Department of Mathematics
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Item Heat and Mass Flow of Viscoelastic Maxwell Model Fluid Over Variable Thicker Stretching Sheet(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Qursam Shahzadi; CIIT/SP20-RMT-005/LHR; Dr. Mohsan HassanIn the current thesis, the flow of Non Newtonian fluid over variable thicker surface is investigated. For a Non-Newtonian fluid, the system is formulated by using both upper and lower convected Maxwell model. The mathematical formulation of the problems leads to partial differential equations (PDEs) which are first converted into ordinary differential equations (ODEs) via suitable similarity transformations and then solved numerically through Runge-Kutta method. The results are evaluated in velocity and temperature profiles and discussed in graphical form.Item Study On The Heat And Mass Transport Of Non Newton(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Sajid Ali; FA19-RMT-051; Dr. Mohsan Hassan; LHR TP 7398This study investigates heat and mass transport phenomena in non-Newtonian fluid flow under various physical effects. The analysis focuses on the behavior of complex fluids whose viscosity depends on shear rate, temperature, and concentration gradients. Governing nonlinear partial differential equations describing momentum, energy, and species concentration are formulated for the system. Appropriate similarity transformations are employed to reduce the governing equations, which are then solved using analytical and numerical techniques. The effects of key parameters such as thermal conductivity, diffusion rate, and non-Newtonian fluid characteristics on heat and mass transfer rates are examined in detail. The results highlight significant deviations from Newtonian behavior and provide insights relevant to industrial processes, chemical engineering, and thermal systems involving complex fluids.Item Viscoelastic Maxwell Model Fluid Flow Over Rotating Sheet(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Rameen Aslam Khan; CIIT/FA19-RMT-003/LHR; Dr. Mohsan Hassan; LHR TP 7397The viscoelastic fluids have mechanical properties that are intermediate between ordinary liquid and solids. The present work will be concerned with the rheological modeling of viscoelastic materials through differential method. For the material, Maxwell model is used. This model is used in governing equations of the flow problem. For the flow of viscoelastic fluid, the rotating sheet will be used. The solution of these equations will be obtained by numerical technique. The results are displayed in the velocity and temperature profiles for discussion.Item Non-Newtonian Fluid Flow Over Variable Thicker Surface: A Five Parameters Contained Carreau Model(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Abdul Ghafar; CIIT/FA19-RMT-113/LHR; Dr. Mohsan Hassan; LHR TP 7407In current thesis, the flow of non-Newtonian fluid over variable thicker surface is investigated. For the non-Newtonian fluid, five parameters contained Carreau Model is used. To achieve the goal, thesis is divided into three chapters. One chapter contains the basic definitions and some terminologies. Chapter two contains basic governing equations which are used for flow problem. In the last chapter, the mathematical model is developed by using equations of chapter two. The solution of this model is obtained by RK-method. The results are displayed in form of velocity and temperature profile for discussion.Item Coupled Parallel Fluid Flow in Porous Medium Adjacent to Free Flow Domain(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2019) Ifrah Tehreem; CIIT/SP17-RMT-023/LHR; Dr. Mohsan Hassan; LHR TP 5746Fluid flow through a partially filled porous channel, in which porous layer is considered at center of the channel bounded by free flow regions. Fluid flow over a partially filled porous channel is directed by different types of mathematical model with various kinds of boundary conditions at interface. In chapter 2, we consider the fluid flow through fluid-porous channel in which the flow in free region is governed by Stokes equation and Darcy-Forchheimer model. At interface, we assume the velocity for the free fluid is proportional to the shear rate of the permeable region. In this chapter, we examined the effects of the Darcy number, interfacial velocity slip coefficient and Knudsen number on the velocity distribution. In chapter 3, we consider the same channel in which porous media, but here mathematical model is govern by Stokes equation for free region and Brinkman model for porous region. In addition, at the interface, we use the continuity condition of velocity and shear stress with jump effect to find the fluid flow behavior through the channel. In this case, the effect of different values of Darcy number on the velocity distribution is analyzed and compare with the results of Chapter 2.Item Mathematical Study to Control the Measles Disease Through Social Media Awareness(Library Information Services COMSATS University Lahore Campus, 2024-03-18) Dania Khalil; SP23-RMT-007; Dr. Mohsan Hassan; LHR TP 9580In this study, a mathematical framework is applied to examine how awareness-based preventive strategies affect the patterns measles spread. Qualitative theory is used to investigate the occurrence of equilibrium points and their stability features. In case where the basic reproduction number 0 R 1 , disease-free equilibrium is globally asymptotic. To see the impact of social media awareness, computational simulations are applied to study individuals from different groups: susceptible, exposed, infectious, and recovered from measles. It is found that social media awareness is a useful tool to control measles spread and reduce the number of individuals in the exposed group.Item Study on Boundary Layer Flow of Viscoelastic Fluid under Application of Lower Convected Derivative(Library Information Services COMSATS University Lahore Campus, 2024-03-17) Sana Mehmood; FA22-RMT-030; Dr. Mohsan Hassan; LHR TP 9375Viscoelastic fluids are types of non-Newtonian fluids that show both viscous and elastic behavior under stress. This combination of properties makes them more complex than Newtonian fluids that only show viscous characteristics. These fluids commonly exist in nature and are generated in various industries as well. Some examples of these fluids include polymer solutions, biological fluids, slime, paints, etc. The aim of the research study is to study the complex viscoelastic fluids for different applications. To gain a better understanding of these fluids, the mathematical models of rheological properties is developed and further used in transport equations to see the flow behavior as well as used in various engineering parametersItem Mathematical Model and Stability Analysis on the Dynamics of Malaria Transmission with Social Media Awareness(Library Information Services COMSATS University Lahore Campus, 2024-03-17) Farooq Ahmad; FA22-RMT-016; Dr. Mohsan Hassan; LHR TP 9356In this study, a mathematical framework is put out to examine how awareness-based preventive strategies affect the patterns of the spread of malaria. Qualitative theory has been used to investigate the occurrence of equilibrium points and their stability features, which are some fundamental aspects of the suggested model. In the event where the basic reproduction number R0 < 1, disease-free equilibrium is globally asymptotic. To verify the statistical conclusions, computational simulations have been made available. The least expensive method to manage malaria, according to this research, is through social media awareness efforts.Item Study on Thin Film Mass Flow and Heat Transfer Over an Inclined Plat(Library Information Services COMSATS University Lahore Campus, 2024-03-17) Warda Mushtaq; FA22-RMT-054; Dr. Mohsan Hassan; LHR TP 9349The study investigates the dynamics of thin film flow over an inclined plane, with a focus on the influence of magnetic parameters and instability factors on fluid behavior. By employing numerical solutions to the governing equations using the Runge-Kutta method, the research explores the variations in film thickness, surface velocity, temperature profiles, and wall shear stress under different magnetic conditions. Key findings indicate that increasing the s parameter leads to a decrease in film viscosity and a consistent alteration in film thickness. The results also demonstrate the significant impact of s parameters on the thermal boundary layer, suggesting practical implications for applications in coating technologies and microfluidic devices. Comparative analysis with previous studies validates the consistency and reliability of the obtained resultItem Study on Bioheat in Biological Tissue through Different Mathematical Models(Library Information Services COMSATS University Lahore Campus, 2023-03-13) Muhammad Shakeel; SP22-RMT-006; LHR TP 8714; Dr. Mohsan HassanIn this thesis, we have used the classical Pennes, Single-phase-lag (SPL) and Dual phase-lag (DPL) bio-heat transfer models to explore the temperature distribution at the tumor position in multi-layered skin tissues such as (tumor, fat, dermis, muscle and subcutaneous). We studied the impact of heat transmission, including external heat source, and metabolic heat source, in various layers of skin tissue under these three models and use the boundary conditions different tissue. The problem is solved by finite difference method for predicting and comparing the results of the models.