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    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 Khan
    The 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.
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    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 Tauseef
    The 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.
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    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, Ali
    The 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.