000			04155nam a22001577a 4500
082			_a621
100			_aSultan, Badar _9124967
245			_aLie Similarity Solutions and Control Parameters for Casson Fluid Flow and Heat Transfer with Slip Velocity and Variable Heat Flux / _cBadar Sultan
264			_aIslamabad : _bSMME- NUST; _c2025.
300			_a107p. _bSoft Copy _c30cm
500			_aThis study examines the heat and mass transfer in a steady Casson fluid over a stretching sheet. It considers the behavior of Casson fluid with and without slip velocity and variable heat flux boundary conditions under the influence of various control parameters. The mathematical model describing continuity, x-momentum, concentration, and energy transfer in the fluid is formulated along with necessary boundary conditions. To simplify the PDEs of this model, a new set of generalized transformations is derived using the Lie similarity method. A general vector field Lie symmetry generator is extended twice and applied to the fluid model and subjected boundary conditions, resulting in the invariance criteria in the form of linear PDEs. This invariance criterion, when applied to PDEs of the fluid model, yields the invariants, which, when applied to the model, reduce the number of independent variables, turning the complex set of PDEs into simpler ODEs while retaining the key physical features of the flow. These transformations, while satisfying the continuity equation, further reduce one dependent variable, decreasing the complexity of the system even further. This system of ODEs is then solved using the homotopy perturbation method. It is a semi-analytical technique that combines homotopy and perturbation methods to handle nonlinear problems. A higher-order perturbation series, written in the terms of the homotopy parameter and dependent variables is inserted in the system, which, during integration, helps refine the solution. This resulting system is then integrated with modified set of initial conditions having arbitrary constants. The equations resulting from integration, when subjected to final conditions, evaluate these arbitrary constant, which convert the boundary value problem into an initial values problem, which is then solved to get the solution of model. Different boundary condition sets are imposed on the considered flow model: one with slip velocity and variable heat flux, and the other without these conditions. The response of the velocity and temperature towards these conditions is observed and it is reported that for boundary conditions without slip velocity and variable heat flux, velocity increases with permeability and decreases with Casson fluid and magnetic field parameters; xix temperature increases with permeability, Prandtl number, radiation parameter and ratio of Lie control parameters and decreases with Casson fluid and magnetic field parameters; and concentration increases with permeability, Casson fluid parameter, ratio of Lie control parameters, and decreases with magnetic field parameter and Schmidt number. For slip velocity and variable heat flux boundary conditions, velocity increases with permeability and decreases with Casson fluid, slip velocity and magnetic field parameters; temperature decreases with permeability, Prandtl number, radiation parameter and ratio of Lie control parameters and increases with Casson fluid, slip velocity, heat flux and magnetic field parameters; and concentration increases with permeability, Schmidt number, ratio of Lie control parameters, and decreases with magnetic field, slip velocity and Casson fluid parameters. The use of Lie symmetry transformations and homotopy perturbation method proves to be a practical approach for solving complex fluid problems modeled using nonlinear PDEs, offering valuable insights for optimizing industrial processes like polymer extrusion, metal coating, and thermal management.
650			_aMS Mechanical Engineering
700			_aSupervisor: Dr. Muhammad Safdar _9119644
856			_uhttp://10.250.8.41:8080/xmlui/handle/123456789/54588
942			_2ddc _cTHE
999			_c614594 _d614594