Engineering design and mathematical modelling: Concepts and applications

Guest Editors Nnamdi NwuluDepartment of Electrical & Electronic Engineering Science, University of Johannesburg, South Africa & Mammo Muchie 

Engineering design and mathematical modelling are key tools/techniques in the Science, Technology and Innovation spheres. Whilst engineering design is concerned with the creation of functional innovative products and processes, mathematical modelling seeks to utilize mathematical principles and concepts to describe and control real world phenomena. Both of these can be useful tools for spurring and hastening development in developing countries. They are also areas where Africa needs to ‘skill-up’ in order to build her technological base. This special issue of the African Journal of Science, Technology, Innovation and Development (AJSTID) contains 13 original articles that cover relevant research trends in the fields of both engineering design and mathematical modelling. These articles can be broadly classified into status of engineering design in African nations (3 papers) and applications of mathematical modelling in the following areas: emissions modelling (1 paper), education (1 paper), urban city dynamics (2 papers), finance (1 paper) and energy (5 papers).

The article by Hailemichael Teshome Demissie, ‘Current state and trajectory of Design Engineering in Kenya’ explores the state of engineering design in Africa and highlights the present challenges in the country. The author highlights the shortage of engineers in the country and the use of archaic engineering design tools as key challenges that plague the engineering design landscape in Kenya. Lawrence Joseph Kerefu and Juliana Zawadi Machuve in their article ‘Students’ perception of engineering design for competitiveness in Africa: The case of Tanzania, East Africa’ investigate the perception of students regarding the quality of the engineering education they receive in the country’s tertiary institutions and the proportion that explicitly handles engineering design. Empirical evidence obtained points to the need for a review of the curricula in line with the severe engineering challenges of the country. In ‘Barriers hindering biomimicry adoption and application in the construction industry’, Olusegun Oguntona and Clinton Aigbavboa discuss biomimicry which is an engineering design philosophy that studies nature or biological processes and mimics them in the design of engineering systems and products. The approach has found wide application and has the potential to enable sustainability in many industries, but has yet to find widespread deployment in the African context. The authors used the South African construction industry as a case study and argued that four factors or barriers hamper the widespread deployment of biomimicry in the construction industry, namely: information and technology-related barriers, risk and cost-related barriers, knowledge-related barriers and regulation-related barriers. It can also be argued that these factors affect the widespread deployment of engineering design techniques on the African continent.

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There are numerous papers in this special issue that deal with applications of mathematical modelling approaches that can be used to understand, predict and control various phenomena of interest. Solomon O. Giwa, Collins N. Nwaokocha and Abayomi T. Layeni in ‘Inventory of kiln stacks emissions and health risk assessment: Case of a cement industry in Southwest Nigeria’ utilized mathematical modelling techniques to estimate the quantity of emissions from a cement factory in southwest Nigeria. A comparison between the air quality index of the cement plant and the World Health Organization (WHO) standards was also performed. Their results show that the amount of emission from the cement industry is more than the recommended limit and constitutes a health hazard.

In his paper, Ibrahim Niankara focused on the education sector in ‘Modelling the effects of exposure to risk on junior faculty productivity incentives under the academic tenure system’ and deployed concepts from probability theory and economics of risk to model outputs under the academic tenure system. The major premise is that scientific outputs can be modelled like any other form of production; consequently, faculty scientific output can be quantified. However, as publications are requirements for academic staff promotion, it has a corresponding effect on the risks faculty face as publications hold some inbuilt uncertainty. Increasing values of this uncertainty has an effect of reducing faculty research incentives. The author is of the opinion, in view of modelling results, that tenure track rules for junior faculty members should be well thought out and implemented in order to simultaneously maintain faculty productivity and institutional reputation.

Cities are a key component of developing nations and have a significant effect on national and regional economic development. Mathematical modelling tools can be used to understand underlying dynamics of cities which is necessary for effective planning and to mitigate urban poverty. The two papers by O. C. Collins, T. S. Simelane and K. J. Duffy study population dynamics and socioeconomic dynamics in key urban cities on the African continent. Their first paper ‘Analyses of mathematical models for city population dynamics under heterogeneity’ studies the population dynamics in three African cities and investigates the impact of heterogeneity in income and expenditure on cities residents. The results show that income and expenditure can have different but significant effects on the population dynamics of different population groups (students, workers, visitors, business people, and job seekers). In their second paper, ‘Mathematical model showing how socioeconomic dynamics in African cities could widen or reduce inequality’ the authors investigate socioeconomic dynamics in African cities considering income, employment and educational opportunities and their effect on social inequality. They arrive at the conclusion that policymakers should actively pursue synergism between various socioeconomic classes in order to stem the tide of worsening inequality in African cities.

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Mathematical modelling definitely plays an important role in the financial sector. Nyasha Mahonye and Tatenda Zengeni in ‘Exchange rate impact on output and inflation: A historical perspective from Zimbabwe’ investigated the effect of exchange rate fluctuations on real output growth and inflation in Zimbabwe. Using historical data and regression analysis, the author determines that exchange rate fluctuations have an impact in the short and long term on real output growth. It was also discovered that exchange rate fluctuations have no impact on inflation in the short run but have an impact in the long run. Without a doubt, these results have significant policy implications especially for export policy.

Recent trends in the energy sphere have seen increased penetration of renewable energy resources (RES) in the electrical grid. They have also seen the advent of prosumers (electricity end-users who simultaneously produce and consume electricity). Uyikumhe Damisa, Nnamdi Nwulu and Yanxia Sun in ‘A mathematical formulation of the joint economic and emission dispatch problem of a renewable energy-assisted prosumer microgrid’ determine how to optimize operations in a setup involving prosumers with renewables whilst minimizing cost and emissions. The authors opine that incentives have a ripple effect on minimizing emissions in a RES prosumer setup. Another recent trend that has seen increased penetration in modern energy systems is the rise of electric vehicles (EVs). EVs have however found limited penetration in the African continent in spite of their environmental benefits. Kabeya Musasa, Musole Muheme, Nnamdi Nwulu and Mammo Muchie in their article ‘A simplified control scheme for electric vehicle-power grid circuit with DC distribution and battery storage systems’ consider a pure battery EV with a direct current circuit and battery storage system (BSS). The developed control scheme yields an acceptable performance in spite of parameter variations in the EV-circuits and the impact of the BSS charging/discharging process. Observing the DC voltage characteristics indicates no overshoot or ringing whilst the steady-state error is kept to zero.

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Njabulo Kambule, Kowiyou Yessoufou, Nnamdi Nwulu and Charles Mbohwa in ‘Temporal analysis of electricity consumption for prepaid metered low- and high-income households in Soweto, South Africa’ utilized historical data and regression analysis to perform a temporal analysis of prepaid metered electricity consumption in Soweto, South Africa. Both low-income and high-income consumers were analyzed and the key research finding was that electricity consumption had decreased by 48% since the inception of prepaid meters; however, 60% of household income is spent on electricity bills. This has important policy implications as 60% of income spent on electricity connotes energy poverty. The authors call for special measures to protect energy poor households.

In ‘A novel approach for the identification of critical nodes and transmission lines for mitigating voltage instability in power networks’, Akintunde Alayande and Nnamdi Nwulu develop a novel method for determining critical power system components (nodes and lines) in order to maintain a power system stability. Their approach is based on the graph theory approach and has practical applications, especially on the African continent where there are frequent occurrences of blackouts and brown outs.

‘Design, construction and mathematical modelling of the performance of a biogas digester for a family in the Eastern Cape province, South Africa’ by Patrick Mukumba, Golden Makaka, Samposn Mamphweli and Peacemaker Masukume mathematically modelled the expected yield from a 1m3 biogas digester with donkey dung as the substrate. The biogas digester was also constructed, and results obtained from the constructed prototype show a strong agreement with the mathematical model. The designed biogas digester should find many practical uses, especially on the African continent.

Viewed holistically, the papers in this volume seek to unearth important insights about various facets of life in developing countries. Utilizing tools from engineering design and mathematical modelling, they proffer policy recommendations useful in the economic, healthcare and financial sectors. Taken together, they can help lead to an improvement in the lives of people in the developing nations of the world.


We extend our gratitude to the Swedish International Development Agency (SIDA), the African Network for Economics of Learning, Innovation, and Competence Building Systems (AfricaLics), AJSTID’s Chief Editor, Anga Baskaran, and the editorial office for their support towards this special issue. We also thank the reviewers for volunteering their time and submitting their reviews timeously.

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