Competition Problems

Water security is a major priority in the United Arab Emirates, where desalination plays an important role in meeting freshwater demand. Large facilities such as DEWA's Jebel Ali Power and Desalination Complex illustrate the scale of desalination infrastructure in the country [1]. Desalination also produces a concentrated saline stream known as brine. When discharged into the marine environment, brine can increase salinity in the receiving water and may affect marine ecosystems [2].

Consider a simplified coastal region near a UAE desalination facility. Brine from the facility is continuously discharged into this region, where it mixes with the seawater already present. At the same time, seawater from the surrounding Arabian Gulf enters the region while an equivalent amount of mixed water leaves.

The facility is considering increasing its freshwater production to meet growing demand. Increased production, however, would also increase the amount of brine discharged into the receiving water.

Your team has been asked to investigate whether freshwater production can be increased while keeping the salinity of the receiving coastal water within an acceptable environmental limit.

Develop a mathematical model that can be used to investigate the behaviour of the system as production increases. Consider how the receiving water responds over time and determine the operating conditions under which increased freshwater production could be considered environmentally sustainable.

Based on your analysis, provide a recommendation to the facility. Clearly state and justify the assumptions used in developing your model and discuss the limitations of your conclusions.

Temperature control is critical during the transportation of many pharmaceutical products. UAE Ministry of Health and Prevention guidance requires pharmaceutical products to be transported under appropriate temperature and humidity conditions so that their quality is not adversely affected [1]. Some pharmaceutical products require refrigerated storage, commonly within a temperature range of 2°C to 8°C [2].

Consider a temperature-sensitive medical shipment being transported from a distribution facility in Abu Dhabi to a healthcare facility elsewhere in the city. The shipment leaves the distribution facility inside an insulated container at an appropriate initial temperature. The container has no active refrigeration. During transportation, its internal temperature gradually changes as the container is exposed to the much warmer surrounding environment.

Under normal conditions, the journey can be completed while the shipment remains within its required temperature range. On a particularly hot afternoon, however, the delivery vehicle experiences an unexpected delay. The logistics team must decide whether the shipment can safely continue to its destination or whether the increasing temperature creates an unacceptable risk.

Your team has been asked to investigate how long a temperature-sensitive shipment can remain in transit under these conditions before its temperature exceeds the acceptable limit.

Develop a mathematical model that can be used to describe the thermal behaviour of the shipment during transportation. Use your model to investigate how factors such as the initial temperature, surrounding temperature, journey duration and insulation of the container affect the time available for safe delivery.

Based on your analysis, determine when a delayed shipment should be allowed to continue and when it should be returned or replaced. Clearly state and justify the assumptions used in developing your model and discuss the limitations of your conclusions.

Solar energy is an important component of the UAE's transition toward cleaner energy. The country's high levels of solar irradiation make photovoltaic systems particularly attractive, but operating solar panels in a desert environment presents a practical challenge. Dust and sand can accumulate on photovoltaic panels and reduce their energy output [1]. DEWA has identified photovoltaic soiling as an operational concern and has developed monitoring technology to detect dust-related performance losses and improve the timing of cleaning and maintenance [2].

Consider a solar installation operating under UAE desert conditions. Immediately after cleaning, its photovoltaic panels operate close to their expected performance. As time passes, dust gradually accumulates on their surfaces, reducing the amount of solar energy that can be converted into electricity. At the same time, wind and other environmental processes may naturally remove some of the deposited dust.

The facility currently cleans its panels according to a fixed schedule. Cleaning more frequently can reduce energy losses caused by dust, but every cleaning operation requires resources. Waiting longer between cleaning events reduces the frequency of cleaning but allows the panels to operate at reduced performance for a longer period.

Your team has been asked to investigate whether the facility's current cleaning schedule provides an appropriate balance between maintaining solar-energy production and the resources required for cleaning.

Develop a mathematical model that can be used to investigate how dust accumulation and panel performance change over time between cleaning events. Use your model to determine when cleaning should take place and investigate how different environmental conditions could affect that decision.

Based on your analysis, recommend a cleaning strategy for the facility. Clearly state and justify the assumptions used in developing your model and discuss the principal limitations of your conclusions.