“…The entropy analysis for nanofluid with different type of nano particles and water type base fluid for unsteady MHD flow was studied by 8 . The impact of magnetic field on free convection of nanofluid in a porous medium is presented by 9 . The effects of heat transfer on MHD nanofluid in a porous semi annulus has investigated by 10 using numerical methods.…”
Casson nanofluid, unsteady flow over an isothermal vertical plate with Newtonian heating (NH) is investigated. Sodium alginate (base fluid)is taken as counter example of Casson fluid. MHD and porosity effects are considered. Effects of thermal radiation along with heat generation are examined. Sodium alginate with Silver, Titanium oxide, Copper and Aluminum oxide are added as nano particles. Initial value problem with physical boundary condition is solved by using Laplace transform method. Exact results are obtained for temperature and velocity fields. Skin-friction and Nusselt number are calculated. The obtained results are analyzed graphically for emerging flow parameters and discussed. It is bring into being that temperature and velocity profile are decreasing with increasing nano particles volume fraction.
“…The entropy analysis for nanofluid with different type of nano particles and water type base fluid for unsteady MHD flow was studied by 8 . The impact of magnetic field on free convection of nanofluid in a porous medium is presented by 9 . The effects of heat transfer on MHD nanofluid in a porous semi annulus has investigated by 10 using numerical methods.…”
Casson nanofluid, unsteady flow over an isothermal vertical plate with Newtonian heating (NH) is investigated. Sodium alginate (base fluid)is taken as counter example of Casson fluid. MHD and porosity effects are considered. Effects of thermal radiation along with heat generation are examined. Sodium alginate with Silver, Titanium oxide, Copper and Aluminum oxide are added as nano particles. Initial value problem with physical boundary condition is solved by using Laplace transform method. Exact results are obtained for temperature and velocity fields. Skin-friction and Nusselt number are calculated. The obtained results are analyzed graphically for emerging flow parameters and discussed. It is bring into being that temperature and velocity profile are decreasing with increasing nano particles volume fraction.
“…Enhancement of heat transfer employing ns is important in a multitude of heat exchange equipment [3][4][5][6][7][8][9][10][11][12][13][14][15][16]. It is clear from the literature review that the research has been greatly focused on the theoretical and experimental thermal analysis of both solid ns and porous ns with different pro les and thermophysical properties due to wide range of applications [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34], also see the refs [35][36][37][38][38][39][40][41][42][43][44] to receive more information.…”
Section: Preliminaries and Problem Formulationmentioning
In this paper, the problem of determining heat transfer from convecting-radiating fin of triangular and concave parabolic shapes is investigated.We consider one-dimensional, steady conduction in the fin and neglect radiative exchange between adjacent fins and between the fin and its primary surface. A novel intelligent computational approach is developed for searching the solution. In order to achieve this aim, the governing equation is transformed into an equivalent problem whose boundary conditions are such that they are convenient to apply reformed version of Chebyshev polynomials of the first kind. These Chebyshev polynomials based functions construct approximate series solution with unknown weights. The mathematical formulation of optimization problem consists of an unsupervised error which is minimized by tuning weights via interior point method. The trial approximate solution is validated by imposing tolerance constrained into optimization problem. Additionally, heat transfer rate and the fin efficiency are reported.
“…Ahmad and Pop [16] investigated the mixed convection flow through a vertical flat plate filled with nanofluids and porosity from a porous media, and they reported that two branches appeared, which are termed the lower and upper branches defined to the curves where the critical point of mixed convection parameter occurs. Sheikholeslami et al [17] worked on nanofluid in porous media with magnetoyhydrodynamic transportation. In this study, they considered CuO-water as the nanoparticles in a porous cavity, and models of Darcy and Koo-Kleinstreuer-Li approach (KKL) were used to solve porous media and nanofluid, respectively.…”
The study of hybrid nanofluid and its thermophysical properties is emerging since the early of 2000s and the purpose of this paper is to investigate the flow of hybrid nanofluid over a permeable Darcy porous medium with slip, radiation and shrinking sheet. Here, the hybrid nanofluid consists of Cu/water as the base nanofluid and Al2O3–Cu/water works as the two distinct fluids. The governing ordinary differential equations (ODEs) obtained in this study are converted from a series of partial differential equations (PDEs) by the appropriate use of similarity transformation. Two methods of shooting and bvp4c function are applied to solve the involving physical parameters over the hybrid nanofluid flow. From this study, we conclude that the non-uniqueness of solutions exists through a range of the shrinking parameter, which produces the problem of finding a bigger solution than any other between the upper and lower branches. From the analysis, one can observe the increment of heat transfer rate in hybrid nanofluid versus the traditional nanofluid. The results obtained by the stability of solutions prove that the upper solution (first branch) is stable and the lower solution (second branch) is not stable.
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