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Item Exact Analysis of Heat and Mass Transfer Flow of Second Grade fluid with Caputo-Fabrizio Fractional Derivatives(UMT Lahore, 2018) Kinza ArifThe present work deals with the analytic solutions of incompressible second grade fluid with convective boundary conditions. In addition, heat and mass transfer are also considered. The governing equations for temperature, concentration, and velocity field are converted into non-dimensional form and exact solutions are obtained using the Laplace transform method. The coefficients of the rate of heat and mass transfer are also obtained for non-integer and integer order derivatives. From our general solutions, some known results are recovered as limiting cases. At the end, we justify our solutions from the existing literature when Gm=0.Item 4-Total edge mean cordial labeling of some standard classes of graphs(UMT Lahore, 2018-07-27) Hafiz M Tariq MahmoodIn this thesis, we introduce new labeling and called it as k-total edge mean cordial (k-TEMC) labeling of graphs, which is a generalization of edge mean cordial labeling (see [9]). We discussed path graph, ladder graph, comb graph, double comb graph, cycle graph, wheel graph, sun-let graph, helm graph, gear graph and prism graph in the context of k-TEMC labeling for k = 4.Item Hybridization of AHP with GTMA(UMT Lahore, 2018-07-12) Hina TaufeeqThe principle purpose of this thesis is hybridization of analytical hierarchy process (AHP) with graph theory-matrix approach (GTMA). In this proposal, hybridization of AHP is being done in the matter of basic leadership. In this proposal, we are required to choose a PET scan machine for a cancer hospital. There are such a significant number of PET scan machines accessible in the market, and the choice to choose a correct machine more often than not includes various criteria. In this way, with a specific end goal to survive vulnerabilities, hybridization of AHP-GTMA has been made. Since AHP has been an outstanding technique for mining the DM’s psyche and the GTMA approach is utilized for data mining, both of these mining forms are hybridized so as to choose the machine with the best highlights. Further, the hybridization is checked with soft expert set, and the stability of the hybrid method is checked by Satty’s scale.Item Hybridization of soft expert set with AHP in decision making(UMT Lahore, 2018-05-17) Sahrish MahmoodThe principle point of this thesis is hybridization of soft expert set (SES) with analytical hierarchy process (AHP) in decision making. In this dissertation, hybridization of SES is being done in the matter of choice making. There are certain problems in which SES neglects to give one correct choice to be picked. One might say that SES ends up indecisive in some particular cases. A particular issue of choosing a manager is considered where SES is hesitant. In view of this uncertainty, hybridization of SES with the AHP strategy has been created, and the arrangement is accomplished. Additionally, the viability of the result is verified by applying the TOPSIS procedure. In the AHP technique, pairwise comparison becomes long; to adapt to this issue, at first SES lessens choices in the matter of chosen people, and so on. After that, AHP is applied to the reduced number of alternatives, which works effectively. To check the adequacy, results can be confirmed with other standard multi-criteria decision-making (MCDM) techniques. In this thesis, the TOPSIS technique is utilized for verification purposes.Item 3-Total edge mean cordial labeling of some classes of graphs(UMT Lahore, 2018-07-19) Fakhir AslamItem Convective flow in a rectangular region with variable temperature and mass diffusion(UMT Lahore, 2018-10) Tuba AfzalThe convective flow in a rectangular region with changeable temperature and mass dispersion has been presented in the existence of the thermic dispersion. The dimensionless governing partial differential equations on the flow are solved by using the Laplace transform and inverse Laplace transform technique. For the velocity, temperature, and the mass dispersion of the fluid, the exact solutions have been obtained. The numerical results for Nusselt number, Sherwood number, and shear stresses at both plates are presented. These numerical results have been illustrated graphically for the various admissible flow parameters like Grashof number, Prandtl number, Schmidt number, radiation parameter, and time. In the present study, these parameters have great impact on the fluid velocity, temperature field, mass dispersion, shear stresses, and heat flux at the plates. The results of this study might be useful as a mechanism to improve the design of cooling and energy systems.Item Soret effect on convective flow of a non-Newtonian fluid with chemical reaction using Caputo-Fabrizio derivative(UMT Lahore, 2018-10) Hina KhursheedSoret effect on convective flow of a non-Newtonian fluid has been analyzed taking into consideration the chemical reaction together with heat absorption and thermal radiation by means of Caputo-Fabrizio derivative technique. Mathematical modelling of momentum, energy and diffusion equations has been developed in terms of partial differential equations accompanied by some physical conditions. Closed form solution of the governing equations assisted by suitable dimensionless variables has been attained through Laplace transform approach. Additionally, comparison of fractional second grade with fractional Newtonian has been performed for the second grade parameter when α2 → 0 as a limiting case. Graphical illustrations have been constructed through the use of Mathcad software in order to find the numerical solution. Conclusively, flow parameters have been observed to have a significant influence on the flow field.Item Exact solutions of time fractional free convection flows of viscous fluid over an isothermal vertical plate with Caputo and Caputo–Fabrizio derivatives(UMT Lahore, 2018-07) Fizza MirajTime fractional free convection flow for unsteady incompressible Newtonian fluid which is lying above an infinite vertical plate owing to a spontaneous movement of plate also analyze the stable temperature at boundary layer. The previous (Caputo) and new (Caputo–Fabrizio) fractional derivative approach are accustomed to develop a new physical model and draw a comparison between their results. By applying the Laplace transforms techniques to boundary layer equations to get a non-dimensional form of these equations and they are solved analytically. We found exact solutions for temperature and velocity in the form of Wright’s function. For transferring heat rate in both cases are also determined their expressions too. Limiting case results are obtained for the solution of integer order derivatives. By using Mathcad software to drawn numerical computations and see the influence of some physical aspect of material and fractional parameters are accessible. We found the results of Caputo–Fabrizio model are much higher worth than the Caputo model as we have a tendency to redouble the worth of fractional parameter and fractional fluids be apt to super-pose to that of standard fluid.Item Natural convection of a viscous fluid in rectangular channel(UMT Lahore, 2018-10) Neelam Rubab SyedaThe unsteady natural convection of an incompressible viscous fluid in a rectangular channel has been presented. The non-dimensional governing partial differential equations on the flow are solved by using the Laplace transform and inverse Laplace transform technique. The exact solutions are obtained for fluid velocity and temperature field. The numerical results for velocity and temperature field are presented graphically for various appropriate parameters such as Prandtl number and time. The computed values represent the non-dimensional shear stress and rate of heat transfer at different values of parameters for both plates. The study shows that the velocity and temperature field are asymmetric and are affected by Prandtl number. The present study will be useful for design calculation of rectangular plate solar heaters.Item Metric dimension of some pendant convex polytopes and prism combination of convex polytopes(UMT Lahore, 2018) Sadia MalikIn this work, we expand the study of metric dimension by adding pendant edges and prism graph to outer cycle of some convex polytopes determined in [21, 24]. These pendant and prism combination of convex polytopes have surprisingly metric dimension 3.Item New classes of charged polytropes with generalized polytropic equation of state(UMT Lahore, 2018-02-27) Waseem ShahzadIn this thesis, new classes of polytropic models have been developed using generalized polytropic equation of state (GPEoS) in region of spherical symmetry by using isotropic coordinates. The inner fluid configuration is charged anisotropic and models are developed for different values of polytropic index n = 1,2,2by3, and, 1by2. Mass and radii of five stars 4U 1608-52, 4U 1820-30, PSR J1614-2230, PSR J1903-0327 and Vela X-1 have been regained. Stability of model is discussed by using speed of sound technique. It is concluded that all models are well behaved and physically acceptable.Item New models of polytropes with generalized polytropic equation of state(UMT Lahore, 2018-02-27) Muhammad HussaanIn this thesis, three new classes of polytropic models have been developed by using anisotropic inner fluid configuration for spherical symmetry. Generalized polytropic equation of state (GPEoS) has been used in the development of these models for values of polytropic index n = 1, 1/2, 1/3. We regain mass and radius of stars Vela X-1, 4U 1820-30, 4U 1608-52, PSR J1903+0327 and PSR J1614-2230. The values obtained for mass are very close to the observational values. The stability of models is determined by using speed of sound technique. Finally, it is concluded that all models are physically viable and well behaved.Item 4-total mean cordial labeling of some convex polytopes(UMT Lahore, 2018) Nelofar ShamiIn this thesis, we study k-total mean cordial (k-TMC) labeling of graphs (see [2]), which is a generalization of mean cordial labeling (see [14]). We discussed different convex polytopes in the context of k-TMC labeling for k = 4.Item 4-total edge product cordial labeling of some standard classes of graphs(UMT Lahore, 2018) Javeed IqbalOur task in this thesis is focuses on 4-total edge product cordial (4-TEPC) labeling of some standard classes of graphs and the main aim of the study is to discuss path graph, cycle graph, wheel graph, helm graph, banana tree graph, recracker graph, gear graph and tadpole graph in the context of 4-TEPC labeling.Item On topological properties of the line graphs of certain chemical structures(UMT Lahore, 2018) Raheela SohailLet G = (V(G) E(G)) be a simple connected graph, where V(G) is the set of vertices and E(G) is the set of edges. A topological index of a graph is a number related to a graph which is invariant under graph automorphisms. In this thesis, we give theoretical results for some topological indices such as geometric arithmetic index GA(G), fifth geometric–arithmetic index GA₅(G), atom–bond connectivity index ABC(G), fourth atom–bond connectivity index ABC₄(G), Zagreb indices M₁(G), M₂(G), M₃(G), M₁(G), M₂(G), Zagreb coindices M̄₁(G), M̄₂(G), M̄₂(G), Randić index R(G), hyper-Zagreb index HM(G), general sum-connectivity index χ(G) and augmented Zagreb index AZI(G) by considering graph G as a line graph of V-phenylenic nanotube, V-phenylenic nanotorus, linear pentacene and multiple pentacene.