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Öğe Closed-form solutions of higher order parabolic equations in multiple dimensions: A reliable computational algorithm(Elsevier, 2023) Qayyum, Mubashir; Khan, Amna; Saeed, Syed Tauseef; Akgul, Ali; Riaz, Muhammad BilalParabolic equations play an important role in chemical engineering, vibration theory, particle diffusion and heat conduction. Solutions of such equations are required to analyze and pre-dict changes in physical systems. Solutions of such equations require efficient and effective tech-niques to get reasonable accuracy in lesser time. For this purpose, current article proposes residual power series algorithm for higher order parabolic equations with variable coefficients in multiple dimensions. The proposed algorithm provides closed-form solutions without linearization, discretization or perturbation. For efficiency testing of the proposed methodology, initially it is implemented to homogeneous multidimensional parabolic models, and exact solutions are com-puted. In next stage of testing, proposed algorithm is enforced to three-dimensional non-homoge-neous fourth order parabolic equation, and closed form solutions are recovered. The obtained results indicate the validity and effectiveness of proposed methodology, hence proposed algorithm can be extended to more complex scenarios in engineering and sciences. (c) 2023 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).Öğe Dual solution of thin film flow of fuzzified MHD pseudo-plastic fluid: numerical investigation in uncertain environment(Taylor & Francis Ltd, 2024) Qayyum, Mubashir; Tahir, Aneeza; Saeed, Syed Tauseef; Afzal, Sidra; Akgul, Ali; Hassani, Murad KhanThe pseudoplastic fluids have wide range of applications in industrial areas including cyclone separation, bearings, paper fibre separation, heat exchangers and also in food industry. In this regard, the current manuscript investigates the impact of transverse magnetic field on thin pseudo-plastic film flow on a vertical wall in a fuzzy (uncertain) environment. The uncertainty in a model is characterized through triangular fuzzy numbers (TFNs) along with $ \mathbbm {r} $ r-cut approach, which is computationally effective in capturing the uncertainties in physical phenomena. This results in the modelling of highly nonlinear fuzzified problem. For solution and analysis purposes, Runge-Kutta Fehlberg (RKF) is utilized. Also, RKF solutions are validated by comparing them to homotopy perturbation solutions in the current manuscript. The impact of $ \mathbbm {r} $ r-cut, and fluid parameters including non-Newtonian parameter beta, magnetic field M and Stoke's number $ \mathcal {S}_{t} $ St on the upper and lower velocity profiles are captured and analysed numerically and graphically. Analysis reveals that velocity profile decreases with an increase in applied magnetic field at upper and lower bounds. Also, increase in $ \mathcal {S}_{t} $ St and beta increases the velocity profile at lower bound, while inverse behaviour is recorded in the case of upper bound. The results also indicate that as $ \mathbbm {r} $ r goes from 0 to 1, the crisp solution always lies between upper and lower profiles, and becomes coherent at 1. Moreover, all fuzzy level set values of $ \mathbbm {r} \in [0,1] $ r is an element of[0,1] satisfy the fuzzy solution in the form of TFN.Öğe Exact Analysis of Second Grade Fluid with Generalized Boundary Conditions(Tech Science Press, 2021) Saeed, Syed Tauseef; Riaz, Muhammad Bilal; Baleanu, Dumitru; Akg, Ali; Husnine, Syed MuhammadConvective flow is a self-sustained flow with the effect of the temperature gradient. The density is non-uniform due to the variation of temperature. The effect of the magnetic flux plays a major role in convective flow. The process of heat transfer is accompanied by mass transfer process; for instance condensation, evaporation and chemical process. Due to the applications of the heat and mass transfer combined effects in different field, the main aim of this paper is to do comprehensive analysis of heat and mass transfer of MHD unsteady second-grade fluid in the presence of time dependent generalized boundary conditions. The non-dimensional forms of the governing equations of the model are developed. These are solved by the classical integral (Laplace) transform technique/method with the convolution theorem and closed form solutions are developed for temperature, concentration and velocity. Obtained generalized results are very important due to their vast applications in the field of engineering and applied sciences. The attained results are in good agreement with the published results. Additionally, the impact of thermal radiation with the magnetic field is also analyzed. The influence of physical parameters and flow is analyzed graphically via computational software (MATHCAD-15). The velocity profile decreases by increasing the Prandtl number. The existence of a Prandtl number may reflect the control of the thickness and enlargement of the thermal effect.Öğe Heat and mass transport impact on MHD second-grade fluid: A comparative analysis of fractional operators(Wiley, 2021) Rehman, Aziz Ur; Riaz, Muhammad Bilal; Akgul, Ali; Saeed, Syed Tauseef; Baleanu, DumitruThe effect of the magnetic flux plays a major role in convective flow. The process of heat transfer is accompanied by a mass transfer process; for instance, condensation, evaporation, and chemical process. Due to the applications of the heat and mass transfer combined effects in different fields, the main aim of this paper is to do a comprehensive analysis of heat and mass transfer of magnetohydrodynamic (MHD) unsteady second-grade fluid in the presence of ramped conditions. The new governing equations of MHD second-grade fluid have been fractionalized by means of singular and nonsingular differentiable operators. To have an accurate physical significance of imposed conditions on the geometry of second-grade fluid, the constant concentration with ramped temperature and ramped velocity is considered. The fractional solutions of temperature, concentration, and velocity have been investigated by means of integral transform and inversion algorithm. The influence of physical parameters and flow is analyzed graphically via computational software (MATHCAD-15). The velocity profile decreases by increasing the Prandtl number. The existence of a Prandtl number may reflect the control of the thickness and enlargement of the thermal effect.Öğe Modeling and analysis of thin film flow of Fuzzified Johnson Segalman nanofluid using fuzzy extension of He-Laplace scheme(Taylor & Francis Inc, 2023) Qayyum, Mubashir; Tahir, Aneeza; Bariq, Abdul; Akgul, Ali; Saeed, Syed TauseefThe concept of fuzzy calculus in fluid modelling offers a feasible approach to address ambiguity and uncertainty in physical phenomena. This study aims to model and analyse thin film flow of Johnson Segalman nonofluid (JSNF) on a vertical belt in fuzzy environment for lifting and drainage settings. By incorporating Triangular fuzzy numbers (TFNs), a more accurate representation of the uncertain nature of JSNF flow is obtained which leads to a better understanding of fluid behaviour and its potential applications. The fluid problems are modelled with uncertainties and numerically solved through fuzzy extension of He-Laplace algorithm. The validity and convergence of the proposed methodology is checked by computing residual errors in each case. The obtained solutions provide fuzzy velocity profiles and volumetric flow rates in lift and drain cases. As the parameter r - c u t approaches 1, the velocity profiles at the upper and lower bounds merge, indicating solution consistency.Öğe New solutions of fractional 4D chaotic financial model with optimal control via He-Laplace algorithm(Elsevier, 2024) Qayyum, Mubashir; Ahmad, Efaza; Saeed, Syed Tauseef; Akgul, Ali; Din, Sayed M. ElThe objective of current investigation is to propose a solution to predict the interest rate, investment demand, and price index with optimal control in a fractional financial 4D chaotic model. He-Laplace method (HLM) is introduced with fractional derivative in Caputo sense to characterize the memory effect of the 4D chaotic model. For validation and comparison purposes, the given financial model is also solved through fractional residual power series algorithm. Analysis revealed that HLM provide improved results as compared to RPSA. Model is also analyzed graphically for interest rate, investment demand, price index and input control in fractional environment to understand the physical behavior of the model. The impact of variations in saving amount, cost per investment, and elasticity in demand are also presented through contours. It is reported that initially the interest rate, investment demand and price index are uniform, but later on drastic increase have been observed. Analysis also revealed that proposed methodology is stable and performed exceptionally well in chaotic scenarios, and hence can be extended to other complex models.Öğe Series-form solutions of generalized fractional-fisher models with uncertainties using hybrid approach in Caputo sense(Pergamon-Elsevier Science Ltd, 2023) Qayyum, Mubashir; Tahir, Aneeza; Saeed, Syed Tauseef; Akguel, AliThe field of fuzzy calculus has emerged as a powerful mathematical tool which can effectively deal with uncertainties and impressions that are common in real-world situations. In particular, it has proven useful in modeling and analysis of complex biological systems with uncertain parameters. The current study focuses on analysis of (?????? + 1) -dimensional fractional Fisher equations (FFEs) in fuzzy environment. The objective is to provide semi-analytical solutions for fuzzy (?????? + 1)-dimensional FFEs by considering Caputo-gH fractional derivative. The uncertainty in initial conditions is injected through triangular fuzzy numbers and obtained fuzzy (?????? + 1) -dimensional FFEs are solved using hybrid of homotopy perturbation with Laplace transform in fuzzy-Caputo sense, which provides a powerful mathematical framework for examining complex behavior. The derived series solutions are validated against existing results from the literature and found to be improved. The obtained results are analyzed by means of determining the fuzzy solutions and residual errors at varying fractional orders, membership function, spatial coordinate ??????, and time ??????. These analytical findings are visualized in graphical form for ease of comprehension. The conducted study yields significant insights about the behavior of fractional model having uncertain conditions, and highlights the efficiency of proposed methodology. The results of this study have important implications for understanding the dynamics of biological systems with uncertainty, and hence can be useful in wide variety of applications in different fields such as ecology, epidemiology, and economics.Öğe Traveling wave solutions of generalized seventh- order time-fractional KdV models through He-Laplace algorithm(Elsevier, 2023) Qayyum, Mubashir; Ahmad, Efaza; Saeed, Syed Tauseef; Akgul, Ali; Riaz, Muhammad BilalNon-linear evolution equations play a prominent role in describing a wide range of phe-nomena in optical fibers, fluid dynamics, electromagnetic radiation, plasma and solid state physics. An important category of non-linear evolution models that characterizes shallow wave phenomena are the Korteweg-de Vries (KdV) models. In this regard, time-fractional Korteweg-de Vries models of seventh order are the main focus of this research. A general KdV seventh-order equation is con-sidered with different coefficients to form Lax, Kaup-Kuperschimdt and Sawada-Kotera-Ito KdV models. An efficient semi-analytical algorithm named as He-Laplace (HLM) is applied for the solu-tion of these models. In this algorithm, Laplace transform is hybrid with homotopy perturbation method (HPM). This study provides important results as non-linear evolution seventh-order models in fractional sense have not been captured through HLM in current literature. Absolute errors are computed and compared with already existing results to confirm the superiority of proposed algo-rithm over other existing techniques. Numerical and graphical investigations are conducted to eval-uate the approximate series form solutions. The dynamic behavior of fractional parameter is observed by calculating residual errors and plotting two dimensional diagrams throughout the fractional-domain. Analysis confirms that the proposed methodology provides an effective and con-venient way for solving fractional KdV models. (c) 2023 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).Öğe Unsteady hybrid nanofluid (Cu-UO2/blood) with chemical reaction and non-linear thermal radiation through convective boundaries: An application to bio-medicine(Cell Press, 2023) Qayyum, Mubashir; Afzal, Sidra; Saeed, Syed Tauseef; Akgul, Ali; Riaz, Muhammad BilalThis study is focused on modeling and simulations of hybrid nanofluid flow. Uranium dioxide UO2 nanoparticles are hybrid with copper Cu, copper oxide CuO and aluminum oxide A12O3 while considering blood as a base fluid. The blood flow is initially modeled considering magnetic effect, non-linear thermal radiation and chemical reactions along with convective boundaries. Then for finding solution of the obtained highly nonlinear coupled system we propose a methodology in which q-homotopy analysis method is hybrid with Galerkin and least square Optimizers. Residual errors are also computed in this study to confirm the validity of results. Analysis reveals that rate of heat transfer in arteries increases up to 13.52 Percent with an increase in volume fraction of Cu while keeping volume fraction of UO2 fixed to 1% in a base fluid (blood). This observation is in excellent agreement with experimental result. Furthermore, comparative graphical study of Cu, CuO and A12O3 for increasing volume fraction is also performed keeping UO2 volume fraction fixed. Investigation indicates that Cu has the highest rate of heat transfer in blood when compared with CuO and A12O3. It is also observed that thermal radiation increases the heat transfer rate in the current study. Furthermore, chemical reaction decreases rate of mass transfer in hybrid blood nanoflow. This study will help medical practitioners to minimize the adverse effects of UO2 by introducing hybrid nano particles in blood based fluids.
