A Multigrid Approach for Three-Dimensional Inverse Heat Conduction Problems

A two-step multigrid approach is proposed to solve the inverse heat conduction problem in a 3-D object under laser irradiation. In the first step, the location of the laser center is estimated using a coarse and uniform grid system. In the second step, the front-surface temperature is recovered in good accuracy using a multiple grid system in which fine mesh is used at laser spot center to capture the drastic temperature rise in this region but coarse mesh is employed in the peripheral region to reduce the total number of sensors required. The effectiveness of the two-step approach and the multiple grid system are demonstrated by the illustrative inverse solutions. If the measurement data for the temperature and heat flux on the back surface do not contain random error, the proposed multigrid approach can yield more accurate inverse solutions. When the back-surface measurement data contain random noise, accurate inverse solutions cannot be obtained if both temperature and heat flux are measured on the back surface.

Experimental Investigation of Heat Pipe with Annular Fins under Natural Convection at Different Inclinations

Heat pipe is characterised as superconductor of heat because of its excellent heat removal ability. The operation of several engineering system results in generation of heat. This may cause several overheating problems and lead to failure of the systems. To overcome this problem and to achieve desired rate of heat dissipation, there is need to study the performance of heat pipe with annular fins under free convection at different inclinations. This study demonstrates the effect of different mass flow rate of hot fluid into evaporator section on the condenser side heat transfer coefficient with annular fins under natural convection at different inclinations. In this study annular fins are used for the experimental work having dimensions of length of fin, thickness of fin and spacing of fin as 10 mm, 1 mm and 6 mm, respectively. The main aim of present study is to discover at what inclination angles the maximum heat transfer coefficient shall be achieved. The heat transfer coefficient on the external surface of heat pipe condenser section is determined by experimental method and then predicted by empirical correlations. The results obtained from experimental and Churchill and Chu relation for laminar are in fair agreement with not more than 22% deviation. It is elucidated the maximum heat transfer coefficient of 31.2 W/(m2-K) at 25˚ tilt angle and minimal condenser heat transfer coefficient of 26.4 W/(m2-K) is seen at 45˚ tilt angle and 200 ml/min mass flow rate. Inclination angle also affects the thermal performance of heat pipe. Beyond 25o inclination, heat transport rate starts to decrease.

Improving the Optoacoustic Signal by Monitoring the Changes of Coupling Medium

In this paper, we discussed the coupling medium in the optoacoustic imaging. The coupling medium is placed between the scanned object and the ultrasound transducers. Water with varying temperature was used as the coupling medium. The water temperature is gradually varied between 25 to 40 degrees. This heating process is taken with care in order to avoid the bubble formation. Rise in the photoacoustic signal is noted through an unfocused transducer with frequency of 2.25 MHz as the temperature increases. The temperature rise is monitored using a NTC thermistor and the values in degrees are calculated using an embedded evaluation kit. Also the temperature is transmitted to PC through a serial communication. All these processes are synchronized using a trigger signal from the laser source.

Design and Fabrication of a Parabolic Trough Collector and Experimental Investigation of Wind Impact on Direct Steam Production in Tehran

The present paper aims to the techno-economic feasibility of enhancing low-cost parabolic trough collectors in the light of developing the use of solar energy in under-developed regions where expensive high-tech solar devices cannot be afforded. Moreover, the collector is aimed to produce steam so that its performance is based on heat which can be discovered. In this regard, the manufacturing process and the detailed design models in Solidworks software are elaborated. Furthermore, the colletor’s material is chosen in a way to minimize the costs. Finally, to assess the performance of the built collector, it is installed in the site of Shahid Beheshti University, Tehran, and the values of the effective peripheral parameters, such as temperature, wind speed, and most importantly, solar irradiance, are recorded simultaneously in June. According to the results obtained, the manufactured collector with the aperture area of 2 m2 (1×2 m) is capable of producing 350 ml.h-1 steam. Also, the wind influence is comprehensively investigated in this paper. As a case in point, it was measured that as the wind speed maximized to 9.77 km/h, the amount of steam outlet is minimized to 580 ml.

Effect of Filler Metal Diameter on Weld Joint of Carbon Steel SA516 Gr 70 and Filler Metal SFA 5.17 in Submerged Arc Welding SAW

This work describes an investigation on the effect of filler metals diameter to weld joint, and low alloy carbon steel A516 Grade 70 is the base metal. Commercially SA516 Grade70 is frequently used for the manufacturing of pressure vessels, boilers and storage tank, etc. In fabrication industry, the hardness of the weld joint is between the important parameters to check, after heat treatment of the weld. Submerged arc welding (SAW) is used with two filler metal diameters, and this solid wire electrode is used for SAW non-alloy and for fine grain steels (SFA 5.17). The different diameters were selected (Ø = 2.4 mm and Ø = 4 mm) to weld two specimens. Both specimens were subjected to the same preparation conditions, heat treatment, macrograph, metallurgy micrograph, and micro-hardness test. Samples show almost similar structure with highest hardness. It is important to indicate that the thickness used in the base metal is 22 mm, and all specifications, preparation and controls were according to the ASME section IX. It was observed that two different filler metal diameters performed on two similar specimens demonstrated that the mechanical property (hardness) increases with decreasing diameter. It means that even the heat treatment has the same effect with the same conditions, the filler metal diameter insures a depth weld penetration and better homogenization. Hence, the SAW welding technique mentioned in the present study is favorable to implicate for the industry using the small filler metal diameter.

Fatigue Behavior of Friction Stir Welded EN AW 5754 Aluminum Alloy Using Load Increase Procedure

Friction stir welding (FSW) is an advantageous method in the thermal joining processes, featuring the welding of various dissimilar and similar material combinations, joining temperatures below the melting point which prevents irregularities such as pores and hot cracks as well as high strengths mechanical joints near the base material. The FSW process consists of a rotating tool which is made of a shoulder and a probe. The welding process is based on a rotating tool which plunges in the workpiece under axial pressure. As a result, the material is plasticized by frictional heat which leads to a decrease in the flow stress. During the welding procedure, the material is continuously displaced by the tool, creating a firmly bonded weld seam behind the tool. However, the mechanical properties of the weld seam are affected by the design and geometry of the tool. These include in particular microstructural and surface properties which can favor crack initiation. Following investigation compares the dynamic properties of FSW weld seams with conventional and stationary shoulder geometry based on load increase test (LIT). Compared to classical Woehler tests, it is possible to determine the fatigue strength of the specimens after a short amount of time. The investigations were carried out on a robotized welding setup on 2 mm thick EN AW 5754 aluminum alloy sheets. It was shown that an increased tensile and fatigue strength can be achieved by using the stationary shoulder concept. Furthermore, it could be demonstrated that the LIT is a valid method to describe the fatigue behavior of FSW weld seams.

Design of Identification Based Adaptive Control for Fermentation Process in Bioreactor

The biochemical technology has been developing extremely fast since the middle of the last century. The main reason for such development represents a requirement for large production of high-quality biologically manufactured products such as pharmaceuticals, foods, and beverages. The impact of the biochemical industry on the world economy is enormous. The great importance of this industry also results in intensive development in scientific disciplines relevant to the development of biochemical technology. In addition to developments in the fields of biology and chemistry, which enable to understand complex biochemical processes, development in the field of control theory and applications is also very important. In the paper, the control for the biochemical reactor for the milk fermentation was studied. During the fermentation process, the biophysical quantities must be precisely controlled to obtain the high-quality product. To control these quantities, the bioreactor’s stirring drive and/or heating system can be used. Available commercial biochemical reactors are equipped with open loop or conventional linear closed loop control system. Due to the outstanding parameters variations and the partial nonlinearity of the biochemical process, the results obtained with these control systems are not satisfactory. To improve the fermentation process, the self-tuning adaptive control system was proposed. The use of the self-tuning adaptive control is suggested because the parameters’ variations of the studied biochemical process are very slow in most cases. To determine the linearized mathematical model of the fermentation process, the recursive least square identification method was used. Based on the obtained mathematical model the linear quadratic regulator was tuned. The parameters’ identification and the controller’s synthesis are executed on-line and adapt the controller’s parameters to the fermentation process’ dynamics during the operation. The use of the proposed combination represents the original solution for the control of the milk fermentation process. The purpose of the paper is to contribute to the progress of the control systems for the biochemical reactors. The proposed adaptive control system was tested thoroughly. From the obtained results it is obvious that the proposed adaptive control system assures much better following of the reference signal as a conventional linear control system with fixed control parameters.

Simulation of Concrete Wall Subjected to Airblast by Developing an Elastoplastic Spring Model in Modelica Modelling Language

To meet the civilizations future needs for safe living and low environmental footprint, the engineers designing the complex systems of tomorrow will need efficient ways to model and optimize these systems for their intended purpose. For example, a civil defence shelter and its subsystem components needs to withstand, e.g. airblast and ground shock from decided design level explosion which detonates with a certain distance from the structure. In addition, the complex civil defence shelter needs to have functioning air filter systems to protect from toxic gases and provide clean air, clean water, heat, and electricity needs to also be available through shock and vibration safe fixtures and connections. Similar complex building systems can be found in any concentrated living or office area. In this paper, the authors use a multidomain modelling language called Modelica to model a concrete wall as a single degree of freedom (SDOF) system with elastoplastic properties with the implemented option of plastic hardening. The elastoplastic model was developed and implemented in the open source tool OpenModelica. The simulation model was tested on the case with a transient equivalent reflected pressure time history representing an airblast from 100 kg TNT detonating 15 meters from the wall. The concrete wall is approximately regarded as a concrete strip of 1.0 m width. This load represents a realistic threat on any building in a city like area. The OpenModelica model results were compared with an Excel implementation of a SDOF model with an elastic-plastic spring using simple fixed timestep central difference solver. The structural displacement results agreed very well with each other when it comes to plastic displacement magnitude, elastic oscillation displacement, and response times.

Indigenous Dayak People’s Perceptions of Wildlife Loss and Gain Related to Oil Palm Development

Controversies surrounding the impacts of oil palm plantations have resulted in some heated debates, especially concerning biodiversity loss and indigenous people well-being. The indigenous people of Dayak generally used wildlife to fulfill their daily needs thus were assumed to have experienced negative impacts due to oil palm developments within and surrounding their settlement areas. This study was conducted to identify the characteristics of the Dayak community settled around an oil palm plantation, to determine their perceptions of wildlife loss or gain as the results of the development of oil palm plantations, and to identify the determinant characteristic of the perceptions. The research was conducted on March 2018 in Nanga Tayap and Tajok Kayong Villages, which were located around the oil palm plantation of NTYE of Ketapang, West Kalimantan-Indonesia. Data were collected through in depth-structured interview, using closed and semi-open questionnaires and three-scale Likert statements. Interviews were conducted with 74 respondents using accidental sampling, and categorized into respondents who were dependent on oil palm for their livelihoods and those who were not. Data were analyzed using quantitative statistics method, Likert Scale, Chi-Square Test, Spearman Test, and Mann-Whitney Test. The research found that the indigenous Dayak people were aware of wildlife species loss and gain since the establishment of the plantation. Nevertheless, wildlife loss did not affect their social, economic, and cultural needs since they could find substitutions. It was found that prior to the plantation’s development, the local Dayak communities were already slowly experiencing some livelihood transitions through local village development. The only determinant characteristic of the community that influenced their perceptions of wildlife loss/gain was level of education.

Effect of Zinc Oxide on Characteristics of Active Flux TIG Welds of 1050 Aluminum Plates

In this study, characteristics of ATIG welds using ZnO flux on aluminum was investigated and compared with TIG welds. Autogenously AC-ATIG bead on plate welding was applied on Al1050 plate with a coating of ZnO as the flux. Different levels of welding current and flux layer thickness was considered to study the effect of heat input and flux quantity on ATIG welds and was compared with those of TIG welds. Geometrical investigation of the weld cross sections revealed that penetration depth of the ATIG welds with ZnO flux, was increased up to 2 times in some samples compared to the TIG welds. Optical metallographic and Scanning Electron Microscopy (SEM) observations revealed similar microstructures in TIG and ATIG welds. Composition of the ATIG welds slag was also analyzed using X-ray diffraction. In both TIG and ATIG samples, the lowest values of microhardness were observed in the HAZ.

Conventional and Hybrid Network Energy Systems Optimization for Canadian Community

Local generated and distributed system for thermal and electrical energy is sighted in the near future to reduce transmission losses instead of the centralized system. Distributed Energy Resources (DER) is designed at different sizes (small and medium) and it is incorporated in energy distribution between the hubs. The energy generated from each technology at each hub should meet the local energy demands. Economic and environmental enhancement can be achieved when there are interaction and energy exchange between the hubs. Network energy system and CO2 optimization between different six hubs presented Canadian community level are investigated in this study. Three different scenarios of technology systems are studied to meet both thermal and electrical demand loads for the six hubs. The conventional system is used as the first technology system and a reference case study. The conventional system includes boiler to provide the thermal energy, but the electrical energy is imported from the utility grid. The second technology system includes combined heat and power (CHP) system to meet the thermal demand loads and part of the electrical demand load. The third scenario has integration systems of CHP and Organic Rankine Cycle (ORC) where the thermal waste energy from the CHP system is used by ORC to generate electricity. General Algebraic Modeling System (GAMS) is used to model DER system optimization based on energy economics and CO2 emission analyses. The results are compared with the conventional energy system. The results show that scenarios 2 and 3 provide an annual total cost saving of 21.3% and 32.3 %, respectively compared to the conventional system (scenario 1). Additionally, Scenario 3 (CHP & ORC systems) provides 32.5% saving in CO2 emission compared to conventional system subsequent case 2 (CHP system) with a value of 9.3%.  

The Experimental and Numerical Analysis of the Joining Processes for Air Conditioning Systems

In the paper the results of welding of car’s air-conditioning elements are presented. These systems based on, mainly, the environmental unfriendly refrigerants. Thus, the producers of cars will have to stop using traditional refrigerant and to change it to carbon dioxide (R744). This refrigerant is environmental friendly. However, it should be noted that the air condition system working with R744 refrigerant operates at high temperature (up to 150 °C) and high pressure (up to 130 bar). These two parameters are much higher than for other refrigerants. Thus new materials, design as well as joining technologies are strongly needed for these systems. AISI 304 and 316L steels as well as aluminium alloys 5xxx are ranked among the prospective materials. As a joining process laser welding, plasma welding, electron beam welding as well as high rotary friction welding can be applied. In the study, the metallographic examination based on light microscopy as well as SEM was applied to estimate the quality of welded joints. The analysis of welding was supported by numerical modelling based on Sysweld software. The results indicated that using laser, plasma and electron beam welding, it is possible to obtain proper quality of welds in stainless steel. Moreover, high rotary friction welding allows to guarantee the metallic continuity in the aluminium welded area. The metallographic examination revealed that the grain growth in the heat affected zone (HAZ) in laser and electron beam welded joints were not observed. It is due to low heat input and short welding time. The grain growth and subgrains can be observed at room temperature when the solidification mode is austenitic. This caused low microstructural changes during solidification. The columnar grain structure was found in the weld metal. Meanwhile, the equiaxed grains were detected in the interface. The numerical modelling of laser welding process allowed to estimate the temperature profile in the welded joint as well as predicts the dimensions of welds. The agreement between FEM analysis and experimental data was achieved.  

Poultry Manure and Its Derived Biochar as a Soil Amendment for Newly Reclaimed Sandy Soils under Arid and Semi-Arid Conditions

Sandy soils under arid and semi-arid conditions are characterized by poor physical and biochemical properties such as low water retention, rapid organic matter decomposition, low nutrients use efficiency, and limited crop productivity. Addition of organic amendments is crucial to develop soil properties and consequently enhance nutrients use efficiency and lessen organic carbon decomposition. Two years field experiments were developed to investigate the feasibility of using poultry manure and its derived biochar integrated with different levels of N fertilizer as a soil amendment for newly reclaimed sandy soils in Western Desert of El-Minia Governorate, Egypt. Results of this research revealed that poultry manure and its derived biochar addition induced pronounced effects on soil moisture content at saturation point, field capacity (FC) and consequently available water. Data showed that application of poultry manure (PM) or PM-derived biochar (PMB) in combination with inorganic N levels had caused significant changes on a range of the investigated sandy soil biochemical properties including pH, EC, mineral N, dissolved organic carbon (DOC), dissolved organic N (DON) and quotient DOC/DON. Overall, the impact of PMB on soil physical properties was detected to be superior than the impact of PM, regardless the inorganic N levels. In addition, the obtained results showed that PM and PM application had the capacity to stimulate vigorous growth, nutritional status, production levels of wheat and sorghum, and to increase soil organic matter content and N uptake and recovery compared to control. By contrast, comparing between PM and PMB at different levels of inorganic N, the obtained results showed higher relative increases in both grain and straw yields of wheat in plots treated with PM than in those treated with PMB. The interesting feature of this research is that the biochar derived from PM increased treated sandy soil organic carbon (SOC) 1.75 times more than soil treated with PM itself at the end of cropping seasons albeit double-applied amount of PM. This was attributed to the higher carbon stability of biochar treated sandy soils increasing soil persistence for carbon decomposition in comparison with PM labile carbon. It could be concluded that organic manures applied to sandy soils under arid and semi-arid conditions are subjected to high decomposition and mineralization rates through crop seasons. Biochar derived from organic wastes considers as a source of stable carbon and could be very hopeful choice for substituting easily decomposable organic manures under arid conditions. Therefore, sustainable agriculture and productivity in newly reclaimed sandy soils desire one high rate addition of biochar derived from organic manures instead of frequent addition of such organic amendments.

Reaction Rate of Olive Stone during Combustion in a Bubbling Fluidized Bed

Combustion of biomass is a promising alternative to reduce the high pollutant emission levels associated to the combustion of fossil flues due to the net null emission of CO2 attributed to biomass. However, the biomass selected should also have low contents of nitrogen and sulfur to limit the NOx and SOx emissions derived from its combustion. In this sense, olive stone is an excellent fuel to power combustion reactors with reduced levels of pollutant emissions. In this work, the combustion of olive stone particles is analyzed experimentally in a thermogravimetric analyzer (TGA) and in a bubbling fluidized bed reactor (BFB). The bubbling fluidized bed reactor was installed over a scale, conforming a macro-TGA. In both equipment, the evolution of the mass of the samples was registered as the combustion process progressed. The results show a much faster combustion process in the bubbling fluidized bed reactor compared to the thermogravimetric analyzer measurements, due to the higher heat transfer coefficient and the abrasion of the fuel particles by the bed material in the BFB reactor.

Mixed Convection Heat Transfer of Copper Oxide-Heat Transfer Oil Nanofluid in Vertical Tube

In this paper, experiments were conducted to investigate the heat transfer of Copper Oxide-Heat Transfer Oil (CuO-HTO) nanofluid laminar flow in vertical smooth and microfin tubes as the surface temperature is constant. The effect of adding the nanoparticle to base fluid and Richardson number on the heat transfer enhancement is investigated as Richardson number increases from 0.1 to 0.7. The experimental results demonstrate that the combined forced-natural convection heat transfer rate may be improved significantly with an increment of mass nanoparticle concentration from 0% to 1.5%. In this experiment, a correlation is also proposed to predict the mixed convection heat transfer rate of CuO-HTO nanofluid flow. The maximum deviation of both correlations is less than 14%. Moreover, a correlation is presented to estimate the Nusselt number inside vertical smooth and microfin tubes as Rayleigh number is between 2´105 and 6.8´106 with the maximum deviation of 12%.

A Comparative Study of Single- and Multi-Walled Carbon Nanotube Incorporation to Indium Tin Oxide Electrodes for Solar Cells

Alternative electrode materials for optoelectronic devices have been widely investigated in recent years. Since indium tin oxide (ITO) is the most preferred transparent conductive electrode, producing ITO films by simple and cost-effective solution-based techniques with enhanced optical and electrical properties has great importance. In this study, single- and multi-walled carbon nanotubes (SWCNT and MWCNT) incorporated into the ITO structure to increase electrical conductivity, mechanical strength, and chemical stability. Carbon nanotubes (CNTs) were firstly functionalized by acid treatment (HNO3:H2SO4), and the thermal resistance of CNTs after functionalization was determined by thermogravimetric analysis (TGA). Thin films were then prepared by spin coating technique and characterized by scanning electron microscopy (SEM), X-ray diffraction (XRD), four-point probe measurement system and UV-Vis spectrophotometer. The effects of process parameters were compared for ITO, MWCNT-ITO, and SWCNT-ITO films. Two factors including CNT concentration and annealing temperature were considered. The UV-Vis measurements demonstrated that the transmittance of ITO films was 83.58% at 550 nm, which was decreased depending on the concentration of CNT dopant. On the other hand, both CNT dopants provided an enhancement in the crystalline structure and electrical conductivity. Due to compatible diameter and better dispersibility of SWCNTs in the ITO solution, the best result in terms of electrical conductivity was obtained by SWCNT-ITO films with the 0.1 g/L SWCNT dopant concentration and heat-treatment at 550 °C for 1 hour.

A Study on the Effect of Mg and Ag Additions and Age Hardening Treatment on the Properties of As-Cast Al-Cu-Mg-Ag Alloys

This study focuses on the effect of the addition of magnesium (Mg) and silver (Ag) on the mechanical properties of aluminum based alloys. The alloying elements will be added at different levels using the factorial design of experiments of 22; the two factors are Mg and Ag at two levels of concentration. The superior mechanical properties of the produced Al-Cu-Mg-Ag alloys after aging will be resulted from a unique type of precipitation named as Ω-phase. The formed precipitate enhanced the tensile strength and thermal stability. This paper further investigated the microstructure and mechanical properties of as cast Al–Cu–Mg–Ag alloys after being complete homogenized treatment at 520 °C for 8 hours followed by isothermally age hardening process at 190 °C for different periods of time. The homogenization at 520 °C for 8 hours was selected based on homogenization study at various temperatures and times. The alloys’ microstructures were studied by using optical microscopy (OM). In addition to that, the fracture surface investigation was performed using a scanning electronic microscope (SEM). Studying the microstructure of aged Al-Cu-Mg-Ag alloys reveal that the grains are equiaxed with an average grain size of about 50 µm. A detailed fractography study for fractured surface of the aged alloys exhibited a mixed fracture whereby the random fracture suggested crack propagation along the grain boundaries while the dimples indicated that the fracture was ductile. The present result has shown that alloy 5 has the highest hardness values and the best mechanical behaviors.

Closed Greenhouse Production Systems for Smart Plant Production in Urban Areas

The integration of agricultural production systems into urban areas is a challenge for the coming decades. Because of increasing greenhouse gas emission and rising resource consumption as well as costs in animal husbandry, the dietary habits of people in the 21st century have to focus on herbal foods. Intensive plant cultivation systems in large cities and megacities require a smart coupling of information, material and energy flow with the urban infrastructure in terms of Horticulture 4.0. In recent years, many puzzle pieces have been developed for these closed processes at the Humboldt University. To compile these for an urban plant production, it has to be optimized and networked with urban infrastructure systems. In the field of heat energy production, it was shown that with closed greenhouse technology and patented heat exchange and storage technology energy can be provided for heating and domestic hot water supply in the city. Closed water circuits can be drastically reducing the water requirements of plant production in urban areas. Ion sensitive sensors and new disinfection methods can help keep circulating nutrient solutions in the system for a longer time in urban plant production greenhouses.

Adomian’s Decomposition Method to Generalized Magneto-Thermoelasticity

Due to many applications and problems in the fields of plasma physics, geophysics, and other many topics, the interaction between the strain field and the magnetic field has to be considered. Adomian introduced the decomposition method for solving linear and nonlinear functional equations. This method leads to accurate, computable, approximately convergent solutions of linear and nonlinear partial and ordinary differential equations even the equations with variable coefficients. This paper is dealing with a mathematical model of generalized thermoelasticity of a half-space conducting medium. A magnetic field with constant intensity acts normal to the bounding plane has been assumed. Adomian’s decomposition method has been used to solve the model when the bounding plane is taken to be traction free and thermally loaded by harmonic heating. The numerical results for the temperature increment, the stress, the strain, the displacement, the induced magnetic, and the electric fields have been represented in figures. The magnetic field, the relaxation time, and the angular thermal load have significant effects on all the studied fields.

The Boundary Element Method in Excel for Teaching Vector Calculus and Simulation

This paper discusses the implementation of the boundary element method (BEM) on an Excel spreadsheet and how it can be used in teaching vector calculus and simulation. There are two separate spreadheets, within which Laplace equation is solved by the BEM in two dimensions (LIBEM2) and axisymmetric three dimensions (LBEMA). The main algorithms are implemented in the associated programming language within Excel, Visual Basic for Applications (VBA). The BEM only requires a boundary mesh and hence it is a relatively accessible method. The BEM in the open spreadsheet environment is demonstrated as being useful as an aid to teaching and learning. The application of the BEM implemented on a spreadsheet for educational purposes in introductory vector calculus and simulation is explored. The development of assignment work is discussed, and sample results from student work are given. The spreadsheets were found to be useful tools in developing the students’ understanding of vector calculus and in simulating heat conduction.