Flux Boundary Condition Research Articles

A numerical scheme for Darcy-Forchheimer flow of non-Newtonian nanofluid under the effects of convective and zero mass flux boundary conditions

This research aims to propose a numerical scheme for solving boundary value problems. It is a two-stage, third-order accurate scheme known as a predictorcorrector scheme. The two main results are finding the region of the scheme where it is stable and determining the stability criterion for a set of linearized first-order differential equations. In addition, a mathematical model for heat and mass transfer of Darcy-Forchheimer flow of non-Newtonian nanofluid over the sheet is presented. The similarity transformations reduce PDE into a system of ODE for easier manipulation. The results are compared with the past research and those obtained by MATLAB SOLVER BVP4C. The results show that the velocity profile slightly decays by enhancing the Weisenberg number.

MAGNETOHYDRODYNAMIC FLOW AND HEAT TRANSFER THROUGH A CIRCULAR TUBE FILLED WITH HOMOGENEOUS AND HETEROGENEOUS POROUS MEDIUM

In this paper, we study the laminar steady flow of incompressible viscous magnetohydrodynamic (MHD) fluid inside a circular tube filled with homogeneous/heterogeneous porous medium. A transverse uniform/nonuniform magnetic field is applied, along with a uniform heat flux boundary condition. The Brinkman equation is used to model the flow through the saturated porous medium. Exact solutions of velocity and temperature fields, friction factor, and Nusselt number (<i>Nu</i>) in terms of the shape parameter (σ) and Hartmann number (<i>M</i>) are presented. In the limit of the zero shape parameter and the absence of magnetic field, the Brinkman model results converge to the Hagen-Poiseuille flow solution of circular pipe flow. In the opposite limit of the infinite shape parameter and the absence of magnetic field, the solutions approach the Darcy model results. In terms of the hydro-thermal characteristics of the flow, the Poiseuille flow results and the Darcy model results are shown to serve as the lower and upper bounds, respectively. A significant increase in the heat transfer in heterogeneous porous medium with the nonuniform magnetic field (highest <i>Nu</i> = 12) compared to homogeneous porous medium with uniform magnetic field is identified (highest <i>Nu</i> = 8). We also validate the results of homogeneous and heterogeneous porous medium with uniform/nonuniform magnetic field using numerical solutions.

Effect of cooktop cone angle on the performance of thermosyphon heat transport device for indoor solar cooking – A numerical study

Solar cookers are less attractive as their outdoor operation is laborious. A recent innovation encouraged the thermosyphon heat transport device (THTD) based indoor solar cooking. However, the cooktop THTD design is still in the conceptual stage. Hence, in the present study, the cooktop THTD cone angle is optimized through the steady-state and transient analysis using an analytically validated CFD model. Six cooktop cone angles (0° to 75° in steps of 15°) were evaluated and found a drop in heat transfer fluid flow rate with an increase in the cooktop cone angle, due to the existence of recirculating loops, which is confirmed by velocity vector plots. Under concentrated solar flux boundary conditions, the transient analysis showcased the advantage of 15° model over 0° and 45° variants. The efficacy of cooktop THTD is proved as all three lower cone angle designs took a mere 180 s to boil 1 L of water.

STUDY OF THE MAGNETIC TAYLOR-COUETTE FLOW WITH THE AXIAL FLOW IN ROTATING MACHINERY UNDER QUADRUPOLE MAGNETIC FIELD

In this study, the effect of applying a magnetic field resulting from quadrupole magnets on the hydrodynamics and heat transfer in magnetic Taylor-Couette flow with axial flow was investigated numerically for the first time. The studied geometry consisted of two vertical concentric cylinders. The inner cylinder rotated at a specific angular velocity to create the Taylor-Couette flow, while the outer cylinder was stationary. The outer cylinder was also considered to be under constant heat flux boundary conditions. The magnetic nanofluid was a water-based nanofluid consisting of iron oxide nanoparticles with diameters of 8 nm and the magnetic field was produced by quadrupole magnets. The modeling of the problem was implemented by using the two-phase mixture model and control volume technique. The obtained results indicated that in the absence of a magnetic field and using our considered range of Taylor numbers, the flow consisted of many vortices, which is called the Taylor vortex flow. By applying the magnetic field, the ferrofluid flow was pushed toward the outer cylinder wall, which also considerably increased the stability of the flow. Moreover, by imposing the magnetic field, the local heat transfer coefficient increased and the heat transfer coefficient decreased as the Taylor number of the flow increased.

Optimal control of TGF-β to prevent formation of pulmonary fibrosis.

In this paper, three optimal control problems are proposed to prevent forming lung fibrosis while control is transforming growth factor-β (TGF-β) in the myofibroblast diffusion process. Two diffusion equations for fibroblast and myofibroblast are mathematically formulated as the system's dynamic, while different optimal control model problems are proposed to find the optimal TGF-β. During solving the first optimal control problem with the regulator objection function, it is understood that the control function gets unexpected negative values. Thus, in the second optimal control problem, for the control function, the non-negative constraint is imposed. This problem is solved successfully using the extended canonical Hamiltonian equations with no flux boundary conditions. Pontryagin's minimum principle is used to solve the related optimal control problems successfully. In the third optimal control problem, the fibroblast equation is added to a dynamic system consisting of the partial differential equation. The two-dimensional diffusion equations for fibroblast and myofibroblast are transferred to a system of ordinary differential equations using the central finite differences explicit method. Three theorems and two propositions are proved using extended Pontryagin's minimum principle and the extended Hamiltonian equations. Numerical results are given. We believe that this optimal strategy can help practitioners apply some medication to reduce the TGF-β in preventing the formation of pulmonary fibrosis.

Thermal performance analysis of Sutterby nanoliquid subject to melting heat transportation

In the recent years, nanotechnology has been widely used in several fields regarding its rapid developments which create a lot of prospects for researchers and engineers. More specifically, replacement of conventional liquid with nanofluid is considered as an innovative solution to heat transfer problems. Keeping aforesaid pragmatism of nanofluid in view, we considered a time-dependent mathematical model to formulate the heat sink-source based Sutterby nanofluid model under thermophoretic and Brownian movements. New mass flux and melting boundary conditions are used for heat/ mass transfer analyses. Moreover, Prandtl’s boundary-layer idea is employed for mathematical formulation. The leading nonlinear set of partial differential equations is transformed to nonlinear set of ordinary differential equations. Numeric outcomes are acquired through bvp4c algorithm, graphical results are found via MATLAB technique. Acquired numerical data shows that temperature of nanofluid boosts for greater thermophoretic and unsteady parameters. Intensification is measured in concentration distribution.

Numerical Study of Jet Impingement on Heated Sink Covered by a Porous Layer

This numerical study aims to enhance the heat transfer efficiency by dissipating the heat Emitted from electronic processors. A jet impingement technique is utilized with porous layer covering a metal fin as a heat sink. Forced convection and normal convection (due to the buoyancy effect) are taken into consideration. The two equations model (Local Thermal Non-Equilibrium LTNE) employed to describe the energy equations of the two phases of the porous surface. Finite Element Method (FEM) used to discretize these equations to obtain the numerical solution. To make this study closest to the reality, constant heat flux boundary condition is applied underneath the metallic heat sink. The geometry comprises of three domains: Free flow channel, Porous layer and Metal fined heat sink. In order to simulate the heat transfer, isotherms; streamlines and Nusselt number have been considered. Investigation has been done by inspecting the effects of the pertinent non-dimensional parameters such as: Reynolds number (Re = 100-900), Darcy number (Da = 10-1-10-6), Richardson number (Ri = 0.1-100) and Porosity (ε = 0.85-0.95). The results show that increasing Re and decreasing ε lead to enhance Nusselt number. Richardson number below 100 has no significant effects on Nu. At Re above 400, Nusselt number proportional with Darcy number. The enhancement of Nusselt number is found to be 250 % by increasing Re from 100 to 900, 290 % by decreasing ε from 0.95 to 0.85 and about 13 % by increasing Darcy number from 10-6 to 10-1.

Shape optimization of pin fin array in a cooling channel using genetic algorithm and machine learning

This article reports the optimization of pin fin shape using a genetic algorithm (GA) coupled either to a machine learning (ML) model or a computational fluid dynamics (CFD) model. The ML model evaluates the temperature and pressure induced by the fins within a second and allows us to replace the time-consuming CFD simulations during the design stage. The optimization is conducted for a cooling channel with a uniform heat flux boundary condition (5 W/cm2) in the Reynolds numbers range of 3000 – 12000. The optimization identifies a funnel-shaped fin that enhances the heat transfer coefficient by 20% without an apparent increase of pressure drop as compared to the standard cylindrical pin fins. The funnel-shaped fin outperforms other conventional fins of elliptical, cubic, and drop shapes that induce a similar level of pressure drops. This work demonstrates the potential of ML-based optimization in searching unexplored shapes of heat transfer systems with superior performance.

Comparative studies on convective heat transfer behaviour of nanofluids under turbulent flow with inserts

ABSTRACT In this paper, the thermal performance of novel spiraled rod inserts in the turbulent flow of Al2O3/water, CuO/water, and TiO2/water nanofluids through a circular tube with constant heat flux boundary conditions is compared. The nanofluids used in this study contain particle volume concentrations of 0.25 and 0.5%. According to the study's findings, nanofluids have a greater Nusselt number than deionised water. Among the nanofluids used, CuO nanofluid with a spiraled rod insert of the lesser pitch gives the maximum enhancement in Nusselt number, and the enhancement value is 49.6% for 0.5% volune concentration compared to deionised water. The increase in friction factor for the above condItion is 17.59%. The maximum thermal performance factor value with a pitch of 30 mm spiraled rod insert and 0.5% volume concentration of CuO nanofluids is about 1.41.The novelty of this present study is the simple and easily manufactured inserts used to enhance heat transfer.

Characteristics of Heat Transfer and Turbulent Flow in a Baffled Pipe with Different Arrangements

In the heat transfer, fluid flow and energy fields, baffles are an advanced enhancer to improve heat transfer and fluid mixing by working as an obstacle to the flow particles and then increasing the turbulence. The present paper numerically investigates the thermal performance of a circular pipe with a centralized baffle in two arrangements, with a Reynolds number (Re) (ranging from 10,000-50,000) under constant wall heat flux boundary conditions. Ansys Fluent software is used to solve the flow field considering six conical baffles with different Pitch ratios (PR) (from 1 to 5). Results show that baffles shape, arrangement, and PR have a significant impact on the properties of flow and heat transfer. The obtained results show an effective role for the baffles to promote thermal performance when it is used in heated pipes. Heat transfer rate is increased for the baffled pipe by 1-2 compared with the smooth pipe. Moreover, the best value of friction factor, thermal performance, and Nusselt number is recorded at PR= 5 at Re=30000 in the baffled pipe for the second arrangement.

Analytical solutions for heat conduction problems with three kinds of periodic boundary conditions and their applications

In the present study, a general analytic expression for solving heat conduction problem in finite domain under periodic boundary conditions was suggested by using the variable separation method. Heat conduction problems under three kinds of periodic upper boundary conditions and constant temperature or zero-flux as bottom boundary conditions were solved respectively. By applying the analytical solutions, an equivalent method for transferring the periodic heat flux and convection combination boundary condition to the Dirichlet boundary condition was proposed. In addition, the proposed solution was generalized to solve the heat conduction problem infinite domain with periodic sine-like law boundary conditions. The present study can provide references for investigating the evolution law of temperature field under complex periodic boundary conditions.

ANALYSIS OF TEMPERATURE DISTRIBUTION IN LASER ALLOYING OF PURE COPPER

In many cases, the use of copper is limited by the unsatisfactory properties of its surface layer, i.e., low hardness and wear resistance. Laser surface-layer treatment may be a better alternative to other techniques used in surface engineering intended for the elements, whose high conductivity, combined with high functional properties, is required. In the present work, laser alloying of pure copper with Ni powder is performed. Thermographic measurements during the process and measurements of the melt-pool dimensions after the alloying are performed. A 3-D model of a cylindrical specimen is developed. The enthalpy-based material model involving the phase change is applied. The nickel powder is taken into account with an appropriate value of the workpiece absorptance in the heat flux boundary condition imposed in the moving laser spot area. This study utilized the ANSYS-based Simulation software. Results of the temperature simulation show acceptable agreement with the experiment. The developed model can be used to predict the temperature distribution and identify the workpiece absorptance.

Interaction of Variable Fluid Properties with Electrokinetically Modulated Peristaltic Flow of Reactive Nanofluid: A Thermodynamical Analysis

In the present study, the interaction of variable fluid properties with electrokinetically regulated peristaltic transportation of a reactive nanofluid embedded in a porous space is studied. The nanofluid saturates the porous space/medium with inhomogeneous porosity, which changes with distance from the channel boundary. It is assumed that nanofluids are accompanied by variable thermal conductivity and viscosity. The impacts of magnetic field, Brownian motion, electric field, viscous dissipation, chemical reaction, mixed convection, and thermophoresis are incorporated. Moreover, the contribution of zero mass flux boundary condition is executed. The complexity of the equations describing the flow of a nanofluid is reduced by applying the lubrication theory. The fully non-linear equations are solved by utilizing a numerical technique. Particular attention is paid to the analysis of entropy optimization, since its minimization is the best measure to enhance the efficiency of thermal systems. These results demonstrate that a positively oriented external electric field contributes to an increase in nanofluid velocity. Temperature of nanofluid increases more rapidly due to an augmentation in Joule heating parameter. It is noticed that the temperature of water is comparatively lower than that of kerosene. The system’s energy loss can be reduced when the thermal conductivity parameter enhance. The magnitude of Bejan number is enhanced by increasing electroosmotic parameter. Further, a substantial decrement in concentration profile is perceived when the Schmidt number is augmented.

Benchmark Al-Cu Solidification Experiments in Microgravity and on Earth

Predicting macrosegregation and grain structure, including the columnar to equiaxed transition (CET), in alloy solidification is an ongoing challenge. Gravity-driven melt convection and transport of unattached solid grains complicate such efforts. Cylindrical samples of aluminum alloys containing 4, 10, and 18 wt pct copper are solidified from the bottom upwards on Earth and in microgravity conditions aboard the International Space Station. The chosen alloys possess primary solid densities that are greater than, equal to, and less than their melt densities promoting different gravity-driven solid transport phenomena. Significant differences in grain structure are observed between microgravity and terrestrial samples. All microgravity samples are entirely equiaxed, while the terrestrial samples exhibit a CET. The columnar grains near the cooled surface in the terrestrial samples can only be attributed to melt convection. The Al-4 wt pct Cu terrestrial sample shows evidence of grain sedimentation, while the Al-18 wt pct Cu terrestrial sample exhibits the effects of grain floatation. Measurements of eutectic fraction and solute concentration in the samples show inverse segregation due to shrinkage-driven flow in all samples. Terrestrially solidified samples have areas of high solute concentration that are not uniformly distributed over the diameter, indicating the presence of melt convection. The eutectic and macrosegregation measurements generally have good correspondence. Temperature, grain structure, eutectic fraction, and macrosegregation data are presented as benchmark data to validate future modeling efforts. Heat flux boundary conditions on the sample are determined using thermal modeling. Thermal process parameters are calculated for all samples.

Thermodynamic characteristics of counter flow and cross flow plate fin heat exchanger based on distributed parameter model

The distributed parameter models of counter flow and cross flow plate fin heat exchanger (PFHE) are constructed to investigate their thermodynamic characteristics. In practical application, the cold end of PFHE may be directly connected to the cold equipment. Therefore, the effect of longitudinal heat conduction (LHC) under different thermal boundary conditions set on two ends of the separating plates (SPs) is investigated based on the model of counter flow PFHE. It is found that LHC effect transmits the effect of boundary condition on two ends of the SPs into the inner domain of PFHE. The LHC effect on the heat transfer performance of PFHE is positive when setting appropriate boundary condition on two ends of the SPs. When considering LHC, compared with the adiabatic boundary conditions on two ends of the SPs, the effectiveness of constant wall temperature boundary conditions increases by 31.7 ∼ 35.8 %, and the effectiveness of constant heat flux boundary conditions increases by 22.8 %. The model of cross flow PFHE is used to investigate the effect of configuration and operation parameters on the heat transfer amount and the pump power. The cross flow PFHE is optimized to arrive at the maximization of heat transfer amount per unit pump power (HTPUP). In the three-stream cross flow PFHE studied, the heat transfer amount almost doesn’t change when the xz projected area is maintained and one projected length (z side length) is changing. The pump power is the lowest and the HTPUP is the largest when z side length of PFHE (z side is the flow direction of the fluid with large mass flowrate) is 0.15 ∼ 0.2 m.

Bénard convection in a slowly rotating penny-shaped cylinder subject to constant heat flux boundary conditions

We consider axisymmetric Boussinesq convection in a shallow cylinder of radius $L$ and depth $H (\ll L)$ , which rotates with angular velocity $\varOmega$ about its axis of symmetry aligned to the vertical. Constant heat flux boundary conditions, top and bottom, are adopted, for which the onset of instability occurs on a long horizontal length scale provided that $\varOmega$ is sufficiently small. We investigate the nonlinear development by well-established two-scale asymptotic expansion methods. Comparisons of the results with the direct numerical simulations (DNS) of the primitive governing equations are good at sufficiently large Prandtl number $\sigma$ . As $\sigma$ is reduced, the finite amplitude range of applicability of the asymptotics reduces in concert. Though the large meridional convective cell, predicted by the DNS, is approximated adequately by the asymptotics, the azimuthal flow fails almost catastrophically, because of significant angular momentum transport at small $\sigma$ , exacerbated by the cylindrical geometry. To appraise the situation, we propose hybrid methods that build on the meridional streamfunction $\psi$ derived from the asymptotics. With $\psi$ given, we solve the now linear azimuthal equation of motion for the azimuthal velocity $v$ by DNS. Our ‘hybrid’ methods enable us to explain features of the flow at large Rayleigh number, found previously by Oruba et al. (J. Fluid Mech., vol. 812, 2017, pp. 890–904).

Sensitivity of simulating Typhoon Haiyan (2013) using WRF: the role of cumulus convection, surface flux parameterizations, spectral nudging, and initial and boundary conditions

Abstract. Typhoon (TY) Haiyan was one of the most intense and highly destructive tropical cyclones (TCs) to affect the Philippines. As such, it is regarded as a baseline for extreme TC hazards. Improving the simulation of such TCs will not only improve the forecasting of intense TCs but will also be essential in understanding the potential sensitivity of future intense TCs with climate change. In this study, we investigate the effects of model configuration in simulating TY Haiyan using the Weather Research Forecasting (WRF) Model. Sensitivity experiments were conducted by systematically altering the choice of cumulus schemes, surface flux options, and spectral nudging. In addition to using the European Centre for Medium-Range Weather Forecasts Reanalysis fifth-generation (ERA5) single high-resolution realization as initial and boundary conditions, we also used 4 of the 10 lower-resolution ERA5 data assimilation system (EDA) ensemble members as initial and boundary conditions. Results indicate a high level of sensitivity to cumulus schemes, with a trade-off between using Kain–Fritsch and Tiedtke schemes that have not been mentioned in past studies of TCs in the Philippines. The Tiedtke scheme simulates the track better (with a lower mean direct positional error, DPE, of 33 km), while the Kain–Fritsch scheme produces stronger intensities (by 15 hPa minimum sea level pressure). Spectral nudging also resulted in a reduction in the mean DPE by 20 km, and varying the surface flux options resulted in the improvement of the simulated maximum sustained winds by up to 10 m s−1. Simulations using the EDA members initial and boundary conditions revealed low sensitivity to the initial and boundary conditions, having less spread than the simulations using different parameterization schemes. We highlight the advantage of using an ensemble of cumulus parameterizations to take into account the uncertainty in the track and intensity of simulating intense tropical cyclones.

Heat transfer enhancement of nanofluid flow at the entry region of microtubes

A numerical investigation on laminar nanofluid flow and convective heat transfer at the entry region of microtubes subjected to constant wall temperature and constant heat flux boundary conditions has been carried out employing a multiphase Eulerian–Lagrangian method. The impacts of the Peclet number (175 ≤ Pe ≤ 3500), nanoparticle volume fraction (0.1 ≤ φ ≤ 1.0%), and nanoparticle diameter (40 ≤ dp ≤ 130 nm) on thermal characteristics of Al2O3-water nanofluid flow through a microtube are analyzed in detail. The results indicate that the influence of the Reynolds number on apparent friction factor and the impact of the axial heat conduction on the Nusselt number for the nanofluids have to take into account in the entry region. Compared with the influences of particle concentration and particle size, the entrance effect dominates pressure drop and thermal performance of the nanofluids near the entrance of the channel. As the dimensionless axial distance increases, the entrance effect is weakened, and the influences of particle concentration and particle size are gradually reflected in flow and heat transfer results. Besides, the particle effects on thermal performance of the nanofluids are earlier and higher than that on flow resistance. Performance evaluation demonstrates that the nanofluids in the entrance region have not only heat transfer enhancement but also a good economy. When Pe = 175, the PEC of Al2O3-water nanofluids with particle concentrations of 0.1, 0.2, 0.5, and 1% increased by 104.0, 103.1, 113.8, and 128.5% under constant heat flux condition, respectively, at the dimensionless axial distance x* = 0.01 compared with deionized water; the PEC improved by 74.6, 77.2, 85.6, and 102.5% under constant wall temperature condition compared with deionized water, respectively.

The Forced Convection Analysis of Water Alumina Nanofluid Flow through a 3D Annulus with Rotating Cylinders via κ−ε Turbulence Model

We investigated the dynamics of nanofluid and heat transfer in a three-dimensional circular annular using the κ−ε turbulence model and energy equations. The pipe contained two concentric and rotating cylinders with a constant speed in the tangential direction. A heat flux boundary condition was executed at the inner cylinder of the annular. The pipe was settled vertically, and water alumina nanofluid was allowed to enter, with the initial velocity depending on the Reynolds number, ranging from 30,000 to 60,000. The volume fraction of the solid particles was tested from 0.001 to 0.1. The speed of the rotation of the cylinders was tested in the range from 0.5 to 3.5. The simulations were developed using COMSOL Multiphysics 5.6, adopting the finite element procedure for governing equations. The results were validated using the mesh independent study and the average Nusselt number correlations. We found that the average Nusselt number in the middle of the channel decreases linearly with the increase in the volume fraction of the water alumina nanofluid. The novelty of the present work is that various correlations between the average Nusselt number and volume fraction were determined by fixing the Reynolds number and the rotation of the inner cylinder. We also found that fixing the Reynolds number and the volume fraction improves the average Nusselt number at the outlet linearly. In addition, it was stated that the increase in the total mass of the nanofluid would decrease the average temperature at the outer cylinder of the annular. Moreover, the maximum average improvement percentage in the average Nusselt number, which is about 21%, was observed when the inner cylinder rotation was changed from 1.5 to 2.5 m/s.

Thermal radiation effect on Viscoelastic Walters’-B nanofluid flow through a circular cylinder in convective and constant heat flux

The investigation on flow of nanofluid are well known amongst researchers due to its utilization in the industrial and engineering sector. It is useful for cooling purposes in the electronic devices, which has shown good results in energy saving. Thus, this study focusses on the analysis of radiation effects on mixed convection of Walters’-B nanofluid flow through a circular cylinder in the constant heat flux (CHF) and convective boundary conditions (CBC) horizontally. The sodium carboxymethyl cellulose (CMC-water) nanofluid is considered as conventional fluid containing copper nanoparticles. The numerical method of Keller-box is conducted to simplify the partial differential equations. Graphical profiles are plotted and discussed to examine the impacts of various physicals terms on velocity, skin friction, temperature and thermal transfer. The results discover the fluid velocity and temperature boost for increasing radiation and Biot number caused by the raise of energy supply in the fluid flow. The velocity profile decreases when nanoparticles volume fraction increases as the increment of fluid concentration slowing down the fluid flow. The convective heat transfers and skin friction increases as mixed convection parameter rises by varying the thermal boundary region. Furthermore, the temperature and velocity in CHF condition are comparatively higher than CBC condition.