A Numerical scheme to Solve Boundary Value Problems Involving Singular Perturbation

نستخدم المصفوفات العملياتية لمشتقات وانج-بول متعددة الحدود في هذه الدراسة لحل المعادلات التفاضلية الشاذه المضطربة من الدرجة الثانية (WPSODEs) ذات الشروط الحدية. باستخدام مصفوفة كثيرات حدود وانج-بول، يمكن تحويل مشكلة الاضطراب الرئيسية الشاذ إلى أنظمة معادلات جبرية خطية. كما يمكن الحصول على معاملات الحل التقريبي المطلوبة عن طريق حل نظام المعادلات المذكور. وتم استخدام أسلوب الخطاء المتبقي أيضًا لتحسين الخطأ، كما تمت مقارنة النتائج بالطرق المنشورة في عدد من المقالات العلمية. استُخدِمت العديد من الأمثلة لتوضيح موثوقية وفائدة مصفوفات وانج بول العملياتية. طريقة وانج بول لديها القدرة على تحسين النتائج عن طريق تقليل درجة الخطأ بين الحلول التقريبية والدقيقة. أظهرت سلسلة وانج-بول فائدتها في حل أي نموذج واقعي كمعادلات تفاضلية من الدرجة الأولى أو الثانيةThe Wang-Ball polynomials operational matrices of the derivatives are used in this study to solve singular perturbed second-order differential equations (SPSODEs) with boundary conditions. Using the matrix of Wang-Ball polynomials, the main singular perturbation problem is converted into linear algebraic equation systems. The coefficients of the required approximate solution are obtained from the solution of this system. The residual correction approach was also used to improve an error, and the results were compared to other reported numerical methods. Several examples are used to illustrate both the reliability and usefulness of the Wang-Ball operational matrices. The Wang Ball approach has the ability to improve the outcomes by minimizing the degree of error between approximate and exact solutions. The Wang-Ball series has shown its usefulness in solving any real-life scenario model as first- or second-order differential equations (DEs)

Thermal Analysis of Ventilated Wall Cavities with Spray Evaporative Cooling Systems

For low-rise buildings, it is well known that envelope systems are the main contributors to heating and cooling energy consumption. Over the last decades, there have been significant research efforts to improve the performance of building envelope systems by integrating passive cooling strategies to reduce cooling loads and maintain acceptable indoor thermal comfort. The ventilated wall cavity system is one of these passive-cooling strategies that have received considerable attention recently due to the significant benefits of reducing building thermal loads. In particular, evaporative cooling inside ventilated wall cavities is an attractive passive cooling technique especially in hot and dry climates.Very few research studies have investigated evaporative cooling using spray systems within the ventilated wall cavities. Some reported research studies have suggested that the spray droplet size has a significant impact on the evaporative cooling performance. In this dissertation, a detailed analysis of ventilated wall cavities with spray evaporative cooling systems is carried out. First, a simulation environment has been developed using numerical models of droplet evaporation and droplet dynamics for spray systems. Then, the predictions from spray and ventilated cavity models were validated against experimental measurements and CFD analyses. The validation analyses have shown good agreement for all predicted variables. Moreover, thermal comfort indicators have been modeled using energy balance methods to estimate Predicted Mean Value (PMV) for conditioned buildings and Thermal Sensation Vote (TSV) for naturally ventilated buildings. Mold growth has been accounted for in the developed simulation environment using experimental correlations that consider temperature, humidity, and time in addition to favorable and unfavorable conditions for mold growth. The mold growth model was used as an indicator of mold risk inside the ventilated wall cavity. The developed simulation environment has been used to predict the thermal performance of the ventilated wall cavity system by integrating four modules based on the developed and validated models including indoor thermal comfort, cooling energy savings, mold growth potential, and water use.A simple ON/OFF control algorithm has been developed to control the spray system and three dampers which regulate the amount of water usage and air flow rate. Control sequences have been developed in order to minimize water consumption, prevent mold growth inside the cavity, and eventually to maintain acceptable indoor thermal comfort. Moreover, multi-objective optimization analyses have been performed using the developed simulation environment to identify an optimum control strategy and optimum droplet size depending on both indoor and outdoor conditions. Specifically, four objective functions are considered: cooling energy, indoor comfort, water use, and mold growth index. Near optimum control strategies were provided for conditioned buildings and naturally ventilated buildings. Moreover, a new concept of evaporative cooling spray system has been introduced to generate different droplet sizes according to the changes of the surrounding environment to maintain acceptable indoor thermal comfort.A series of sensitivity analyses have been performed to evaluate the impact of various design variables on the performance of the ventilated cavity wall and on the selection of the optimum control strategy. Overall, the ventilated cavity wall system has been found to be an energy efficient passive cooling system for buildings located in hot and dry climates especially when operated by the near optimal control strategy developed in this dissertation

Evaluation of the Biological Activities of Two Macro-Algae Collected from the Red Sea of Jeddah

Marine algae were used in many biological applications. Two marine algal samples, Halimeda tuna and Dictyota dichotoma, were collected from Obhur region, Jeddah, Saudi Arabia, washed with water, dried and extracted with methanol. The antimicrobial activities were conducted against some pathogenic bacteria. The results showed that the extracts of both Halimeda tuna and Dictyota dichotoma were active against at least one of the tested organisms. The highest antimicrobial activities of the extracts Halimeda tuna and Dictyota dichotoma were against Staphylococcus aureus and Streptococcus pneumonia. On contrast, both Halimeda tuna and Dictyota dichotoma showed weak inhibition against Pseudomonas aeruginosa and Acinetobacter baumannii. Moreover, the mixture of the two algal extracts showed excellent inhibition for all the tested bacteria. In addition, a toxicological experiment was conducted for the two algal extracts using Artemia salina as test organism. No toxicity was found for the two tested methanolic extracts.   Furthermore, moderate antitumor activity was recorded for the two tested algal extracts against two cell lines, MCF-7 (breast cancer) and HepG2 (hepatocellular carcinoma) using in vitro MTT and Neutral Red assays. Also, the chemical analysis of each algal extract was carried out. In conclusion, these algal extracts inhibited some pathogenic microbes and can be used as antimicrobial agents.  In conclusion, the two collected macro- algae showed antibacterial activities specially against Salmonella which contaminate food, thus the powder or the extracts of these two algae can be used safely as food additive

Are Historical Buildings More Adaptive to Minimize the Risks of Airborne Transmission of Viruses and Public Health? A Study of the Hazzazi House in Jeddah (Saudi Arabia)

The coronavirus (COVID-19) pandemic has brought immense challenges to the natural and built environment to develop an antivirus-enabled model for reducing potential risks of spreading the virus at varied scales such as buildings, neighborhoods, and cities. Spatial configurations of structures may hinder or assist the spread of viruses in the built environment. In this study, we have hypothesized that suitable air ventilation in historic buildings may enhance the built environment to combat the spreading of infectious viruses. To provide such quantitative shreds of evidence, we have generated and estimated an integrated model to summarize obtained information by considering natural ventilation, wind speed, inflow and outflow, wind direction, and forecasting the associated risks of airborne disease transmission in a historical building (i.e., the Hazzazi House in particular). Intrinsically, the results have demonstrated that the effectiveness of natural ventilation has directly influenced reducing the risks of transmitting airborne infectious viruses for the selected heritage building in Jeddah (Saudi Arabia). The adopted methods in this research may be useful to understand the potentials of conserving old heritage buildings. Consequently, the results demonstrate that natural air ventilation systems are critical to combat the spread of infectious diseases in the pandemic

Transient Behavior Analysis of the Infiltration Heat Recovery of Exterior Building Walls

This research study investigated the transient behavior of the convection–diffusion model for the infiltration heat recovery (IHR) and the influence of the building envelope heat capacity, along with other factors. A transient numerical model was developed and validated to analyze the IHR under various conditions. The results highlight the role of heat capacity, thermal conductivity, wall thickness, airflow rate, airflow direction, and wall porosity on the temperature distribution and the heat recovery factor within the wall. Higher-heat-capacity walls displayed a delayed temperature rise, while low-thermal-conductivity walls reduced the conduction heat transfer and increased the IHR factor. The impact of heat capacity diminished with very low thermal conductivity walls but became evident for high-thermal-conductivity walls, particularly at higher Peclet numbers. Thicker walls enhanced the heat retention and improved the IHR, with a reduced influence of airflow rate. Higher IHR factors were associated with thicker walls, lower Peclet numbers, and higher heat capacities. The analysis also showed that the wall porosity affected the IHR with less significance than the other factors. Incorporating these findings into building energy modeling tools could improve the prediction accuracy of the thermal behavior of buildings. Accordingly, this study contributes to building physics by understanding IHR dynamics and thermal mass interactions, as well as improving building energy modeling accuracy for performance prediction. Future research can explore the impacts of additional factors on IHR and investigate the effect of IHR on the overall energy consumption of buildings

Impact of Passive Cooling Strategies on Energy Consumption Reduction of Residential Buildings in the Kingdom of Saudi Arabia

In this paper, passive cooling strategies have been investigated to evaluate their effectiveness in reducing cooling thermal loads and air conditioning energy consumption for residential buildings in Kingdom of Saudi Arabia (KSA). Specifically, three passive cooling techniques have been evaluated including: natural ventilation, downdraft evaporative cooling, and earth tube cooling. These passive cooling systems are applied to a prototypical KSA residential villa model with an improved building envelope. The analysis has been carried using detailed simulation tool for several cities representing different climate conditions throughout KSA. It is found that both natural ventilation and evaporative cooling provide a significant reduction in cooling energy for the prototypical villa located in Riyadh. Natural ventilation alone has reduced the cooling energy end-use by 22% and the total villa energy consumption by 10%, while the evaporative cooling system has resulted in 64% savings in cooling energy end-use and 32% in the total villa energy consumption. When applying both passive cooling systems together to the villa, the cooling energy end-use is significantly reduced by about 84.2% and the total villa energy savings by 62.3% relative to the un-insulated basecase residential building model. Moreover, natural ventilation is found to have a high potential in all KSA climates, while evaporative cooling can be suitable only in hot and dry climates such as Riyadh and Tabuk.</jats:p