Abstract
In this work, the heat transfer features and stagnation point flow of Magnetohydrodynamics (MHD) hybrid second-grade nanofluid through a convectively heated permeable shrinking/stretching sheet is reported. The purpose of the present investigation is to consider hybrid nanofluids comprising of Alumina left( {{text{Al}}_{{2}} {text{O}}_{{3}} } right) and Copper left( {{text{Cu}}} right) nanoparticles within the Sodium Alginate (SA) as a host fluid for boosting the heat transfer rate. Also, the effects of free convection, viscous dissipation, heat source/sink, and nonlinear thermal radiation are considered. The converted nonlinear coupled fuzzy differential equations (FDEs) with the help of triangular fuzzy numbers (TFNs) are solved using the numerical scheme bvp4c. The numerical results are acquired for various engineering parameters to study the Nusselt number, skin friction coefficient, velocity, and temperature distribution through figures and tables. For the validation, the current numerical results were found to be good as compared to existing results in limiting cases. It is also inspected by this work that with the enhancement of the volume fraction of nanoparticles, the heat transfer rate also increases. So, it may be taken as a fuzzy parameter for a better understanding of fuzzy variables. For the comparison, the volume fraction of nanofluids and hybrid nanofluid are said to be TFN [0, 0.1, 0.2]. In the end, we can see that fuzzy triangular membership functions (MFs) have not only helped to overcome the computational cost but also given better accuracy than the existent results. Finding from fuzzy MFs, the performance of hybrid nanofluids is better than nanofluids.
Highlights
List of symbols x, y Cartesian coordinates u, v Velocity components B0 Uniform Magnetic field g Acceleration due to gravity α2 Second grade fluid parameter T Temperature Tw, T∞ Reference and ambient temperature Q0 Heat absorption/generation coefficient qr Heat source of radiativity ρhnf Density of hybrid nanofluid ρf Density of fluid μhnf Dynamic viscosity of hybrid nanofluid μf Dynamic viscosity of the fluid η Similarity variable ψ Stream function β Shrinking/stretching rate parameter
The numerical solutions of non-dimensional governing coupled highly non-linear differential equations are obtained via a built-in numerical technique bvp4c
The numerical results are examined through figures and in the tabular forms for the various values of control dimensionless parameters such as buoyancy ratio parameter (Gr), second-grade fluid parameter (K), heat source or sink parameter (H), magnetic parameter (M), rate of mass transfer parameter (s), thermal radiation parameter (Nr), Prandtl number (Pr), temperature ratio parameter, Eckert number (Ec), velocity ratio parameter (β), and volume fraction of hybrid nanoparticles (φ1, φ2)
Summary
An incompressible steady two-dimensional,ilaminar,iboundary-layer and stagnationipointiflow of a non-Newtonian electrically conducting second-gradeihybridinanofluid Al2O3 + Cu/SA is studied over a convectivelyiheated permeable shrinking/stretchingisheet with nonlinearithermal radiationiand viscousidissipation. The physical flow problem and governing equations for a specific sort of second-grade hybrid nanofluid were considered by the researchers[18,31]. Thermo-physical features of the hybrid nanofluids are exposed in the following e quation[31]: αhnf khnf (ρcP )hnf. W here, σr = σhnf σf , μr = μhnf μf , (βT )r = (βT )hnf (βT )f , ρr = ρhnf ρf , αhnf = khnf (ρcP )hnf , αr = αhnf αf , (ρcP)r = (ρcP)hnf (ρcP)f , Gr = (Tw − T∞)g(βT )f bx[2], M = σf B02 bρf , K = bα[2] μf , Pr = vf αf , H = Q0 b(ρcP)f , θw = Tw T∞, Nr = 16σ ∗T∞3 3kf k∗vf , Ec = (bx)[2] ρcp f (Tw − T∞), β = a b the velocity ratio parameter, vw(x) = −s bvf and s is the rate of mass transfer through the permeable sheet.
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