Dissertations/Theses - Department of Mathematics
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Item Natural convective heat transfer of nanofluid inside a prismatic enclosure under the influence of inclined magnetic field(Department of Mathematics, BUET, 2024-11-24) Baby Naznin; Parveen, Dr. NazmaIn this thesis, the fundamental concepts of nanofluids and literature reviews have been discussed, and two-dimensional natural convection flow and heat transfer inside the prismatic enclosure charged by nanofluid with the presence of the inclined magnetic field has been investigated numerically. Copper- ethylene glycol nanofluid has been taken as default nanofluid. The top two walls are cold Tc while the bottom wall is heated Th (Tc < Th). Moreover, thermal boundary condition are employed along the bottom diameter. The non-linear governing equations with boundary conditions have been transformed into dimensionless forms using a set of non-dimensional variables. The highly powerful partial differential equations solver finite element technique (FEM) of Galerkin weighted residual type has been employed for the numerical simulations in the present problem. The outcomes illustrate an excellent agreement with previously published research. The different physical model parameters such as Hartmann number, Rayleigh number, Volume fraction of nanoparticle and different angles have been investigated using streamline contours, isothermal lines, and heat transfer in terms of average Nusselt number and an inclined magnetic field are applied at an angle (α) with horizontal direction. The implications of the Rayleigh number (103 ≤ Ra ≤ 106), Prandtl number of base fluid, Ethylene Glycol (210.5), Hartmann number (0 ≤ Ha ≤ 50), and the magnetic field inclination angle (0 ≤ α ≤ 2/3π) are visualized by the streamlines, isotherms and the heatlines. The outcomes the present study may be a useful guide for experiments and research on natural convection flow of nanofluid in a prismatic enclosure to control the flow and heat transfer. The mentioned parameters have significant effects on flow and heat transfer. Moreover, inclined magnetic field play a key role on flow field. The results indicate that the mentioned parameters strongly affect the flow phenomenon and temperature field inside the cavity. By suitable combination of parameters heat transfer can be maximized. Comparisons with previously published work are performed and the results are found to be in excellent agreement.Item Bifurcation analysis of multi-control strategy- an epidemiological approach(Department of Mathematics, BUET, 2024-10-06) Ali Ahmad; Manirul Alam Sarker, Dr. Md.For a long time, serious public health concerns have been related to the COVID-19 outbreak caused by SARS-CoV-2. Mathematical models are useful in examining the dynamics of the disease transmission, prediction and control when a suitable drug or vaccine is unavailable. In this study, vaccination and quarantine strategies with mask efficiency, a susceptible, vaccinated, exposed, infected, quarantined and recovered (SVEIQR) compartmental model for COVID-19 is presented. Qualitative properties for the proposed model, such as positivity and boundedness of solutions, existence and uniqueness of solutions and analysis of equilibria will be performed. The control reproduction number is calculated using the next-generation matrix method. Local stability for both disease-free equilibrium (DFE) and disease-endemic equilibrium (DEE) will be tested. With Lyapunov's direct method, the global stability of the model is established. Explicit conditions are obtained to classify different bifurcations, including saddle-node bifurcation, transcritical bifurcation, pitch-fork bifurcation, forward and backward bifurcation. The forward bifurcation phenomenon in the model is demonstrated when the control reproduction number is greater than one. It is also noticed that under the perfect vaccine efficacy, the model exhibits the transcritical bifurcation phenomenon. However, the proposed model will not exhibit the saddle-node and pitch-fork bifurcation. Furthermore, it is found that an effective vaccination strategy with proper face mask usage is highly necessary to reduce the burden of diseases instead of a quarantine strategy.Item Exploring the eco-evolutionary dynamics of cyclic dominance in rock-paper-scissors strategies within pairwise dilemma games(Department of Mathematics, BUET, 2024-06) Fahimur Rahman Shuvo, Md.; Ariful Kabir, Dr. K MCooperation, selfishness, and dilemma are prevalent in diverse contexts, spanning from biological systems to human societies. Gaining insight into the mechanisms that facilitate and sustain cooperation is essential for effectively tackling global challenges such as climate change, resource depletion, and epidemics. This study presents a new ecological-evolutionary game theory model called the Pairwise Loner Game (PLG). The model combines the Optional Prisoner's Dilemma (OPD) and Rock-Paper-Scissors (RPS) games by incorporating an environmental feedback variable. The study alters the payoff matrices of the OPD and RPS games to guarantee compatibility and generates a comprehensive PLG payoff matrix that includes the environmental state. The replicator dynamics that govern the changes in strategy frequencies and the differential equation that describes the dynamics of the environment are established. Numerical simulations and analyses demonstrate that the environmental influence function is pivotal in determining environmental tipping points. This function models how the environment responds to the frequencies of different strategies, which in turn affects the availability of resources and the overall stability of the system. The simulations reveal that minor changes in the environmental influence function can lead to significant shifts in tipping points, highlighting the sensitivity of the system to environmental feedback. Additionally, the presence of all three strategies—cooperators, defectors, and loners—is significant for promoting a stable and sustainable environment. Cooperators contribute to resource replenishment, defectors exploit resources, and loners abstain from interaction, creating a dynamic balance that prevents the dominance of any single strategy and supports the long-term sustainability of the environment. This intricate interplay underscores the importance of maintaining diversity in strategies to enhance the resilience of ecosystems and social systems against external shocks and internal fluctuations.Item Dynamic optimization technique to reduce the health complexity of covid-19 Co-infection with severe diseases(Department of Mathematics, BUET, 2025-01-19) Abdul Hye, Md.; Forhad Uddin, Dr. MohammedThis research presents a comprehensive study of the transmission dynamics and control strategies for co-infections involving COVID-19 and other significant health conditions, using advanced mathematical modeling. Existing research on COVID- 19 transmission has primarily focused on single-disease models and standard com- partmental frameworks, leaving critical gaps in understanding how co-infections evolve and how best to manage them.To address this shortfall, the thesis investi- gates COVID-19 co-infections with severe diseases such as dengue, diabetes, kidney disease, and lung cancer, introducing four distinct yet interrelated models. These models extend traditional SIR-based approaches by integrating Pontryagin’s Max- imum Principle to derive optimal control measures, incorporating real-world data, and adopting a hybrid Bayesian–least squares and root mean square error parame- ter estimation technique for rigorous calibration. Such methodological innovations tackle recognized research gaps, including the scarcity of analytical and numerical studies on the interplay between COVID-19 and other diseases, the limited ex- ploration of vaccination and targeted treatments in dual-disease contexts, and the underutilization of advanced optimization methods in epidemiological models.By analyzing basic reproduction numbers, equilibrium points, and stability conditions for each co-infection, the thesis demonstrates that comprehensive interventions— such as public health education, specialized treatment protocols, early screening, targeted chemotherapy, and vaccination—significantly reduce infection rates. The findings underscore that implementing optimal control measures significantly re- duces co-infected cases, supporting strategic interventions to mitigate COVID-19 and dengue’s impact. Results show that vaccination substantially lowers the inci- dence of COVID-19 and its co-infections with diabetes. The model offers crucial insights into the role of vaccination in mitigating disease spread among diabetic populations and lays the groundwork for developing targeted disease control strate- gies. Furthermore, the findings demonstrate that applying these controls collectively can significantly reduce co-infection rates, underscoring the necessity of integrated healthcare solutions.Moreover, the pioneering model examining the intersection of COVID-19 and lung cancer offers an innovative perspective on how co-infections exacerbate disease burdens, emphasizing that combined strategies can guide popu- lations toward a disease-free equilibrium. Overall, this research not only enhances the theoretical understanding of multi-disease dynamics but also provides action- able insights for policymakers and healthcare professionals, illustrating that strate- gic, data-driven interventions can substantially mitigate the global impact of the COVID-19 pandemic and reduce the risks posed by concurrent illnesses. Finally, this study provides a robust mathematical foundation for understanding and controlling the dynamics of COVID-19 co-infections with severe disease. The insights and strategies developed herein aim to inform public health policies and optimize intervention approaches, contributing to the global effort to mitigate the impact of the COVID-19 pandemic.Item Predicting age-specific female population of Bangladesh in 2026 using the leslie matrix model(Department of Mathematics, BUET, 2024-02-17) Nurain Arju; Farid Uddin Ahmed, Dr. KhandkerBangladesh is one of the most densely populated countries in the world. According to the preliminary census report of Bangladesh Census and Household Census 2022, at the period of the census in 2022 population of Bangladesh in total is 16,51,58,616. Among them, the total number of females and males is 8,33,47,206 and 8,17,12,824, respectively. As a country’s equilibrium in environment, economics, and even administration is highly influenced by its population, these demographic data are essential for a well-regulated impact. Population projection aids in obtaining a country’s desired population for its overall prosperity. A widely used model to project the population is the Leslie matrix model. In this work, by using female survival and birth rates, the Leslie matrix model is applied to predict the age-specific female population and population growth of Bangladesh in 2026. The eigenvalues of the Leslie matrix are used to calculate the female population growth rate, where the principal eigenvalue is taken as the desired growth rate and the eigenvector is used to obtain the number of age-specific female populations. According to this research, the female population of Bangladesh will increase with a growth rate of 1.22 (approximately).Item Prediction of double diffusive mixed convection in a partially heated and concentrated polygonal enclosure using artificial neural network and hybrid nanofluid(Department of Mathematics, BUET, 2025-04-23) Al-Amin, Md.; Mustafizur Rahman, Dr. Md.The objective of the present study is to perform a numerical analysis of double-diffusive mixed convection within a polygonal cavity subjected to lid-driven motion. The cavity, partially heated and concentrated, is filled with a hybrid nanofluid composed of Al2O3 (50%) and Cu (50%) nanoparticles suspended in water. The lower middle portion of the cavity is heated, while the upper horizontal boundaries are maintained at a low temperature. The upper left wall moves at a constant velocity in the positive direction, whereas the other walls are thermally insulated. The physical problem is mathematically represented by a set of governing equations along with appropriate boundary conditions. Using a class of suitable transformations, the governing equations and boundary conditions are converted into a non-dimensional form, which are then solved using a finite element-based Galerkin weighted residual method. An artificial neural network (ANN) model is also developed using simulation data obtained from the numerical solution to predict different performance parameters within the present framework. The study investigates the effects of dimensionless parameters such as Richardson number (Ri), Reynolds number (Re), Lewis number (Le), Buoyancy ratio (Br), and nanoparticle volume fraction (ϕ), with a constant Prandtl number (Pr = 6.8377). The results are presented in terms of flow patterns, temperature distributions, solute distributions, average Nusselt number, and average Sherwood number. It is observed that the average Nusselt number increases with increasing Ri, Re, Br, and ϕ, but decreases with increasing Le. Additionally, all parameters show an upward trend in the average mass transfer rate. Specifically, the average heat transfer rate increases by 37.42% when Ri increases from 0.01 to 10, and decreases by 11.25% when Le increases from 0 to 5. Using the simulation data, an innovative ANN model is developed for accurate prediction. For training and validation data, the model predicts the average Nusselt number with 99.57% accuracy and the average Sherwood number with 99.63% accuracy. For test data, the model predicts the average Nusselt number with 99.34% accuracy and the average Sherwood number with 99.49% accuracy. Therefore, the proposed ANN model accurately predicts the responses for the current framework.Item Study on thermal performance of windows in Bangladesh(Department of Mathematics, BUET, 2025-03-04) Trisha Debnath; Abdul Hakim Khan, Dr. Md.In this study, the thermal performance of window structures is analyzed using two- dimensional simulation. The primary objective is to determine the optimal combination of frame materials and glass panes for enhancing thermal efficiency in buildings across Bangladesh. The analysis covers temperature variations for both winter and summer seasons, with thermal conductance (L2D), frame thermal transmittance (Uf), and surface temperatures of individual window components calculated using the Finite Element Method. Additionally, a three-dimensional simulation is performed to determine time- dependent heat flux through the wooden window structure, providing a more comprehensive understanding of heat transfer behavior. Five frame materials: aluminum, PVC, aluminum-polyamide, PVC-polyamide, and wood are evaluated for single glass pane and double glass pane windows. The findings indicate that while wood provides excellent insulation for certain parts of windows, its widespread use could pose significant environmental risks due to the limited availability of wood resources in Bangladesh. Alternatives such as PVC and PVC-polyamide not only offer comparable or superior thermal performance but also represent a more sustainable choice. Double-pane windows offer significantly better insulation than single-pane windows, with improvements in thermal performance ranging from approximately 8% to 68% in L2D, and from 23% to 91% in Uf, depending on the material and part of the window. The significance of implementing these materials to address the dual issues of resource sustainability and energy efficiency in developing nations such as Bangladesh is emphasized in this study. The findings can be applied to real-world construction projects and inform policymaking to promote sustainable building practices, ensuring both thermal comfort and environmental conservation.Item Three-dimensional study of bio-heat transfer in human skin due to flash fire(Department of Mathematics, BUET, 2024-06-29) Arobi, Thonoya; Parvin, Dr. SalmaBio-heat transfer indicates the transfer of heat between biological organisms. It has become quite attractive to people in different professions due to widespread application in different fields. Analyzing bio-heat transfer to human skin in various burning conditions can provide effective treatment for burn injuries. For a long time, many researchers have been researching to determine the proper temperature of burn injuries. By analyzing the exact temperature of the burn injury, the impact of the burn injury can be reduced. In this thesis, a three-dimensional model of human skin consisting of epidermis, dermis, subcutaneous layers are considered. The physical problems are represented mathematically by different sets of governing equations along with the corresponding boundary conditions. To analyze the effect of burn injury on human skin Penne’s unsteady bio- heat equation is considered as a governing equation and to calculate the burn intensity on skin Henrique’s burn integral equation can be used which relates the temperature with burn intensity. Flash fire boundary condition applied for a short time (10 seconds) and then zero flux condition applied for the cooling period (50 seconds) to solve the governing equation Finite Element method (FEM) is used. The effects of different heat fluxes, different thermal conductivities and specific heats of different skin layers are analyzed. Time to 1st degree burn, 2nd degree and 3rd degree burns are predicted for different heat fluxes. The results can be useful for analyzing burn injuries caused by flash fire and to make protective clothing.Item Magnetohydrodynamic Effect on Rayleigh-Benard convection In a Rectangular Porous Enclosure with Sinusoidal Wall Temperature(Department of Mathematics, BUET, 2022-11-15) Biswas, Anita; Rahman, Dr. Md. MustafizurA numerical study of the magnetohydrodynamic (MHD) effect on the Rayleigh-Benard convection in a rectangular porous enclosure has been investigated. For the fluid flow and heat transfer the Darcy’s law and the energy equation are considered as the governing equations. For the boundary conditions of enclosure, the bottom wall is heated with sinusoidal variation and the top wall is cold while the vertical walls are adiabatic. The governing equations are initially transformed into non-dimensional form using appropriate transformations. The non-dimensional governing equations along with boundary conditions are solved numerically, employing the finite difference method, using the Successive Over-Relaxation (SOR) scheme for the Darcy’s law and the energy equation is solved by Alternative Direction Implicit (ADI) scheme. The in-house FORTAN code is used in this study. The Rayleigh number (Ra), Hartmann number (Ha) and the angle of inclination ( ) are the pertinent parameters of this study. The numerical results are presented in terms of the streamlines, isotherms, velocity and temperature distribution as well as the variation of the local rate of heat transfer in terms of the local Nusselt number at the heated wall. Finally, the average Nusselt number has been shown against Rayleigh number (Ra), Hartmann number (Ha) and the angle of inclination ( ).Item Comparative study of human skin burning intensity due to various incidents using bioheat transfer model(Department of Mathematics, BUET, 2024-09-08) Alamgir Hossain, Md.; Nasrin, Dr. RehenaUnderstanding the intensity of burns resulting from different incidents is crucial for improving medical treatments and preventive measures. This study uses the bioheat transfer model to compare human skin's burning intensity due to hot dish, hot fluid, radiation, and flash fire, employing a bioheat transfer model to analyze and quantify burn intensity. The time‐dependent Pennes’ bioheat transfer equation is used as the governing equation and solved with appropriate boundary conditions using Galerkin's weighted residual scheme built‐in finite element method. The primary objective of this research is to solve the governing partial differential equation (three-dimensional) for the triple-layered human skin utilizing the finite element method (FEM), to analyze the burn effects on human skin from hot dish, hot fluid, radiation, and flash fire and to measure the burning intensity in terms of the degree of burn with the change of different thermal properties of the skin. The Arrhenius equation is used to calculate the damage fraction for the skin burn. The burn intensity in terms of degrees of burn (1st-, 2nd-, and 3rd-degree) is measured using Henrique’s burn integral with different burning conditions, and their corresponding time is graphically shown. Six middle points are chosen from the bottom to the top of the considered physical model, maintaining each 1 mm gap along the height to find the local damage fraction. The numerical results are shown in terms of the volume temperature, slice plot of temperature, and volume plot of damage fraction. Line graph of local damage fraction and line graphs of different burn intensity against temperature and time for the considered four cases are shown. From the numerical results, it is observed that 1st-degree burns occur the fastest among the three; 2nd-degree burns require more time than 1st-degree, but less than 3rd-degree, and 3rd-degree burns require the longest time to occur. Also, the effect of a heating dish in direct contact with the skin is more severe than that of free-flowing hot fluid regarding burn injuries. The results from this analysis will help to understand human skin burns under different burning conditions and the treatment of varying burn injuries. This research also highlights the effectiveness of the bioheat transfer model in predicting burn outcomes, demonstrating its potential as a valuable tool in medical and safety engineering applications.