Analytical solution for the flow of second grade fluid over a stretching sheet

Rafiq, Muhammad; Kamran, Muhammad; Ahmed, Naveed; Mohyud‐Din, Syed Tauseef; Bashir, Yasir; Haider, Sajjad; Farwa, Shabieh; Tahir, Madeeha

doi:10.1063/1.5093158

Cited by 13 publications

(6 citation statements)

References 38 publications

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“…It is observed that greater values of and leads to higher estimates of skin friction . The comparison between the current findings of the second-grade fluid parameter influence on skin friction and Rafiq et al 54 is shown in Table 2 . The results of the present study shows great harmony with previous data.…”

Section: Numerical Resultsmentioning

confidence: 74%

Flow investigation of the stagnation point flow of micropolar viscoelastic fluid with modified Fourier and Fick’s law

Khan¹,

Khan²,

Wang³

et al. 2023

Sci Rep

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Non-Newtonian fluids are extensively employed in many different industries, such as the processing of plastics, the creation of electrical devices, lubricating flows, and the production of medical supplies. A theoretical analysis is conducted to examine the stagnation point flow of a 2nd-grade micropolar fluid into a porous material in the direction of a stretched surface under the magnetic field effect, which is stimulated by these applications. The stratification boundary conditions are imposed on the surface of the sheet. Generalized Fourier and Fick’s laws with activation energy is also considered to discuss the heat and mass transportation. To obtain the dimensionless version of the flow modeled equations, an appropriate similarity variables are used. These transfer version of equations is solved numerically by the implement of the BVP4C technique on MATLAB. The graphical and numerical results are obtained for various emerging dimensionless parameters and discussed. It is noted that by the more accurate predictions of $$\varepsilon$$ ε and M, the velocity sketch is decreased due to occurrence of resistance effect. Further, it is seen that larger estimation of micropolar parameter improves the angular velocity of the fluid.

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Section: Numerical Resultsmentioning

confidence: 74%

Flow investigation of the stagnation point flow of micropolar viscoelastic fluid with modified Fourier and Fick’s law

Khan¹,

Khan²,

Wang³

et al. 2023

Sci Rep

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show abstract

“…The accuracy and consistency of the current numerical solution are gauged by means of a quantitative comparison with a prior study conducted by Rafiq et al 47 This comparison serves to authenticate the precision of the present numerical data. The results are quantitatively assessed by comparing them against the data from the aforementioned study, as demonstrated in Table 1.…”

Section: Verification Of the Numerical Codementioning

confidence: 69%

Physical insight into thermal analysis of magnetohydrodynamic stagnation point flow of micropolar nanofluid across a flexible surface equipped with porous medium and Fourier and Fick's law

Rasheed,

Shah,

Khan

et al. 2023

Heat Trans

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Nanofluids represent a novel heat transfer liquid, making them an efficient medium for enhancing energy transmission. Nevertheless, significant knowledge gaps still exist concerning current strategies for improving heat transfer in nanofluids, underscoring the necessity for comprehensive research on these fluid systems. Therefore, this study considered theoretical analysis retrieves the influence of radiative two‐dimensional stagnation point flow of second‐grade micropolar fluid flow about an elongated channel surface implanted in porous media with magnetic effect, and modified heat and mass flux is under consideration. The major novel effect of the current study is to analyze the activation energy and thermal aspect of the system in the presence of nonlinear radiation effects that are considered in the revised mathematical framework by utilizing the boundary layer theory. The resulting set of coupled partial differential equations is further reduced and transformed into a dimensionless system of ordinary differential equations through appropriate scaling invariants. We initiate the RKF‐45 investigation scheme to numerically analyze the transformed dimensionless system, considering relevant parameters. The computational algorithm is implemented using MATLAB programming syntax. Plotted visuals are revealed for leading parameters against pertinent flow profiles graphically and with numerical data. Additionally, the convergence analysis of the numerical results for various flow profiles of the fluids were compared to establish the authenticity of the proposed flow problem. These research findings play a significant role in controlling heat transfer rates and fluid velocities in diverse manufacturing processes and industrial applications, ultimately aiding in achieving the desired product quality.

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“…Figures 2-8 examine the performance of parameters across subjective fields. The current results are compared with Rafiq et al [31] and Jamshed et al [32] as described in Table 3. Table 1 contains Figure 2 analyzes the effect of suction parameters via the velocity of fluid.…”

Section: Resultsmentioning

confidence: 95%

Computational Analysis of Nanoparticle Shapes on Hybrid Nanofluid Flow Due to Flat Horizontal Plate via Solar Collector

et al. 2022

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The present work discusses the 2D unsteady flow of second grade hybrid nanofluid in terms of heat transfer and MHD effects over a stretchable moving flat horizontal porous plate. The entropy of system is taken into account. The magnetic field and the Joule heating effects are also considered. Tiny-sized nanoparticles of silicon carbide and titanium oxide dispersed in a base fluid, kerosene oil. Furthermore, the shape factors of tiny-sized particles (sphere, bricks, tetrahedron, and platelets) are explored and discussed in detail. The mathematical representation in expressions of PDEs is built by considering the heat transfer mechanism owing to the effects of Joule heating and viscous dissipation. The present set of PDEs (partial differential equations) are converted into ODEs (ordinary differential equations) by introducing suitable transformations, which are then resolved with the bvp4c (shooting) scheme in MATLAB. Graphical expressions and numerical data are obtained to scrutinize the variations of momentum and temperature fields versus different physical constraints.

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Analytical solution for the flow of second grade fluid over a stretching sheet

Cited by 13 publications

References 38 publications

Flow investigation of the stagnation point flow of micropolar viscoelastic fluid with modified Fourier and Fick’s law

Flow investigation of the stagnation point flow of micropolar viscoelastic fluid with modified Fourier and Fick’s law

Physical insight into thermal analysis of magnetohydrodynamic stagnation point flow of micropolar nanofluid across a flexible surface equipped with porous medium and Fourier and Fick's law

Computational Analysis of Nanoparticle Shapes on Hybrid Nanofluid Flow Due to Flat Horizontal Plate via Solar Collector

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