MHD free convection-radiation interaction in a porous medium - part II : Soret/Dufour effects

This paper is focused on the study of two dimensional steady magnetohydrodynamics heat and mass transfer by laminar free convection from a radiative horizontal circular cylinder in a nonDarcy porous medium by taking account the Soret/Dufour effects. The boundary layer equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller–Box finite-difference scheme. Numerical results obtained for the velocity, temperature and concentration distributions, as well as the local skin friction, Nusselt number and Sherwood number for several values of the parameters, namely the buoyancy ratio parameter, Prandtl number, Forchheimer number, magnetohydrodynamic body force parameter, Soret and Dufour numbers. The dependency of the thermophysical properties has been discussed on the parameters and showed graphically. Increasing Forchheimer inertial drag parameter reduces velocity but elevates temperature and concentration. Increasing Soret number and simultaneously reducing Dufour number greatly boosts the local heat transfer rate at the cylinder surface. A comparative study between the previous published and present results in a limiting sense is found in an excellent agreement

Free and forced convection around line sources of heat and heated cylinders in porous media

An analysis is presented for the steady, two-dimensional, free convection around line sources of heat and heated cylinders in unbounded saturated porous media. It is extended to account also for the effects of forced convection. The study is based on the Boussinesq equations, with the velocities calculated using Darcy's law. The analysis begins with the non-dimensional formulation and numerical solution of the problem of pure free convection around a line source of heat. When this analysis is extended to include the effects of forced convection, two parameters appear in the non-dimensional formulation: the non-dimensional value, V/sub infin/, of the free-stream velocity and its angle gamma of inclination with respect to the vertical. We first describe the asymptotic form of the solution for large and small values of the distance to the source. The far-field description, which is also applicable to the flow around heated cylinders, is needed to facilitate the numerical solution of the problem. It includes a thermal wake, aligned with the free stream, and an outer irrotational flow with a sink and a vortex at the line source. The temperature distribution near the source involves a constant A/sub 0/(V/sub infin/, gamma), to be calculated with the numerical solution of the complete problem, which is used in the evaluation of the heat transfer from heated cylinders when the Rayleigh and Peclet numbers are small compared with unity. In this case we find an inner region where heat conduction is dominant, and an outer region where the cylinder appears as a line source of heat. The asymptotic analysis is complemented with the numerical solution of the general problem for circular cylinders with a wide range of Rayleigh numbers and some representative values of V/sub infin/ and gamma. We give correlations for the Nusselt number in the limiting cases of pure free convection and pure forced convectio

Effects of Conjugate Heat Transfer on Steady MHD Mixed Convective Heat Transfer Flow over a Thin Vertical Plate Embedded in a Porous Medium with High Porosity

This study investigates mixed convection heat transfer about a thin vertical plate in the presence of magneto and conjugate heat transfer effects in the porous medium with high porosity. The fluid is assumed to be incompressible and dense. The nonlinear coupled parabolic partial differential equations governing the flow are transformed into the nonsimilar boundary layer equations, which are then solved numerically using the Keller box method. The effects of the conjugate heat transfer parameter p, the porous medium parameter k1, the Forchheimer parameter F*, the mixed convection parameter Ri, the magnetic parameter Mn, and the electric field parameter E1 on the velocity and temperature profiles as well as on the local skin friction and local heat transfer are presented and analyzed. The validity of the methodology and analysis is checked by comparing the results obtained for some specific cases with those available in the literature

Network Simulation of Laminar Convective Heat and Mass Transfer over a Vertical Slender Cylinder with Uniform Surface Heat and Mass Flux

The steady, laminar axisymmetric convective heat and mass transfer in boundary layer flow over a vertical thin cylindrical configuration in the presence of significant surface heat and mass flux is studied theoretically and numerically. The governing boundary-layer equations for momentum, energy and species conservation are transformed from a set of partial differential equations in a (x,r) coordinate system to a () system using a group of similarity transformations. The resulting equations are solved using the Network Simulation Method (NSM) for the buoyancy-assisted pure free convection and also the pure forced convection cases, wherein the effects of Schmidt number, Prandtl number and surface mass parameter on velocity, temperature and concentration distributions in the regime are presented graphically and discussed. For the buoyancy-assisted pure free convection case, nondimensional velocity (f/) is found to increase with a rise in surface mass transfer (S) but decrease with increasing Prandtl number (Pr), particularly in the vicinity of the cylinder surface (small radial coordinate, ). Dimensionless temperature () decreases however with increasing S values from the cylinder surface into the free stream; with increasing Prandtl number, temperature is strongly reduced, with the most significant decrease at the cylinder surface. Dimensionless concentration () is decreased continuously throughout the boundary layer regime with an increase in S; conversely is enhanced for all radial coordinate values with an increase in Prandtl number. For the pure forced convection case, velocity increases both with dimensionless axial coordinate () and dimensionless radial coordinate () but decays smoothly with increasing Prandtl number and increasing Schmidt number, from the cylinder surface to the edge of the boundary layer domain. The model finds applications in industrial metallurgical processes, thermal energy systems, polymer processing, etc

Finite element computation of transient dissipative double diffusive magneto-convective nanofluid flow from a rotating vertical porous surface in porous media

This paper aimed to investigate the transient dissipative MHD double diffusive free convective boundary layer flow of electrically-conducting nanofluids from a stationary or moving vertical porous surface in a rotating high permeability porous medium, considering buoyancy, thermal radiation and first order chemical reaction. Thermo-diffusion (Soret) and diffuso-thermal (Dufour) effects are also considered. Darcy’s law is employed. The mathematical model is formulated by considering water-based nanofluids containing metallic nano-particles for both stationary and moving plate cases. Three nanofluids are examined, namely copper, aluminium oxide or titanium oxide in water. The transformed non-linear, coupled, dimensionless partial differential equations describing the flow are solved with physically appropriate boundary conditions by using Galerkin weighted residual scheme. For prescribed permeability, numerical results are presented graphically for the influence of a number of emerging parameters. Validation of finite element solutions for skin friction and Nusselt number is achieved via comparison with the previously published work as special cases of the present investigation and very good correlation obtained. Increasing rotational parameter is observed to reduce both primary and secondary velocity components. Primary and secondary velocities are consistently elevated with increasing Soret, Dufour, thermal Grashof and solutal Grashof numbers. Increasing Schmidt number, chemical reaction and suction parameter both suppress nano - particle concentration whereas the converse behavior is computed with increasing Soret number. The study is relevant to high temperature rotating chemical engineering systems exploiting magnetized nanofluids and also electromagnetic nanomaterial manufacturing processes

Modeling magnetic nanopolymer flow with induction and nanoparticle solid volume fraction effects : solar magnetic nanopolymer fabrication simulation

A mathematical model is presented for the nonlinear steady, forced convection, hydromagnetic flow of electro-conductive magnetic nano-polymer with magnetic induction effects included. The transformed two-parameter, non-dimensional governing partial differential equations for mass, momentum, magnetic induction and heat conservation are solved with the local non-similarity method (LNM) subject to appropriate boundary conditions. Keller’s implicit finite difference “box” method (KBM) is used to validate solutions. Computations for four different nanoparticles and three different base fluids are included. Silver nanoparticles in combination with various base fluids enhance temperatures and induced magnetic field and accelerate the flow. An elevation in magnetic body force number decelerates the flow whereas an increase in magnetic Prandtl number elevates the magnetic induction. Furthermore, increasing nanoparticle solid volume fraction is found to substantially boost temperatures. Applications of the study arise in advanced magnetic solar nano-materials (fluids) processing technologies

Energy conservation of bio-nanofluids past a needle in the presence of Stefan blowing : lie symmetry and numerical simulation

Thermal energy management associated with the transmission of heat is one of the main problems in many industrial setups (e.g. pharmaceutical, chemical and food) and bioengineering devices (e.g. hospital ventilation, heating, cooling devices, heat exchanger and drying food, etc). The current study aims to examine thermo-bioconvection of oxytactic microorganisms taking place in a nanofluid-saturated needle with the magnetic field. Stefanblowing is applied. The leading equations of continuity, momentum and energy, species transport equations for oxygen concentration and population density of microorganisms are reduced dimensionless and Lie symmetry group transformations are used to generate appropriate invariant transformations. The resulting similarity boundary value problem (in which the blowing parameter is coupled with concentration) have been simulated using MATLAB (2015a) bvp5c built in function. The impact of the emerging factors on the nondimensional velocity, temperature, nanoparticle concentration and motile microorganism density functions and their slopes at the wall, are pictured and tabulated. Justification with published results are included. It is found that all physical quantities decrease with Stefan blowing and increase with power law index parameter. With elevation in magnetic field parameter i.e., Lorentzian drag force, the friction factor reduces while the local Nusselt number, local Sherwood number, and the local motile microorganism density wall gradient increase. Present study could be used in food and pharmaceutical industries, chemical processing equipment, fuel cell technology, enhanced oil recovery, etc

Computation of bio-nano-convection power law slip flow from a needle with blowing effects in a porous medium

Transport phenomena with fluid flow, heat, mass, nanoparticle species and microorganism transferexternal to a needle in a porous medium have many biomedical engineering applications (e. g.hypodermic needles used in hemotology). It is also used to design many biomedical engineeringequipments and coating flows with bio-inspired nanomaterials. Coating flows featuringcombinations of nanoparticles and motile micro-organisms also constitute an important applicationarea. A mathematical model for convective external boundary layer flow of a power-law nanofluidcontaining gyrotactic micro-organisms past a needle immersed in a Darcy porous medium isdeveloped. Multiple slips boundary conditions and Stefan blowing effects at the needle boundaryare taken into account. The model features a reduced form of the conservation of mass, momentum,energy, nanoparticle species and motile micro-organism equations with appropriate coupledboundary conditions. The governing nonlinear partial differential equations (NPDEs) areconverted to dimensionless form and appropriate invariant transformations are applied to obtainsimilarity ordinary differential equations (SODE). The transformed equations have been solvednumerically using the in-built Matlab bvp4c function. The influence of the emerging parameterson the dimensionless velocity, temperature, nanoparticle concentration, motile micro-organismdensity functions, skin friction, heat, mass, and micro-organism transfers) are discussed in detail.It is found that velocity decreases whilst temperature, concentration, and density of motile microorganism increase with an increase in blowing parameter for shear thinning (pseudoplastic),Newtonian, and shear thickening (dilatant) fluids. It is also found that skin friction, Nusselt number(dimensionless heat transfer rate), Sherwood number (dimensionless nanoparticle mass transferrate) and motile micro-organism wall density gradient decrease with increasing blowing, Darcy,power law and needle size parameters. Comparison with the earlier published results is alsoincluded and an excellent agreement is obtained

Investigation of flow and heat transfer in a large-scale spent nuclear fuel cooling pond

The recent focus on nuclear power has led to the need for more efficient and economical methods of operating the Spent Nuclear Fuel (SNF) cooling ponds as well as complying with the strict safety and environmental legislations imposed by the IAEA and the UK Government. Like many other industrial applications, the design and operation of the SNF cooling ponds have evolved from experience; trial and error. Since the stored materials in such ponds are radioactive, it is very difficult to perform experimental studies. As a result, a rigorous scientific study based on fundamental principles has to be performed. The present research explores analytically and numerically the main processes that take place across the pond installation. The body of the present study includes four main parts: the first part is involved in modelling the heat loss from the free water surface, mainly due to evaporation, using analytical and single-phase numerical approaches, which represents a critical factor in the modelling of the large-scale cooling ponds. The predicted results were in good agreement with experimental data available in open literature. In the second part, a thermal model using Microsoft Excel spreadsheet was developed for the cooling pond based on an analytical approach. The well-mixed hypothesis was adopted to describe the water zone as well as the humid air zone. Also, the ventilation system was considered within this model. The developed spreadsheet tool was validated against reliable data available for Maine Yankee pool as well as temperature measurements collected from the Sellafield site. This spreadsheet tool is able to describe the transient behaviour with low computational cost, allowing many "what-if" scenarios to be rapidly investigated. In the third part, Computational Fluid Dynamics (CFD) was used to model the cooling pond at both macro and micro levels. The macro level modelling involved in developing a CFD model for Sellafield’s cooling pond where the fuel regions were approximated to porous medium. The computational domain was produced for the water zone only, where the humid air zone was introduced to the model by coupling of the spreadsheet model with the CFD model. This model was validated and used to examine the distribution of water temperature to confirm the reliability of the adopted well-mixed approach in the analytical model. The outcomes from the CFD and spreadsheet models were used to provide some boundary conditions to the micro-level model of the fuel assemblies. The modelling methodology of the fuel assemblies was partially validated with experimental data for heat transfer around vertical cylinder. The maximum temperature of the water within the rack arrangement was determined under various conditions and a correlation was proposed. Finally, a sensitivity study was performed using Taguchi method and the statistical method of ANOVA to assess the influence of the cooling systems as well as the environmental conditions on the thermal performance of the cooling pond. The spreadsheet model was implemented to carry out the calculations. The outcomes from this study were presented in the form of recommendations that may be able to aid the organisation to manage their cooling pond more efficiently and safely during the normal operating conditions as well as recovery from an accident scenario

Self-sculpting of a dissolvable body due to gravitational convection

© 2018 American Physical Society. Natural sculpting processes such as erosion or dissolution often yield universal shapes that bear no imprint or memory of the initial conditions. Here we conduct laboratory experiments aimed at assessing the shape dynamics and role of memory for the simple case of a dissolvable boundary immersed in a fluid. Though no external flow is imposed, dissolution and consequent density differences lead to gravitational convective flows that in turn strongly affect local dissolving rates and shape changes, and we identify two distinct behaviors. A flat boundary dissolving from its lower surface tends to retain its overall shape (an example of near perfect memory) while bearing small-scale pits that reflect complex near-body flows. A boundary dissolving from its upper surface tends to erase its initial shape and form an upward spike structure that sharpens indefinitely. We propose an explanation for these different outcomes based on observations of the coupled shape dynamics, concentration fields, and flows