MHD flow in a vertical channel under the effect of temperature dependent physical parameters

Mixed convective flow in a vertical channel filled with electrically conducting viscous fluid with isothermal wall conditions is investigated for variable properties. The combined effects of temperature dependent viscosity and temperature dependent thermal conductivity are analyzed. The solutions are obtained both analytically by perturbation method and numerically by Runge–Kutta method with shooting technique. The dimensionless governing parameters affecting velocity and temperature fields are variable viscosity parameter (−0.5 ≤ bν ≤ 0.5), variable thermal conductivity parameter (−0.5 ≤ bk ≤ 0.5), Hartmann number (1 ≤ M ≤ 3), applied electric field parameter (E0 = ±1, 0), wall temperature ratio parameter (−2 ≤ m ≤ 2) and buoyancy parameter (0 < N ≤ 1.5). For some limiting cases, the obtained results are validated by comparing with those available from the existing literature. Correlations for skin friction and Nusselt number in terms of governing parameters are developed

Heat transfer of chemically reacting mixed convection fluid using convective surface condition: Non-Darcy model

This work reports the study of mixed convection of permeable fluid with Robin conditions in the vertical channel including the effects of chemical reactions. The fluid transport is designed by the Darcy-Forchheimer-Brinkman model. The series method is adopted for approximate solutions for governing equations considering the Brinkman number as the perturbation characteristic whose outcomes correspond to magnitudes of Brinkman number less than one. Adopting a numerical scheme followed by fourth order Runge–Kutta algorithm with shooting method, the solutions for bigger magnitudes of the Brinkman number are obtained. The present results for limiting cases are compared with the literature and good agreement is seen. For various values of thermal and mass Grashof numbers, porous parameter, inertial parameter, Darcy number and first order chemical reaction the problem is resolved for the same and distant Biot numbers reflecting the border temperatures symmetric and asymmetric. Finally, the outcomes are tabulated for wall friction parameters, Nusselt and Sherwood numbers for innovated parameters. It is noticed that enhancing buoyancy and dissipations, thermal Grashof number helps to improve the flow rate for all values of Biot number. The Schmidt and Soret parameters can improve concentration patterns. Nusselt number can be improved with thermal Grashof number and Brinkman number and it is dropped with inertia and porous parameters. The solutions have a very good agreement with Zanchini data without mass Grashof number

Double diffusion in a rectangular duct using metals or oxides suspended in a viscous fluid

In this study, double diffusive free convection of nanofluid within a confined rectangular duct is investigated numerically. The momentum and energy equations are placed in the form of difference equations and solved numerically. The left wall conditions for the concentration and temperature are lesser than those of the right wall and the upper and lower walls are insulated. Different nanofluids are considered such as mixtures with copper, diamond, silicon oxide and titanium oxide, suspended in water. Brinkman and Maxwell models are used to characterize the nanofluid. Tiwari and Das model is opted to define the nanofluid behavior. The simulations are conducted using different nanoparticles, thermal Grashof number 1 ≤ GrT ≤ 20, solute Grashof number 1 ≤ GrC ≤ 15, solid volume fraction 0 ≤ Φ ≤ 0.05, Dufour number 0 ≤ Df ≤ 1, Brinkman number 0 ≤ Br ≤ 2, and Soret number 0 ≤ Sr ≤ 5. Additionally, behavior of volumetric flow strength, skin friction, heat transport intensity and Sherwood number is also examined. The thermal Grashof number, Brinkman number, Dufour, Soret and Schmidt parameters accelerate the velocity and temperature and dwindle the concentration whereas the reversal effect was obtained for the solid volume fraction. The concentration Grashof number diminishes the velocity and temperature and intensifies the concentration. The silver nanoparticles produce the highest velocity whereas diamond nanoparticles cause the lowest velocity and temperature. The maximum temperature is attained with silicon oxide

Chemical reaction influence on nanofluid flow in a porous layer: Stability analysis

An influence of exothermic chemical reaction on the natural thermo-solutal convection in a horizontal channel filled with sparsely packed permeable nanofluid is investigated. It is assumed that the fluid viscosity is different from the effective viscosity. The Brinkman approach is engaged for the porous material, while the nanofluid approach features the Buongiorno model. To figure out the stability of the linear terms, normal mode analysis is opted. Galerkin technique is selected to work out the nonlinear terms. The Rayleigh number and its relevant wave numbers are assessed for all dimensionless parameters and exposed in the form of graphs. It is found that there is a critical value of Frank – Kamenetskii number at which the system is most unstable. It is found that increasing the viscosity ratio delays the onset of convection. With exothermic chemical reactions, the fluid in the porous medium is more prone to instability as compared to the case in which chemical reactions are absent. A critical value of Frank – Kamenetskii number is also identified at which the system is most unstable, and this is shown to be independent of both porous media parameter and the viscosity ratio. Applications of the study arise in nano-doped geothermal energy extraction, chemical and bio reactors and other engineering systems

Heat transfer of viscous fluid in a vertical channel sandwiched between nanofluid porous zones

Mixed convection in vertical parallel channels is analyzed with the viscous fuid sandwiched between nanofuids within porous material flled in a vertical channel. The concept of single-phase transport of nanofuids is employed to defne the nanofuid fow and heat transfer and the Darcy approach is incorporated to describe the circulation within the porous material. Formulated ordinary diferential equations which are non-linear and coupled along with the corresponding boundary and interface conditions are solved by the regular perturbation method. The main objective is to investigate the efects of the Grashof and Brinkman numbers, solid volume fraction, porous parameter on the velocity and temperature felds. Results are shown in the graphical and tabular form. The physical characteristics governing the fow such as skin friction and rate of heat transfer are also investigated considering fve diferent materials of nanoparticles

Computation of swirling hydromagnetic nanofluid flow containing gyrotactic microorganisms from a spinning disk to a porous medium with hall current and anisotropic slip effects.

Prompted by the advancements in hybrid bio-nano-swirling magnetic bioreactors, a mathematical model for the swirling flow from a rotating disk bioreactor to a magnetic fluid saturating a porous matrix and containing nanoparticles and gyrotactic micro-organisms has been developed. An axial magnetic field is administered which is perpendicular to the disk and Hall currents are included. The disk is assumed to be impervious and stretches in the radial direction with a power-law velocity. The Buongiorno nanoscale, Kuznetsov bioconvection and Darcy porous media models are deployed. Anisotropic momentum, thermal, nanoparticle concentration and motile micro-organism slip effects are incorporated. Stefan blowing is also simulated. The governing conservation equations are transformed with appropriate variables to ordinary nonlinear differential equations. MATLAB bvp4c shooting quadrature is used to solve the emerging nonlinear, coupled ordinary differential boundary value problem under transformed boundary conditions. Verification with earlier solutions for the non-magnetic Von Karman bioconvection nanofluid case is conducted. Further validation of the general magnetic model is conducted with the Adomian decomposition method (ADM). Extensive visualization of velocity, temperature, nanoparticle concentration and motile microorganism density number profiles is presented for the impact of various parameters including magnetic interaction parameter, Hall current parameter, Darcy number, momentum slip, thermal slip, nanoparticle slip and microorganism slip. Computations are also performed for skin friction, Nusselt number, Sherwood number and motile micro-organism density number gradient. The simulations provide a useful benchmark for further studies

Linear Model for Two-Layer Porous Bed Suspended with Nano Sized Particles

Two immiscible fluids flows are materialized in science and technology; the combined convection of the two immiscible fluids in a square conduit is reviewed in this study. The nanofluid and pure viscous fluid which do not mix are discussed, and both layers saturated with a porous matrix have different permeabilities. The Dupuit–Forchheimer and Tiwari–Das models are applied to outline the permeability of the layer and nanofluids, respectively. The finite difference method is utilized to find the solutions of conservation equations along with suitable boundary and interface conditions. The boundary condition for the velocity is no slip at all the boundaries, while continuity of velocity and shear stress are used at the interface. The left and right walls are kept at constant but different temperatures, the top and bottom walls are isolated, and the continuity of temperature and heat flux is assumed at the interface. Grashof number, Brinkman number, Darcy number, inertia parameter, permeability ratio, solid volume fraction, thermal conductivity and viscosity ratios, different nanoparticles, and various base liquids of the two-layered fluids are engaged. The velocity is depleted by the inertia and viscosity ratio while it is accelerated with the Darcy and Grashof numbers. The energy distribution was not modulated significantly with any of the dimensionless numbers. Using copper nanoparticles doped in mineral oil and ethylene glycol produced the peak momentum. Diamond nanoparticles dropped in water catalysis showed the best heat transfer rate

Soret effects on the mixed convection flow using Robin boundary conditions

An investigation has been undertaken as Soret an

Unsteady natural convection with temperature-dependent viscosity in a square cavity filled with a porous medium

A numerical investigation is implemented on the unsteady natural convection with a temperature-dependent viscosity inside a square porous cavity. The vertical walls of the cavity are kept at constant but different temperatures, while the horizontal walls are adiabatic. The mathematical model formulated in dimensionless stream function, vorticity and temperature variables is solved using implicit finite difference schemes of the second order. The governing parameters are the Rayleigh number, Darcy number, viscosity variation parameter and dimensionless time. The effects of these parameters on the average Nusselt number along the hot wall as well as on the streamlines and isotherms are analyzed. The results show an intensification of convective flow and heat transfer with an increase in the viscosity variation parameter for the porous media, while in the case of pure fluid, the effect is opposite