε-constraint
  • Mehdi Deiranlou, Farzad Dehghanian *, Mohammad Ali Pirayesh Pages 1643-1655
    In this paper, we develop an economic production quantity (EPQ) model under machine breakdown and two types of repair (corrective and preventive). also, study the simultaneous effect of holding safety stock and purchasing policy. In order to avoid shortages occurring as a result of the random repair time, in addition to keep safety stock, we suppose that the manufacturer could purchase some quantities from an external supplier. This paper addresses the following question: how the manufacturer determine the optimal values of safety stock, production and purchasing lot sizes, simultaneously, to minimize the expected total cost? The introduced model is then compared with the situations in which the manufacturer only keeps safety stock or just uses an external supplier, respectively. The results through the analysis show that using the simultaneous policy when the system is prone to shortages due to long repair times, have more improvement in the performance of the system rather than using the safety stock or purchasing policies, separately.
    Keywords: Economic Production Quantity, machine breakdown, purchasing, Safety Stock
  • E. Daneshfar, M. Amini *, M. M. Doustdar, H. Fazeli Pages 1656-1664
    Using heat shield, especially in throat area has a significant effect on combustion chamber pressure and thermal efficiency of solid fuel engines. Precise prediction of the regression of throat area for different pressures, will lead to optimal design of the motors, specifically for those of long burnout times. In this work, erosion of graphite nozzles employed in solid propellant motors with a specific composite propellant and variable pressures, is investigated. The numerical model utilized includes the Naiver-Stokes equations, chamber gas thermodynamic equations and thermochemical and heat conduction equations for the nozzle surface. In order to validate the numerical results, a cartridge type solid propellant motor with a graphite nozzle is experimentally tested. Using a 3D scanner in the experimental setup, the amount of inner surface regression for variable pressures (60, 90, 120 and 200 bars) is measured. Numerical and experimental results are in a proper conformity with each other. There is a direct relationship between convection heat transfer coefficient and the pressure. The overall erosion is the same for all four engine pressures. The erosion rate increases with increasing pressure. This rate for the fuel is about 0.21 mm/s for every 100 times the pressure up to 300 times. For a pressure higher than 300 times, a significant leakage occurs at the corrosion rate.
    Keywords: Solid Fuel Engine, Graphite, Erosion
  • Ali Hosseini Rad, H Ghadamian *, Hamid Reza Haghgou, Faramarz Sarhadi Pages 1665-1680
    In this research, a pilot study and analysis of an innovative multi-channel photovoltaic/thermal (MCPV/T) system in a geographic location (35° 44' 35'' N, 50° 57' 25'' E) has been carried out. This system consists of integrating a photovoltaic panel and two PV/T heat-sink converters. The total electrical, exergy and energy efficiencies of the system at air flow rate of 0.005 kg/s and radiation intensity of 926 w/m2 were 9.73%, 10.72%, and 47.24%, respectively. An air flow rate of 0.011 kg/s and the radiation intensity of 927 w/m2 were also achieved to be  9.35%, 10.40% and 65.10%, respectively. Based on simulation results considering experiments validations, as the air flow rate increases, the overall energy efficiency increases to the maximal amount of 80%. However, the maximum exergy efficiency value has a local optimal point of 13.46% at a fluid flow rate of 0.024 kg/s. Similarly, with increasing channel heights, the total energy efficiency decreased to 70%, and the maximum exergy efficiency has a local optimal point of 13.64% at channel height of 0.011 m. As an overall achievement, the system has higher energy quality (exergy efficiency) in laminar flow regime and has higher energy efficiency under turbulent flow conditions.
    Keywords: Computational Modeling, Exergy, Energy Analysis, Multichannel System, Laminar, Turbulent Flows, Photovoltaic, Thermal
  • Mehdi Safari *, Jalal Joudaki, Younes Ghadiri Pages 1681-1688
    In this paper, for the first time, a comprehensive experimental study is performed on hydroforming process of metallic bellows. For this purpose, the effects of the main process parameters and their interactions on the characteristics of hydroformed metallic bellows are investigated using Response Surface Methodology (RSM). The selected parameters as input variables are internal pressure, die stroke and die fillet. The measured characteristics of metallic bellows are convolution height and thickness of the top point of bellows congress. A set of experiments are carried out and the convolution height and thickness of the top point of bellows congress are measured. Then a mathematical model is developed according to the second-order linear regression equations to maximize the convolution height and thickness of the top point of bellows congress. The results show that the increase in the convolution height and decrease in the thickness of the top point of bellows congress will occur by increasing the internal pressure and die stroke. Also, the convolution height and thickness of the top point of bellows congress are increased with an increase in the die fillet.
    Keywords: Hydroforming Process, Metallic Bellows, Response Surface Methodology, mathematical model, Multi-Objective Optimization
  • Tohid Adibi *, Omid Adibi, Seyed Esmaeil Razavi Pages 1689-1695
    In this paper, forced and free convection in the cavity is simulated numerically with complex boundary conditions. Temperature changes sinusoidally at the upper and right walls and the temperature of the other walls is kept at zero. The effects of Prandtl and Grashof numbers variations on flow patterns are surveyed. A wide range of materials, e.g. molten metals, gases, water, and coolant liquid are considered. For this purpose, an in-house code is written in FORTRAN-95 within the finite volume framework. For time discretization, the fifth-order Rung-Kutta method is applied. The convective terms are calculated by a novel characteristic-based scheme along with artificial compressibility. The flow is assumed to be incompressible, laminar and two dimensional. It was found that higher Nusselt numbers have affected increasing Grashof numbers. The effect of Gr on Nu at the upper wall is stronger than that of the down wall. However, the effect of Pr on Nu at upper wall is almost equal with that of the down wall.
    Keywords: complex boundary conditions, convection, Grashof number, Numerical method, Nusselt Number, Prandtl number