Mathematical modeling and thermodynamics of Prandtl–Eyring fluid with radiation effect: a numerical approach

Ullah, Zakir; Ullah, Ikram; Zaman, Gul; Khan, Hassan; Muhammad, Taseer

doi:10.1038/s41598-021-01463-4

Cited by 37 publications

(23 citation statements)

References 53 publications

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“…Due to its shear-thinning properties, this model can precisely predict the rheology of blood. Furthermore, for the ongoing flow model, the extra stress tensor is portrayed by 21,23,27…”

Section: Mathematical Modelingmentioning

confidence: 99%

“…In expression (1), A and B render the material factors of Prandtl-Erying fluid and A 1 refers to the first Rivilin-Erickson tensor. In addition, the essential component for the Prandtl-Erying fluid model is expressed by 21,27 and nanoparticles is addressed here. For this appraisal, some novel phenomena, such as for instance, bioconvection, thermophoresis particle deposition, Arrhenius activation vitality, exothermic/endothermic process, and triple stratification are also contemplated.…”

Section: Mathematical Modelingmentioning

confidence: 99%

“…The controlling expressions for the nano-bioconvective flow of Prandtl-Erying fluid containing microbes and nanoparticles in the presence of assorted features are sculptured in the following manner, 12,13,22,26,27,40,46,47,60 Continuity equation…”

Section: Mathematical Modelingmentioning

confidence: 99%

“…In expression (1), A and B render the material factors of Prandtl–Erying fluid and A 1 refers to the first Rivilin‐Erickson tensor. In addition, the essential component for the Prandtl–Erying fluid model is expressed by 21,27

{S}_{xy}=\frac{A}{B}\left[\left(\frac{\partial u}{\partial y}\right)-\frac{1}{6{B}^{2}}{\left(\frac{\partial u}{\partial y}\right)}^{3}\right].

…”

Section: Mathematical Modelingmentioning

confidence: 99%

“…Recently, Hayat et al 26 articulately deliberated the nature of Prandtl–Erying fluid containing microbes and nanomaterials in a melting stretched surface. Very recently, comprehensive work has been studied on the stagnation point flow of Prandtl–Erying fluid over stretching sheet by Ullah et al 27 The author concluded that fluid velocity displays direct behavior with the velocity ratio factor.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Swimming of microbes in entropy optimized nano‐bioconvective flow of Prandtl–Erying fluid

Rana

Arifuzzaman²,

Islam

et al. 2022

Heat Trans

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Microbes swimming in a fluid that contains nanoparticles is an intriguing characteristic having ramifications in biomedicine, petroleum science, biofuels, and biotechnology applications. This study gives a theoretical evaluation of the bioconvection phenomena with swimming microorganisms in a Prandtl-Erying nanofluid constructed by an exponential stretched surface, given the amazing applications of bioconvection and nanoparticles. Additionally, the problem is modeled by considering intriguing phenomena such as thermophoretic particle deposition, Darcy-Forchheimer medium, exothermic/endothermic process, and activation energy vitality.The leading problem comprises nonlinear, coupled, partial differential expressions. To run the appraisal process, the controlling problem is transfigured into dimensionless patterns through the usual transformations. A computational finite difference approach is used to quantify the numerical evaluation of fabricated flow problems. To obtain the parametric constraints, stability and convergency were also assessed. Improved visualizations (streamlines, isothermal line, iso-concentration,

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“…Due to its shear-thinning properties, this model can precisely predict the rheology of blood. Furthermore, for the ongoing flow model, the extra stress tensor is portrayed by 21,23,27…”

Section: Mathematical Modelingmentioning

confidence: 99%

Section: Mathematical Modelingmentioning

confidence: 99%

Section: Mathematical Modelingmentioning

confidence: 99%

{S}_{xy}=\frac{A}{B}\left[\left(\frac{\partial u}{\partial y}\right)-\frac{1}{6{B}^{2}}{\left(\frac{\partial u}{\partial y}\right)}^{3}\right].

…”

Section: Mathematical Modelingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Swimming of microbes in entropy optimized nano‐bioconvective flow of Prandtl–Erying fluid

Rana

Arifuzzaman²,

Islam

et al. 2022

Heat Trans

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Exploring tubular steady‐state laminar flow reactors with orthogonal collocation

Soares,

de Sousa Santos,

Binous

et al. 2024

Comp Applic In Engineering

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The laminar flow reactor (LFR) is one of the most comprehensive problems in chemical reaction engineering, as its modeling involves mass, heat, and momentum conservation equations coupled with chemical reaction rate equations. It is relatively easy to grasp its basic operation, but the solution of the problem is far from trivial. Although there are analytical solutions that simplify the problem, students and tutors must use efficient numerical strategies to appropriately solve some LFR problems. In the present investigation, we solve several different cases of two‐dimensional cylindrical LFR, beginning with the isothermal case, as a benchmark. Calculations were performed using the Chebyshev orthogonal collocation technique by custom scripts in Scilab, Mathematica©, and Matlab®, and were compared with solutions available from the ECRE Version of COMSOL®, which was used as the reference, as well as available analytical solutions in the literature. After analyzing the case of the isothermal LFR with Newtonian fluid, we explored non‐Newtonian fluids, including Carreau and Bingham fluids, whose LFR results are not available in the preceding literature. For Newtonian fluids, besides (a) the isothermal case, we also explore other three nonisothermal design cases: (b) cooling jacket with a fixed heat exchange coefficient at the wall, (c) adiabatic operation, (d) nonisothermal LFR with isothermal wall. Through a performance criterion, the different operation models are compared and we show that nonisothermal design cases perform better than the isothermal case. Computation times, for different scenarios, are quite short and taking 25 nodal points or more suffice for an accurate and timely solution of the more complex problem Case (b). The numerical modeling approach is useful from a pedagogical standpoint, as one can compare numerical results with classical assumptions, and progress from a more restrictive conceptual model (segregated flow) to an array of different kinds of operation with the LFR in which one needs to consider diffusion and temperature distribution.

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Predictive potential of K‐Banhatti and Zagreb type molecular descriptors in structure–property relationship analysis of some novel drug molecules

Ullah,

Jabeen,

Zaman

et al. 2024

J Chinese Chemical Soc

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Topological indices (TIs) can be used to forecast molecules' biological activity, physicochemical features, and toxicity. The use of topological indices and regression analysis can help us better understand drug behavior and contribute to the development of tailored drugs. This study investigates the predictive potential and efficacy of K‐Banhatti and Zagreb type degree‐based topological indices in quantitative structure–property relationship (QSPR) analysis of a comprehensive set of medications used for diabetes type‐I and type‐II disease. The K‐Banhatti and Zagreb type degree‐based topological indices are computed for 14 anti‐diabetes drug molecules using edge/vertex partitioning techniques. By leveraging these topological indices, QSPR regression models are developed to predict the physicochemical properties of the understudy drugs. The results show that the values of these topological indices are highly correlated with certain physicochemical properties of the anti‐diabetes drugs. Furthermore, the comparative analysis revealed that, for all the considered properties except enthalpy of vaporization, Zagreb type indices outperform K‐Banhatti indices with high predictive ability. Hence, it can be concluded that the Zagreb type indices are the best alternatives to theoretically predict the properties of anti‐diabetes drugs. This theoretical analysis can help chemists in their right choice of the topological indices to theoretically predict the properties of anti‐diabetes drugs without going into laborious experimentation.

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Mathematical modeling and thermodynamics of Prandtl–Eyring fluid with radiation effect: a numerical approach

Cited by 37 publications

References 53 publications

Swimming of microbes in entropy optimized nano‐bioconvective flow of Prandtl–Erying fluid

Swimming of microbes in entropy optimized nano‐bioconvective flow of Prandtl–Erying fluid

Exploring tubular steady‐state laminar flow reactors with orthogonal collocation

Predictive potential of K‐Banhatti and Zagreb type molecular descriptors in structure–property relationship analysis of some novel drug molecules

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