Similarity solution for induced magnetic field boundary layer flow of metallic nanofluids via convectively inclined stationary/moving flat plate: Spectral relaxation computation

Abstract

The present article describes a mathematical model for incompressible free convection flow with convective heat transport from an inclined stationary/moving flat plate under impact of induced magnetic field (IMF). The current flow model is formulated to consider different water-based nanofluids with metallic nanoparticles (Copper and Silver). Effectively a nanoscale formulation with the Tiwari-Das model deployed to study material properties for specific nanoparticles and base fluid. A similarity solution is obtained for non-dimensional form via similarity transformation rendered from basic flow equations for which numerical simulations utilizing the Spectral Relaxation Method (SRM). SRM is a simple iteration scheme that does not require any evaluation of derivatives, perturbation and linearization for solving non-linear system of equations. Graphical results for linear velocity, IMF, temperature, skin friction and Nusselt number distributions are presented for the different metallic-aqueous nanofluid cases as well as stationary/moving flat plate. The results are verified for limiting cases by comparing with various investigators for the case of stationary as well as moving flat plate and found to be in excellent agreement. Furthermore, computed numerical results for skin friction and Nusselt number for different emerging parameters in case Cu and Ag nanofluids for moving plate which are tabulated and discussed in detail.Nomenclature: Bi, biot number; 𝑐, constant; C f , skin friction coefficient; 𝐷, differentiation matrix in spectral algorithm; 𝑓, dimensionless stream function; f ′ , dimensionless velocity; g, dimensionless magnetic induction stream function; g ′ , dimensionless induced magnetic field stream function gradient; F r+1 (𝜂), current iteration level of dimensionless velocity; G r+1 (𝜂)), current iteration level of dimensionless magnetic stream function; Gr , grashof number; H 1 , H 2 , dimensional magnetic stream function components; h f , heat transfer coefficient (𝑊∕𝑚 2 𝐾); 𝐾, thermal conductivity (𝑊∕𝑚𝑘); 𝑀, magnetic body force number; 𝑁, collocation points deployed in spectral method; Nu x , local Nusselt number; Pr, Prandtl number; 𝑃𝑟 𝑚 , magnetic Prandtl number; Re x , local Reynolds number; 𝑇, magnetic nanofluid temperature (K); 𝑇 𝑓 , hot fluid temperature (K); T ∞ , temperature in the free stream (K); 𝑈, velocity of the free stream (at boundary layer edge); U w , velocity of moving wall (sheet); 𝑢, 𝑣, dimensional velocity components along the x-axis and y-axis, respectively (m/s) Greek: 𝛼, angle of inclination; 𝛼 1 , magnetic diffusivity (𝑚 2 ∕𝑠); 𝛽, thermal expansion coefficient; 𝜆, moving wall velocity parameter; 𝜂, dimensionless similarity variable (transverse coordinate),; 𝜂 ∞ , infinity value (to edge of boundary layer domain); 𝜌, density (𝑘𝑔∕𝑚 3 ); 𝜎, electrical conductivity (𝑆𝑚 −1 ); 𝜌𝐶 𝑝 , heat capacity (𝐽∕𝐾); 𝜌𝛽, thermal diffusivity (𝑚 2 ∕𝑠); θ

MHD natural convection heat and mass transfer flow over an inclined porous plate with thermophoresis and nonlinear thermal radiation effects

“…Jha and Samaila 7 recently in their study of the thermal radiation impact on buoyancy‐driven flow past a vertical plate stated that the boundary layer thickness is a diminishing function of the Prandtl number. Some works associated with this study can be seen in Acharya, 8 Akter et al, 9 and Shamshuddin et al 10,11 …”

“…Jha and Samaila 7 recently in their study of the thermal radiation impact on buoyancy-driven flow past a vertical plate stated that the boundary layer thickness is a diminishing function of the Prandtl number. Some works associated with this study can be seen in Acharya, 8 Akter et al, 9 and Shamshuddin et al 10,11 The radiative is significant in space industries such as space vehicles, satellites, and some engineering practices which require high working temperature. Moreover, at substantially high temperatures, thermal radiation can influence heat transfer, temperature curves and in turn promote fluid formation.…”

Heat and mass transfer through MHD Darcy Forchheimer Casson hybrid nanofluid flow across an exponential stretching sheet

“…The upshot of an induced magnetic field on metallic nanoliquids flow over an inclined moving surface was reported by Akter et al. [23]. Shamshuddin et al.…”

“…The magnetized fluid flow across a Riga plate was studied by Shamshuddin et al [22]. The upshot of an induced magnetic field on metallic nanoliquids flow over an inclined moving surface was reported by Akter et al [23]. Shamshuddin et al [24] computationally assessed the steady 2-D nanoliquid flow with the impact joule heating over an exponentially stretching sheet.…”

Viscoelastic boundary layer analysis of constant surface temperature plate embedded in saturated porous media

“…An excellent agreement was found for limiting cases of stationary in addition to moving flat plates. 25 A micropolar fluid medium channel in the existence of mixed and nonlinear convection under consideration of thermal radiation and species reactive agents was investigated theoretically. Using suitable similarity variables with the Runge-Kutta-Fehlberg method, the governing equations were transformed and the resultant equations were solved numerically.…”