Simulation of natural convection heat transfer in a 2-D trapezoidal enclosure

Natural convection within trapezoidal enclosures finds significant practical applications. The natural convection flows play a prominent role in the transport of energy in energy-related applications, in case of proper design enclosures to achieve higher heat transfer rates. In the present study, a two-dimensional cavity with adiabatic right side wall is studied. The left side vertical wall is maintained at the constant hot temperature and the top slat wall is maintained at cold temperature. The dimensionless governing partial differential equations for vorticity-stream function are solved using the finite difference method with incremental time steps. The parametric study involves a wide range of Rayleigh number, Ra, 10(3)<ra<10(5) and Prandtl number (Pr=0.025, 0.71 and 10). The fluid flow within the enclosure is formed with different shapes for different Pr values. The flow rate is increased by enhancing the Rayleigh number (Ra=10(4)). The numerical results are validated with previous results. The governing parameters in the present article, namely Rayleigh number and Prandtl number on flow patterns, isotherms as well as local Nusselt number are reported

Melting heat transfer analysis on magnetohydrodynamics buoyancy convection in an enclosure : a numerical study

Therollof melting heat transfer on magnetohydrodynamic natural convection in a square enclosurewithheatingof the bottom wall is examinednumericallyin this article.The dimensionlessgoverning partial differential equations are transformed into vorticity and stream functionformulationand then solved using the finite difference method(FDM). The effects of thermal Rayleigh number(Ra), melting parameter(M) and Hartmann number(Ha) are illustrated graphically.With an increasing melting parameter and Rayleigh number, the rate of fluid flow and temperature gradients are seen to increase. And in the presence of magnetic field, the temperature gradient reduces and hence the conductionmechanism dominated for larger Ha. Greater heat transfer rate is observed in the case of uniform heating compared with non-uniform case. The average Nusselt number reduces with increasing magnetic parameterin the both cases of heating of bottom wall

Computation of Eyring-Powell micropolar convective boundary layer flow from an inverted non-isothermal cone : thermal polymer coating simulation

Thermal coating of components with non-Newtonian materials is a rich area of chemical and process mechanical engineering. Many different rheological characteristics can be simulated for such coatings with a variety of different mathematical models. In this work we study the steady-state coating flow and heat transfer of a non-Newtonian liquid (polymer) on an inverted isothermal cone with variable wall temperature. The Eringen micropolar and three-parameter Eyring-Powell models are combined to simulate microstructural and shear characteristics of the polymer. The governing partial differential conservation equations and wall and free stream boundary conditions are rendered into dimensionless form and solved computationally with the KellerBox finite difference method (FDM). Validation with earlier Newtonian solutions from the literature is also included. Graphical and tabulated results are presented to study the variations of fluid velocity, micro-rotation (angular velocity), temperature, skin friction, wall couple stress (micro-rotation gradient) and wall heat transfer rate. With increasing values of the first Eyring-Powell parameter temperatures are elevated, micro-rotation is suppressed and velocities are enhanced near the cone surface but reduced further into the boundary layer. Increasing values of the second Eyring-Powell parameter induce strong flow deceleration, decrease temperatures but enhance micro-rotation values. An increase in non-isothermal power law index suppresses velocities, temperatures and micro-rotations i.e. all transport characteristics are maximum for the isothermal case (n =0). Increasing Eringen vortex viscosity parameter significantly enhances temperatures and also micro-rotations. The present numerical simulations find applications in thermal polymer coating operations and industrial deposition techniques and provide a useful benchmark for more general computational fluid dynamics (CFD) simulations

Melting heat transfer analysis of electrically conducting nanofluid flow over an exponentially shrinking/stretching porous sheet with radiative heat flux under magnetic field

Modern magnetic nanomaterials processing operations are progressing rapidly and require increasingly sophisticated mathematical models for their optimization. Stimulated by such developments, in this article, a theoretical and computational study of steady magnetohydrodynamic (MHD) flow of nanofluid from an exponentially stretching/shrinking permeable sheet with melting (phase change) and radiative heat transfer is presented. Wall transpiration i.e. suction and blowing (injection) is included. Buongiorno’s nanofluid model is deployed which simulates the effects of Brownian motion and thermophoresis. The transport equations and boundary conditions are normalized via similarity transformations and appropriate variables and similarity solutions are shown to depend on the transpiration parameter. The emerging dimensionless nonlinear coupled ordinary differential boundary value problem is solved numerically with the Newton-Fehlberg iteration technique. Validation with special cases from the literature is included. Increasing magnetic field i.e. Hartmann number is observed to elevate nanoparticle concentration and temperature whereas it damps the velocity. Higher values of melting parameter consistently decelerate the boundary layer flow and suppress temperature and nanoparticle concentration. Higher radiative parameter strongly increases temperature (and thermal boundary layer thickness) and weakly accelerates the flow. Increasing Brownian motion reduces nanoparticle concentrations whereas greater thermophoretic body force strongly enhances them. Nusselt number and Sherwood number are decreased with increasing Hartmann number whereas they are elevated with stronger wall suction and melting parameter

Numerical simulation and energy flux vector visualization of radiative-convection heat transfer in a porous triangular enclosure

A detailed theoretical examination laminar natural convection heat flow in a triangular porous cavity with significant radiative heat transfer and porosity variation is presented. Twodimensional laminar incompressible flow is considered with the left slant and right walls are low and high temperature respectively, and the remaining (top) wall prescribed as adiabatic. The Darcy-Brinkman isotropic model is utilized, and the coupled governing equations are solved by a numerical method utilizing finite differences. Visualization of isotherms and streamlines is achieved with the method of Energy Flux Vectors (EFVs). The impacts of the different model parameters (Rayleigh number Ra, Darcy number-Da, porosity-E and radiation parameter-Rd) on the thermo fluid characteristics are studied in detail. The computations show that convective heat transfer is enhanced with greater Darcy parameter (permeability) which also leads to intensification in the density of energy flux vector patterns. The flow is accelerated with increasing buoyancy effect (Rayleigh number) and temperatures are also increased with greater radiative flux. Average Nusselt number is decreased with higher porosity. The simulations are relevant to hybrid porous media solar collectors

Numerical simulation and energy flux vector visualization of radiative-convection heat transfer in a porous triangular enclosure

A detailed theoretical examination laminar natural convection heat flow in a triangular porous cavity with significant radiative heat transfer and porosity variation is presented. Twodimensional laminar incompressible flow is considered with the left slant and right walls are low and high temperature respectively, and the remaining (top) wall prescribed as adiabatic. The Darcy-Brinkman isotropic model is utilized, and the coupled governing equations are solved by a numerical method utilizing finite differences. Visualization of isotherms and streamlines is achieved with the method of Energy Flux Vectors (EFVs). The impacts of the different model parameters (Rayleigh number Ra, Darcy number-Da, porosity-E and radiation parameter-Rd) on the thermo fluid characteristics are studied in detail. The computations show that convective heat transfer is enhanced with greater Darcy parameter (permeability) which also leads to intensification in the density of energy flux vector patterns. The flow is accelerated with increasing buoyancy effect (Rayleigh number) and temperatures are also increased with greater radiative flux. Average Nusselt number is decreased with higher porosity. The simulations are relevant to hybrid porous media solar collectors

Feasibility of the porous zone approach to modelling vegetation in CFD

Vegetation within stormwater ponds varies seasonly and its presence affects the flow field, which in turn affects the pond’s Residence Time Distribution and its effectiveness at pollutant removal. Vegetated flows are complex and, as a result, few suitable tools exist for evaluating realistic stormwater pond designs. Recent research has suggested using a porous zone to represent vegetation within a CFD model, and this paper investigates the feasibility of this approach using ANSYS Fluent. One of the main benefits of using a porous zone is the ability to derive the relevant parameters from the known physical characteristics of stem diameter and porosity using the Ergun equation. A sensitivity analysis on the viscous resistance factor 1/α1/α and the inertial resistance factor C2C2 has been undertaken by comparing model results to data collected from an experimental vegetated channel. Best fit values of C2C2 were obtained for a range of flow conditions including emergent and submerged vegetation. Results show the CFD model to be insensitive to 1/α1/α but very sensitive to values of C2C2. For submerged vegetation, values of C2C2 derived from the Ergun equation are under-predictions of best-fit C2C2 values as only the turbulence due to the shear layer is represented. The porous zone approach does not take into account turbulence generated from stem wakes such that no meaningful predictions for emergent vegetation were obtained. C2C2 values calculated using a force balance show better agreement with best-fit C2C2 values than those derived from the Ergun equation. Manually fixing values of kk and εε within the porous zone of the model shows initial promise as a means of taking stem wakes into account

Early motion and directed exercise (EMADE) versus usual care post ankle fracture fixation: study protocol for a pragmatic randomised controlled trial

Background: Following surgical fixation of ankle fractures, the traditional management has included immobilisation for 6 weeks in a below-knee cast. However, this can lead to disuse atrophy of the affected leg and joint stiffness. While early rehabilitation from 2 weeks post surgery is viewed as safe, controversy remains regarding its benefits. We will compare the effectiveness of early motion and directed exercise (EMADE) ankle rehabilitation, against usual care, i.e. 6 weeks’ immobilisation in a below-knee cast. Method/design: We have designed a pragmatic randomised controlled trial (p-RCT) to compare the EMADE intervention against usual care. We will recruit 144 independently living adult participants, absent of tissue-healing comorbidities, who have undergone surgical stabilisation of isolated Weber B ankle fractures. The EMADE intervention consists of a non-weight-bearing progressive home exercise programme, complemented with manual therapy and education. Usual care consists of immobilisation in a non-weight-bearing below-knee cast. The intervention period is between week 2 and week 6 post surgery. The primary outcome is the Olerud and Molander Ankle Score (OMAS) patient-reported outcome measure (PROM) at 12 weeks post surgery. Secondary PROMs include the EQ-5D-5 L questionnaire, return to work and return to driving, with objective outcomes including ankle range of motion. Analysis will be on an intention-to-treat basis. An economic evaluation will be included. Discussion: The EMADE intervention is a package of care designed to address the detrimental effects of disuse atrophy and joint stiffness. An advantage of the OMAS is the potential of meta-analysis with other designs. Within the economic evaluation, the cost-utility analysis, may be used by commissioners, while the use of patient-relevant outcomes, such as return to work and driving, will ensure that the study remains pertinent to patients and their families. As it is being conducted in the clinical environment, this p-RCT has high external validity. Accordingly, if significant clinical benefits and cost-effectiveness are demonstrated, EMADE should become a worthwhile treatment option. A larger-scale, multicentre trial may be required to influence national guidelines. Trial registration: ISRCTN, ID: ISRCTN11212729. Registered retrospectively on 20 March 2017

Nonparametric relevance-shifted multiple testing procedures for the analysis of high-dimensional multivariate data with small sample sizes

<p>Abstract</p> <p>Background</p> <p>In many research areas it is necessary to find differences between treatment groups with several variables. For example, studies of microarray data seek to find a significant difference in location parameters from zero or one for ratios thereof for each variable. However, in some studies a significant deviation of the difference in locations from zero (or 1 in terms of the ratio) is biologically meaningless. A relevant difference or ratio is sought in such cases.</p> <p>Results</p> <p>This article addresses the use of relevance-shifted tests on ratios for a multivariate parallel two-sample group design. Two empirical procedures are proposed which embed the relevance-shifted test on ratios. As both procedures test a hypothesis for each variable, the resulting multiple testing problem has to be considered. Hence, the procedures include a multiplicity correction. Both procedures are extensions of available procedures for point null hypotheses achieving exact control of the familywise error rate. Whereas the shift of the null hypothesis alone would give straight-forward solutions, the problems that are the reason for the empirical considerations discussed here arise by the fact that the shift is considered in both directions and the whole parameter space in between these two limits has to be accepted as null hypothesis.</p> <p>Conclusion</p> <p>The first algorithm to be discussed uses a permutation algorithm, and is appropriate for designs with a moderately large number of observations. However, many experiments have limited sample sizes. Then the second procedure might be more appropriate, where multiplicity is corrected according to a concept of data-driven order of hypotheses.</p