Authors:Rahim Bux Khokhar, Afaque Ahmed Bhutto, Noor Fatima Siddiqui, Fozia Shaikh, Iftikhar Ahmed Bhutto Abstract: This study investigates the behavior of Newtonian fluids in pipes filled with and without porous media under combing and separating flow configurations. Numerical simulations are conducted to analyze the effects of changing flow rates, inertia, and porous media on flow patterns, vortex development, and pressure difference. The aim of this study is to examine the impact of inertia on flow behavior by analyzing the streamline patterns, vortex growth, and intensity at different Reynolds numbers, ranging from Re=1 to Re=5000. PubDate: 2023-06-30 Issue No:Vol. 11 (2023)

Authors:Muhammad Asim Shahzad, Rizwan Ahmed Abstract: This paper examines a discrete predator-prey model's complex dynamics. Using bifurcation and center manifold theory, we study period-doubling and Neimark-Sacker bifurcations at positive fixed points and their direction. Numerical simulations confirm the theoretical conclusions that the model's dynamics rely on Euler method step size. The model's behavior is also affected by the prey population's conservation rate. The model suggests that excessive conservation may reduce predator populations, causing food shortages. Thus, predator-prey dynamics management must account for prey conservation rate PubDate: 2023-06-20 Issue No:Vol. 11 (2023)

Authors:Ibrahim Dayo, Sayed Feroz Shah, Fozia Shaikh, Sanjay Kumar Abstract: In present article, there is studied heat, and the mass transfer characteristics of boundary layer flow of the Maxwell-nanofluid across stretching/shrinking surface along chemical reactions, transverse magnetic field and thermal radiation. Applying similarity transformation, the system of governing nonlinear PDEs are reduced into form of ODEs. The achieved equations are solved with help of bvp4c in Matlab computer software. The impacts of specified parameters include, suction parameter, Deborah number, magnetic parameter, thermophoresis parameter, chemical reaction parameter, Schmidt number, Brownian motion parameter, Prandlt number and thermal slip parameter are examined on velocity, temperature and nanoparticles concentration fields (profiles). Moreover, skin friction, Nusselt number and Sherwood number are achieved at numerous values of applied parameters which are demonstrated through graphs. Some of the key findings show that an increase in suction increases skin friction, Nusselt number and Shewood number along the variation of the stretching/shrinking parameter An increase in thermophoresis, magnetic and Brownian motion parameters increase the temperature fields of Maxwell nanofluid, while Deborah number, Prandtl number, suction parameter and thermal slip parameter decrease it.

Authors:Saeed Ahmed Rajput, Shakeel Ahmed Kamboh, Khuda Bux Amur, Saifullah Memon, Abbas Ali Ghoto Abstract: In this paper the numerical modeling and simulation of 2D shallow water equations is discussed with the non-flat topography. The sets of these equations is solved by means of the Crank-Nicolson finite difference method with constant external body force and Darcy Weisbach equation is used for friction slope parameter. We have obtained the important results that, as soon as we start the time then Height evaluation function has the maximum amplitude wave length which is decreasing when the time increases. The numerical solution algorithm works well and enables to predict the water elevation and velocity at any instance and any location in the domain. PubDate: 2023-06-07 Issue No:Vol. 11 (2023)

Authors:Izhar Ali Amur, Khuda Bux Amur, Muzaffar Bashir Arain, Mohsin Ali Amur, K.N Memon Abstract: The study of the stereo vision problems is most crucial and challenging task in image processing and computer vision. The Stereo Vision problems address the investigation of the correspondence between the two images of same scene (stereo pairs) captured from two different views. Generally, these problems are inverse and ill posed. To deal with such problems the energy-based regularization techniques are considered as an efficient and most successful approaches. The adaptive finite element method is used here as discretization method for the partial differential equation obtained from the optimization of the designed energy functional. Such type of the regularization generally depends on the smoothness parameters, and their suitable choice. The choice of the smoothing parameter in an adaptive way and specifically their choice as a scalar function over the whole computational domain is an interesting idea. In this work, a variational model based on the gradient constancy assumption is proposed, moreover a post optimization method (mesh refinement strategy) is designed which is based on a priori estimate called average absolute disparity error estimate. The post optimization is based on an adaptive intelligent algorithm which is efficient in identifying the less regular regions of the computed disparity image and reduces the value of the parameter to refine the grid. Consequently, the smoothness appears in the solution which is the main goal. PubDate: 2023-06-06 Issue No:Vol. 11 (2023)

Authors:Sanjay Kumar, Asif Ali Shaikh, Hazoor Bux Lanjwani, Sayed Feroz Shah Abstract: In this paper, there is considered incompressible steady two-dimensional laminar MHD boundary layer flow, heat and mass transfer characteristics of micropolar nanofluid across a linearly stretching/shrinking porous surface. The effects of the magnetic, thermal slip, mass slip and heat source sink parameters are also considered. By applyingn appropriate similarity variables, the system of governing partial differential equations associated to micropolar nanofluid flow is transformed into a system of non - linear ordinary differential equations. The resulting equations are numerically solved in the Maple software by using shooting technique. The impact of the different applied parameters on skin friction, couple stress, Nusselt and the Sherwood numbers along the related profiles are determined for both stretching and shrinking cases of the surfaces. It was observed that with an increase in suction and magnetic parameters, the fluid velocity decreased. An increment in the thermal slip, the fluid temperature decreased and nanoparticles concentration decreases as the mass slip parameter is enhanced. An increase in concentration decreases but temperature increases. While, concentration and temperature both increase due to increase in thermophoresis parameter, and concentration also increases by increase in rate of chemical reaction. Thus, suction at the boundary and magnetic parameter acted as flow controlling parameter. It is believed that this type of investigation is very much helpful for the manufacturing of complex fluids and also for cleaning oil from surfaces. PubDate: 2023-05-09 Issue No:Vol. 11 (2023)

Authors:Iftikhar Ahmed Bhutto, Afaque Ahmed Bhutto, Rahim Bux Khokhar, Muhammad Aslam Soomro, Fozia Shaikh Abstract: In this research, we explore the equations of motion governing the behaviour of a finitely conducting incompressible fluid with variable viscosity, heat transfer, and the presence of a transverse magnetic field. By solving these equations, we obtain exact solutions that describe flows in which the vorticity distribution is varying indirect proportion to the stream function perturbed by both uniform and exponent streams. To obtain these exact solutions, we introduce a transformation variable that allows us ttransforming a non-linear system into a linear form the governing equations. From there, we are able to derive several exact solutions that provide insight into the behaviour of the fluid in these conditions. PubDate: 2023-04-29 Issue No:Vol. 11 (2023)

Authors:Prem Kumar Abstract: The main theme of this research paper is to propose an explicit iterative numerical scheme over the modified Euler’s method (MEM) for solving initial value problems in ordinary differential equations. This iterative scheme has been proposed by changing the inner slope of the MEM by the mean of main slope of MEM and slope of explicit forward Euler’s method. The proposed iterative scheme has been tested for its performance by analyzing different numerical factors related to numerical algorithm and found it consistent, more accurate with the order of convergence 2 and it also shows greater stability region as compared to existing methods which are compared with proposed method. PubDate: 2023-04-19 Issue No:Vol. 11 (2023)

Authors:Umair Khalid Qureshi, Muzaffar B. Aarain, Rahim Bux Khokhar, Manzar Bashir Abstract: In this research two iterated methods have been developed for solving non-linear equations, which arises in applied sciences and engineering. The proposed iterated methods are converged cubically, and it is derived from modified euler method and improved euler method with steffensen method. The cubic iterated methods of numerical differential method are work on physical application functions and compared with variant newton iterated method. The numerical outcome of proposed cubic iterated methods of numerical differential method is examined with C++/MATLAB. From the numerical results, it can be observed that the cubic iterated methods of numerical differential method are good for accuracy point of view, iteration perception and function evaluation as the assessment of variant newton iterated method for solving non-linear physical functions. PubDate: 2023-04-13 Issue No:Vol. 11 (2023)

Authors:Rabnawaz Mallah, Inayatullah Soomro, Altaf Ahmed, Dost Muhammad, Sarang Latif, Irshad Ahmed Abstract: In nearest period of time a considerable and remarkable work have been done on the graphic design artificial intelligence, optimization, solving numerical approximation of ordinary as well as Partial differential equation by some differential operator, Discrete Laplacian operator is one of the most modern technique used for discretizatise the Ordinary differential equations (ODES) and Partial Differential equation (PDES). It is most simple technique, the researcher have taken great interest, as they may be able to find the novelty in their results specially in simulation of di-block co-polymer, solving the partial differential equation and also in finding light equation, wave equation in one as well as two dimension and etc. Discrete laplacian operator plays an essential role in the field of science and technology, shape interpolation, smoothing of the surface area, editing the meshes are the best usages of discrete laplacian operator In this study, a finite difference scheme is applied to develop the Laplacian operator using a cylindrical mesh system containing thirteen-point stencils. Laplacian operator has a significant role in the study of numerous mathematical and scientific phenomena. This employed in numerous significant computational and mathematical models, such as the Cell Dynamic Simulation system for the study of cutting-edge materials and image processing. The laplacian operator is necessary for being an isotropic discrete differential operator in a variety of models. When computing discrete isotropic results on curved surfaces, the curvilinear coordinate system may be a good option. PubDate: 2023-03-31 Issue No:Vol. 11 (2023)

Authors:Afaque Ahmed Bhutto, Syed Feroz Shah, Rahim Bux Khokhar, Khanji Harijan, Mukkarum Hussain Abstract: Combustion instability inside a chamber may lead to catastrophic failure. It is due to inappropriate combustion or flow physics. Flow-driven instability is mostly governed by surface, corner, or obstacle vortex shedding. Inhibitors are placed inside a solid fuel combustion chamber to control burning of solid fuel grain. They burn slowly as compare to solid fuel and create protrusions inside the combustion chamber. These protrusions work as flow obstacles. Obstacle vortex are shed from inhibitor and produces pressure oscillations. Effects on inhibitor position on pressure oscillation inside a solid fuel combustion chamber is investigated in the present study. Large eddies must be resolved to compute vortex-driven flow. Therefore, Detached Eddy Simulation is applied cylindrical combustion chambers having inhibitor and nozzle. Five different configurations are simulated. All parameters of different configurations are similar except inhibitor position. The inhibitor is moved upstream and downstream from the reference position to examine its effect on pressure oscillations. Pressure time histories at eight distinct places of the combustion chamber are recorded. Fast Fourier Transform (FFT) has been utilized to get pressure oscillation frequency and amplitude. It is interesting to reveal that the maximum amplitude of pressure oscillation occurs when the inhibitor to stagnation point distance is close to the combustion chamber diameter. It is up to 70% higher as compare to reference inhibitor position results. Computed results are also compared with available experimental data for PubDate: 2023-03-29 Issue No:Vol. 11 (2023)

Authors:Khalil Ullah, Abbas Qadir Abstract: In this paper, our aim is to determined the sharp bounds of coefficients, Fekete-Szegö, Zalcman inequalities for the family SS∗ tanh of starlike function with respect to symmetric points linked with tan hyperbolic function. We also estimate determinant of H2,2 PubDate: 2023-03-23 Issue No:Vol. 11 (2023)

Authors:Tasawar Abbas, Rehan Zafar, Sana Anjum, Ambreen Ayub, Zamir Hussain Abstract: This article seeks to demonstrate the novel properties of soft rough dual hesitant fuzzy sets (DHFSRSs) and dual hesitant fuzzy soft rough sets (SRDHFSs). The fundamental characteristics of DHFSRSs and SRDHFSs are thoroughly investigated. Additionally, we present a portrayal hypothesis for the DHFSRSs and SRDHFSs, which demonstrates that the level arrangements of the DHFSRSs and SRDHFSs can be used to characterize both the lower and upper DHFSRSs and SRDHFSs estimates in an identical manner. PubDate: 2023-03-16 Issue No:Vol. 11 (2023)

Authors:Afaque Ahmed Bhutto, Iftikhar Ahmed, Saeed Ahmed Rajput, Syed Asad Raza Shah Abstract: This study focuses on developing and proving exact solutions for equations of motion involving a fluid with finite conductivity, variable viscosities, and heat transfer in the presence of a transverse magnetic field. By utilizing a transformation variable, the governing equation is transformed into a assortment of simple ordinary differential equations, enabling accurate solutions to be achieved for the problem. The solutions demonstrate that the distribution of vorticity is proportional to the stream function, which is disturbed by oscillating (sine or cosine) or even and exponential streams. This study compares the profiles of steady fluid flow with changing viscosity and heat transfer travelling on a plane. The comparison is used to identify differences in the profiles of providing insight into the changes that occur in interesting factors. These findings have significant implications for understanding fluid dynamics in complex systems and may have important applications in fields such as engineering and physics. PubDate: 2023-03-05 Issue No:Vol. 11 (2023)

Authors:Safdar Ali, Fozia Hanif, Muhammad Ilyas, Rehan Shams, Muhammad Rehan, Syed Inayatullah Abstract: The purpose of this study is to develop the third order time fractional partial differential equations (PDEs) in one and higher dimensions, by taking Laplace Adomian decomposition method (LADM) and q-homotopy analysis transform method (q-HATM). To define fractional derivative, the Caputo operator is used for both fractional and integer orders. The solutions are obtained in the form of series. To understand the procedure of the suggested procedure, three numerical examples are taken. The graphs are plotted for the proposed solution at different values of fractional order '''' which is 0< '''' ≤ 1. Both proposed methods are implemented by using (LADM) and (q-HATM) showing that the proposed technique is found to be better and accurate instrument for solving linear and non-linear time fractional PDEs. The Novelty of the proposed study is that the provided solution for fractional order partial differential equations has never been attempted for third order, this means that the provided solution can solve the third order and could be generalized for the higher order also. PubDate: 2022-12-31 Issue No:Vol. 10 (2022)