Department of Mathematics
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Item Peristaltic flow of a carreau fluid in a channel with different wave forms(Wiley, 2009) Tasawar Hayat; Najma Saleem; Ali, N.This investigation deals with the peristaltic motion of a Carreau fluid in a planar channel by employing long wavelength approximation. Five wave forms are chosen. Explicit solutions of longitudinal velocity and pressure gradient are derived. The pumping and trapping phenomena are properly examined. Comparison is made for the flow characteristics of the various selected wave forms. © 2009Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 26: 519–534, 2010Item A numerical technique for heat equation subject to integral specifications(Science International, 2011) Muhammad Aziz Ur Rehman; M. S. A. TajThis paper deals with numerical method for the approximate solution of one-dimensional heat equation with integral boundary conditions. The integral conditions are approximated by using Simpson’s 1/3 rule while the space derivatives are approximated by third-order finite difference approximations. Then method of lines, semidiscritization approach, is used to transform the model partial differential equation into a system of first-order linear ordinary differential equations whose solution satisfies a recurrence relation involving matrix exponential function. The method developed is L-acceptable, third-order accurate in space and time and do not require the use of complex arithmetic. A parallel algorithm is also developed and implemented on several problems from literature and found to be highly accurate when compared with the exact ones and alternative techniques.Item Isothermal plasma waves properties of the Schwarzschild de-sitter black hole in a veselago medium(Astrophysics Space Science, 2011) M. Sharif; Ifra NoureenIn this paper, we study wave properties of isothermal plasma for the Schwarzschild de-Sitter black hole in a Veselago medium. We use ADM 3 + 1 formalism to formulate general relativistic magnetohydrodynamical (GRMHD) equations for the Schwarzschild de-Sitter spacetime in Rindler coordinates. Further, Fourier analysis of the linearly perturbed GRMHD equations for the rotating (non-magnetized and magnetized) background is taken whose determinant leads to a dispersion relation. We investigate wave properties by using graphical representation of the wave vector, the refractive index, change in refractive index, phase and group velocities. Also, the modes of wave dispersion are explored. The results indicate the existence of the Veselago medium.Item Influence of induced magnetic field and heat transfer on peristaltic transport of a carreau fluid(Elsevier, 2011) Tasawar Hayat; Najma Saleem; S. Asghar; Mohammed Shabab Alhothuali; Adnan AlhomaidanThe effect of an induced magnetic field on peristaltic flow of an incompressible Carreau fluid in an asymmetric channel is analyzed. Perturbation solution to equations under long wavelength approximation is derived in terms of small Weissenberg number. Expressions have been constructed for the stream function, the axial induced magnetic field, the magnetic force function, the current density distribution and the temperature. Trapping phenomenonis examined with respect to emerging parameters of interest.Item Entropy generation in hydrodynamic slip flow over a vertical plate with convective boundary(Springer, 2012) Adnan Saeed Butt; Sufian Munawar; Asif Ali; Ahmer MehmoodThe present article aims to report the effects of hydrodynamic slip on entropy generation in the boundary layer flow over a vertical surface with convective boundary condition. Suitable similarity transformations are used to transform the fundamental equations of hydrodynamic and thermal boundary layer flow into ordinary differential equations. The governing equations are then solved numerically using the shooting method and the velocity and the temperature profiles are obtained for various values of parameters involved in the governing equations. The expressions for the entropy generation number and the Bejan number are presented and the results are discussed graphically and quantitatively for the slip parameter, the local Grashof number, the Prandtl number, the local convective heat transfer parameter, the group parameter and the local Reynolds number. It is observed that due to the presence of slip, entropy production in a thermal system can be controlled and reduced.Item Time-dependent flow and heat transfer over a stretching cylinder(The Physical Society of Republic of China, 2012) Sufian Munawar; Ahmer Mehmood; Asif AliThe unsteady laminar boundary-layer flow and heat transfer of a viscous fluid over a stretching cylinder is discussed in this work. To normalize the governing system of equations a proper set of similarity variables is used. Two types of thermal boundary conditions, prescribed surface temperature (PST) and prescribed heat flux (PHF), are taken into account for thermal analysis. The governing equations are solved using the homotopy analysis method, and the obtained series solution is found to be valid for the entire temporal and spatial domains and for certain ranges of the other physical parameters. The effects of various material parameters on different physical quantities, such as the coefficient of skin friction and the Nusselt number, are illustrated through graphs and tables.Item Suzuki type fixed point theorems for generalized multi-valued mappings on a set endowed with two b-metrics(Elsevier, 2012) Ljubomir C´ iric´; Mujahid Abbas; Miloje Rajovic´; Basit AliIn this paper, we obtained Suzuki type fixed point results for a generalized multi-valued mapping on a set equipped with two b-metrics. As a consequence, existence and uniqueness of solution of functional equation arising in dynamical programming is also derivedItem Fuzzy transitivity and monotonicity of cardinality-based similarity measures(Springer, 2012) S. Ashraf; S. M. Husnine; Tabasam RashidThe interrelationship of notions is presented in fuzzy transitivity and monotonicity of fuzzy similarity measures. It is observed that the axiom of fuzzy transitivity may replace that of monotonicity in the definition of fuzzy similarity measures.Item Thermal analysis of the flow over an oscillatory stretching cylinder(IOP Publishing, 2012) Sufian Munawar; Asif Ali; Ahmer MehmoodAn investigation has been conducted on the convective heat transfer and the entropy production attributable to the presence of an infinitely long cylinder in a viscous fluid exhibiting oscillatory motion. The heat transfer analysis is carried out by assuming that the surface of the cylinder is isothermal. The entropy generation is caused by heat transfer attributable to the finite temperature difference MT and viscous effects produced in the fluid. The number of independent variables in the governing equations is reduced by using a proper set of similarity variables. To obtain the solution of the nonlinear partial differential equation, we use a well-known finite difference scheme by transforming the semi-infinite domain to a finite domain. The numerical results have been analyzed by means of a comprehensive parametric study. It is observed that the entropy production intensifies in the presence of the oscillatory motion of the cylinder.Item Fusion higher -order parallel splitting methods for parabolic partial differential equations(2012) Muhammad Aziz Ur Rehman; S. A Mardan; M. S. A Taj; A Bhatti. A.A family of numerical methods, based upon a rational approximation to the matrix exponential function, was developed for solving parabolic partial differential equations. These methods were partially sixth-order precise in space and time, due to combination of sixth-order finite approximations and fifth-order pde’s approximations. These methods do not involve the use of complex computation. In these methods second-order spatial derivates were approximated by sixth-order finite difference approximations. Parallel algorithms were developed and tested on the one, two and three-dimensional heat equations, with constant coefficients, subject to homogeneous boundary conditions and time dependent boundary conditions. It was observed that the results obtained through these methods were highly accurate and can be easily coded on serial or parallel computers.Item On fuzzy ideals in rings and anti-homomorphism(International Mathematical Forum, 2012) Tariq Shah; Saeed, MuhammadWe investigate anti- homomorphic images and pre images of semiprime, strongly primary, irreducible and strongly irreducible fuzzy ideals of a ring. We also prove that: For a surjective anti-homomorphism f : R → R/, if every fuzzy ideal of R is f-invariant and has a fuzzy primary (respectively, strongly primary) decomposition in R, then every fuzzy ideal of R/ has a fuzzy primary (respectively, strongly primary) decompsition in R/.Item Factorization properties and chain conditions on ideals: A linkage(2012) Saeed, Muhammad; Tariq Shah; Inayatur-Rehman; Waheed Ahmad KhanThe purpose of this study is to find relationship among the various domains. In particular, the domains possessing factorization properties and the domains which hold different chain conditions on ideals.Item Common fixed point theorem for a hybrid pair of mappings in hausdorff fuzzy metric spaces(University of Management and Technology, 2012) M Abbas; Basit Ali; A Amini-HarandiIn this paper, we prove a coupled fixed point theorem for a multivalued fuzzy contraction mapping in complete Hausdorff fuzzy metric spaces. As an application of the first theorem, a coupled coincidence and coupled common fixed point theorem has been proved for a hybrid pair of multivalued and single-valued mappings. It is worth mentioning that to find coupled coincidence points, we do not employ the condition of continuity of any mapping involved therein. Also, coupled coincidence points are obtained without exploiting any type of commutativity condition. Our results extend, improve, and unify some well-known results in the literature.Item Fourth-order method for the solution of diffusion equation subject to the specification of energy(Society of Physics and Natural History of Geneva, 2012) Muhammad Aziz Ur Rehman; M. S. A. Taj; Muhammad Saeed; I. RehmanA fourth-order numerical technique is developed for the solution of the diffusion equation ( ut =uxx + s x, t),0 < x < X,0 < t £ T, subject to u(x,0) = f (x),0 < x < X,u(1, t) = g(t),0 < t £ T and the specification of energy 0 ( , ) ( ), 0 , 0 b u x t dx = M t < b < X < t £ T .Item Unsteady flow and heat transfer in a composite porous annulus with time-dependent injection(VERLAG Z NATURFORSCH, 2012) Muhammad Nasir; Sufian Munawar; Ahmer Mehmood; Asif AliIn the present study, we deal with the momentum and heat transfer analysis in a horizontal annulus of a composite porous medium. The Darcy–Brinkman model is used to develop the governing equations for the flow and heat transfer phenomenon. The annulus injects the time dependent oscillatory velocity normal to its surface. Both the regions of the flow have their own viscosities, and the heat transfer analysis is carried out by retaining viscous dissipation. The governing equations for flow and heat transfer are solved analytically using a perturbation series for solutions in both regions of the annulus. A brief parametric analysis is performed for the velocity and the temperature profiles through graphs.Item Effects of induced magnetic field and slip condition on peristaltic transport with heat and mass transfer in a non-uniform channel(Academic Journals, 2012) Najma Saleem; A. Hayat; A. AlsaediWe study the effects of induced magnetic field and slip on the peristaltic flow of Jeffrey fluid in a non-uniform channel. Flow analysis is discussed in the presence of heat and mass transfer. Main emphasis is given to the study of stream function, the longitudinal pressure gradient, the magnetic force function, the axial induced magnetic field, the current density, the temperature and concentration. Numerical integration is carried out for pressure rise per wavelength. The flow quantities of interest are discussed by graphical illustrations.Item Numerical simulation of sea urchin’s morphogenesis during its structural development at early stage by using PDE methods(2012-05) Noshad Jamil, Raja; Aziz ur Rehman, MuhammadIn this paper, we study a methodology for numerical simulation of sea urchin shapes in biological organism’s development particularly at the blastula phase, consisting of a hollow, two-layered sac of ectoderm and endoderm surrounding an archenteron that communicates with the exterior through the blastopore with the help of newly developed “PDE Methods”. The geometric modeling of the sea urchin shapes are under taken by means of surfaces generated as Partial Differential Equations (PDEs). We merge PDE based geometric modeling technique with numerical optimization in order to study the stable shapes adopted by the sea urchin during its blastula phase. Thus, by using the PDE method we produce a generic model which is then capably parameterized. Using this parameterization to set up a numerical optimization process which enables us to predict a series of sea urchin shapes at the early stage subject to given surface area and volume at that time.Item On a class of controlled functional differential inclusions(2013) Sadia Arshad; Lupulescu, VasileThe aim of this paper is to establish the existence of solutions and some properties of solutions set for a class of functional differential equations with causal operator under assumption that the equation satisfies the Carathéodory type condition. Also, an application for an optimal control problem is given.Item Fixed point of suzuki-zamfirescu hybrid contractions in partial metric spaces via partial hausdorff metric(University of Management and Technology, 2013) M Abbas; Basit AliCoincidence point theorems for hybrid pairs of single-valued and multi-valued mappings on an arbitrary non-empty set with values in a partial metric space using a partial Hausdorff metric have been proved. As an application of our main result, the existence and uniqueness of common and bounded solutions of functional equations arising in dynamic programming are discussed.Item Time-dependent stagnation-point flow over rotating disk impinging oncoming flow(Shanghai University and Springer-Verlag, 2013) Sufian Munawar; Ahmer Mehmood; Asif AliThe unsteady stagnation point flow of an incompressible viscous fluid over a rotating disk is investigated numerically in the present study. The disk impinges the oncoming flow with a time-dependent axial velocity. The three-dimensional axisymmetric boundary-layer flow is described by the Navier-Stokes equations. The governing equations are solved numerically, and two distinct similarity solution branches are obtained. Both solution branches exhibit different flow patterns. The upper branch solution exists for all values of the impinging parameter and the rotating parameter . However, the lower branch solution breaks down at some moderate values of . The involvement of the rotation at disk allows the similarity solution to be transpired for all the decreasing values of . The results of the velocity profile, the skin friction, and the stream lines are demonstrated through graphs and tables for both solution branches. The results show that the impinging velocity depreciates the forward flow and accelerates the flow in the tangential direction.