Two-dimensional Heat Flow Research Articles

Numerical Analysis of Heat and Mass Transfer Flow of Nanofluid over a Moving Wedge Using Spectral Quasilinearization Method

In this paper the problem of unsteady two-dimensional heat and mass transfer flow of nanofluid past a moving wedge is considered. The effects of nanoparticle volume fraction, viscous dissipation, chemical reaction, and convective boundary conditions are studied. The physical problem is modeled using partial differential equations. Using suitable similarity variables, the governing equations and their related boundary conditions are transformed into dimensionless forms of a system of coupled nonlinear ordinary differential equations. The resulting systems of equations are then solved numerically using spectral quasilinearization method (SQLM). The results reveal that the skin friction coefficient increases with increasing the values of nanoparticle volume fraction, unsteadiness and permeability parameters. The local Nusselt number reduces with increasing the value of nanoparticle volume fraction, Prandtl number and Eckert number. The local Sherwood number enhances with greater the value of nanoparticle volume fraction, unsteadiness, pressure gradient and chemical reaction parameters. Moreover, the method is checked against the previously published results and a very good agreement have been obtained.

English

In this paper, unsteady two-dimensional convective heat and mass transfer flow of a viscous, incompressible, electrically conducting optically thin fluid which is bounded by a vertical infinite plane surface was considered. A uniform applied homogeneous magnetic field is considered in the transverse direction with first order chemical reaction. An analytical solution for two-dimensional oscillatory flow on unsteady mixed convection of an incompressible viscous fluid, through a porous medium bounded by an infinite vertical plate in the presence of chemical reaction and thermal radiation are presented. The surface absorbs the fluid with a constant suction and the free stream velocity oscillates about a constant mean value. The resulting nonlinear partial differential equations were transformed into a set of ordinary differential equations using two-term series. The closed form solutions for velocity, temperature, concentration, skin friction, Nusselt number, and Sherwood number have been obtained, using the regular perturbation technique. Numerical evaluation of the analytical solutions was performed and the results are presented in tabular and graphical form. This illustrates the influence of the various parameters involved in the problem on the solutions. Key words: Magnetohydrodynamics (MHD) flow, heat and mass transfer, oscillatory flow, thermal radiation, chemical reaction.

Heat accumulation between scans during multi-pass cutting of carbon fiber reinforced plastics

Matrix evaporation caused by heat accumulation between scans (HAS) was studied in the case of multi-pass scanning of a laser beam over the surface of carbon fiber reinforced plastic (CFRP). The experiments were performed in two regimes, namely, in the process of CFRP cutting and in the regime of low-fluence irradiation avoiding ablation of carbon fibers. The feature of the ablation-free regime is that all absorbed energy remains in the material as heat, while in the cutting regime the fraction of residual heat is unknown. An analytical model based on two-dimensional (2D) heat flow was applied to predict the critical number of scans, after which the HAS effect causes a distinct growth of the matrix evaporation zone (MEZ). According to the model, the critical number of scans decreases exponentially with increasing laser power, while no dependence on the feed rate is expected. It was found that the model fits well to the experimental data obtained in the ablation-free regime where the heat input is well defined and known. In the cutting regime the measured significant reduction of the critical number of scans observed in deep grooves may be attributed to transformation of the heat flow geometry and to an expected increase of the residual heat fraction.

Comparison of FEM calculated heat transfer coefficient in a minichannel using two approaches: Trefftz base functions and ADINA software

The paper presents the methods of heat transfer coefficient determination for boiling research during FC-72 flow in a minichannel. The boundary condition in the form of distributions of temperature on the outer side of the minichannel heated wall was obtained using infrared thermography. It was assumed two-dimensional steady-state heat flow. The local values of the heat transfer coefficients on the surface between the heated foil and boiling liquid, were determined from the Robin boundary condition. Data necessary for the heat transfer coefficient evaluation were obtained from numerical computations using two approaches: calculation procedure based on the Trefftz functions and FEM simulations by ADINA software. The shape functions were linear combinations of the Trefftz functions. Combinations of the Trefftz functions exactly satisfy the differential equation. Coefficients of the linear combination of the shape function in the approximate solution were chosen to minimize residuals on domain boundary and along common edges of adjacent elements. Temperature measurement points were located in boundary nodes. During FEM simulations 4-node FCBI elements were used, fluid flow was assumed to be laminar, incompressible and material constants of the fluid and of the foil were independent on temperature. The results of the comparative analysis were presented and discussed.

Free Convection Heat and Mass Transfer Flow for Magnetohydrodynamic Chemically Reacting and Radiating Elastico-Viscous Fluid Past a Vertical Permeable Plate with Gravity Modulation

An analysis of a two-dimensional unsteady magnetohydrodynamic free convective heat and mass transfer flow of an electrically conducting, optically thin, incompressible, and radiating elastico-viscous fluid (characterised by Walters’ liquid $${B}'$$ ) past a vertical permeable infinite plate embedded in a uniform porous medium with gravity modulation is considered. It is assumed that there exists a homogeneous first-order chemical reaction. Analytical solutions for velocity, temperature and concentration field have been derived. The effects of gravity modulation, radiation, and chemical reaction on velocity profile and shear stress for both Newtonian and elastico-viscous fluid have been studied and presented graphically. It was observed that velocity distribution increases with an increase in gravity modulation parameter and radiation parameter for both Newtonian and elastico-viscous fluid, where as it shows reverse effects in the case of magnetic field parameter and viscoelastic parameter. It is seen that viscous drag on the plate is reduced under the effect of chemical reaction parameter, where as it shows reverse effect in the case of gravity modulation parameter and radiation parameter.

Two parameters Lie group analysis and numerical solution of unsteady free convective flow of non-Newtonian fluid

The two-dimensional unsteady laminar free convective heat and mass transfer fluid flow of a non-Newtonian fluid adjacent to a vertical plate has been analyzed numerically. The two parameters Lie group transformation method that transforms the three independent variables into a single variable is used to transform the continuity, the momentum, the energy and the concentration equations into a set of coupled similarity equations. The transformed equations have been solved by the Runge–Kutta–Fehlberg fourth-fifth order numerical method with shooting technique. Numerical calculations were carried out for the various parameters entering into the problem. The dimensionless velocity, temperature and concentration profiles were shown graphically and the skin friction, heat and mass transfer rates were given in tables. It is found that friction factor and heat transfer (mass transfer rate) for methanol are higher (lower) than those of hydrogen and water vapor. Friction factor decreases while heat and mass transfer rate increase as the Prandtl number increases. Friction (heat and mass transfer rate) factor of Newtonian fluid is higher (lower) than the dilatant fluid.

蒸发式冷凝器传热传质数值模拟研究

采用VOF法，建立二维水蒸气传热传质顺流和逆流的计算模型，计算所得的平均液膜厚度模拟值比实验测量值大3.03%~6.90%，比Nusselt理论的预测值大8.33%~10.34%，在合理的误差范围，说明该模型切实可行。运用该模型计算并分析水与空气顺流和逆流过程中，液态水的流动分布、空气与水流速度分布以及空气中水蒸气的质量含量分布情况，结果表明：在气–液两相逆流过程的气–液界面的总传热量中，潜热传热量所占比值在90%以上，比气–液两相顺流时高，在气–液相界面处是以水蒸发传质引起的潜热换热为主、温差引起的显热传热为辅的换热形式，逆流比顺流更有利于传热。 The VOF (volume of fluid) method is used to establish a two-dimensional water vapor heat and mass transfer parallel flow and counter flow model. The deviation of calculated film thickness, which is changed with Re values, is greater than the experimental measurement’s value by 3.03% - 6.90%, and the predicted value of the Nusselt theory by 8.33% - 10.34%; it indicates that the model is feasible. The model is used to calculate and analyze liquid water flow distribution, air and water quality and velocity distribution, water vapor quality content distribution in the air, in water and air’s parallel flow and counter flow processes. The results show that: in gas-liquid two- phase counter flow process, the ratio of latent heat transfer rate in total heat transfer rate is above 90% at gas-liquid interface, higher than that of gas-liquid two-phase parallel flow; at air-liquid interface, the main heat transfer is latent heat transfer caused by water’s evaporation and mass transfer, and the supplemented heat transfer is sensible heat transfer caused by temperature difference; counter flow is more conducive to heat transfer than parallel flow.

Non-uniform heat source/sink and Soret effects on MHD non-Darcian convective flow past a stretching sheet in a micropolar fluid with radiation

In the current work effects of Soret number, variable thermal conductivity, viscous-Ohmic dissipation, non-uniform heat sources on steady two-dimensional hydromagnetic mixed convective heat and mass transfer flow of a micropolar fluid over a stretching sheet embedded in a non-Darcian porous medium with thermal radiation are studied. The governing non-linear partial differential equations are transformed into a set of non-linear coupled ordinary differential equations which are then solved numerically by using the Runge–Kutta–Fehlberg method with shooting technique. A critical analysis with earlier published papers is done and the results are found to be in accordance with each other. Numerical solutions are then obtained and investigated in details for different physical parameters such as skin-friction coefficient, local Nusselt and Sherwood numbers as well as other parametric values such as the velocity, angular velocity, temperature and concentration.

Finite element analysis for unsteady MHD heat and mass transfer free convection flow of polar fluids past a vertical moving porous plate in a porous medium with heat generation and thermal diffusion

The unsteady two-dimensional magnetohydrodynamic heat and mass transfer free convection flow of an incompressible viscous electrically conducting polar fluid through a porous medium past a semi-infinite vertical porous moving plate in the presence of a transverse magnetic field with thermal diffusion and heat generation is considered. The plate moves with a constant velocity in the longitudinal direction and the free stream velocity follows an exponentially increasing or decreasing. A uniform magnetic field acts perpendicularly to the porous surface which absorbs the polar fluid with a suction velocity varying with time. The equations of conservation of mass, momentum, energy and concentration which govern the case study of heat and mass transfer flow have been obtained. The equations have been solved numerically by Galerkin finite element method. The effect of various flow parameters are presented graphically. Representative results for velocity profiles, temperature profiles and concentration profiles are obtained for several values of pertinent parameters which are of physical and engineering interest.DOI: http://dx.doi.org/10.3329/jname.v11i1.12844

Two-dimensional heat flow apparatus

We have created an apparatus to quantitatively measure two-dimensional heat flow in a metal plate using a grid of temperature sensors read by a microcontroller. Real-time temperature data are collected from the microcontroller by a computer for comparison with a computational model of the heat equation. The microcontroller-based sensor array allows previously unavailable levels of precision at very low cost, and the combination of measurement and modeling makes for an excellent apparatus for the advanced undergraduate laboratory course.

Computation of thermal condition in an induction motor during plugging

The problem of two-dimensional heat flow in the stator of induction motor is solved by use of a finite element formulation and arch-shaped elements in the r-θ plane of the cylindrical coordinate system. The shape functions and exact solution matrices are derived algebraically for utmost economy in computation. The temperature distribution has been determined considering convection from the stator frame and cylindrical air-gap surface. The model is applied to one squirrel cage totally enclosed fan cooled (TEFC) machine of 7.5 kW. Finally, the temperatures obtained by this two-dimensional approximation have been compared for different stator currents for a period of 10 seconds at time intervals of 1 sec during the transient in plugging method of braking.

Combined Effects of Thermophoresis and Chemical Reaction on Magnetohydrodynamics Mixed Convection Flow

The steady two-dimensional MHD mixed convective heat and mass transfer flow of a viscous incompressible electrically conducting second grade fluid past a semi-infinite stretching sheet in the presence of thermal radiation with chemical reaction and thermophoresis is analyzed numerically. Similarity solutions for the transformed governing equations are obtained and the reduced equations are then solved numerically using symbolic software MATHEMATICA. Favorable comparison with previously published work is performed. The features of the flow, heat, and mass transfer characteristics for different values of the material parameters are analyzed and discussed.

Effective foam insulation for single-wythe concrete masonry walls

The objective of this study was to evaluate the effectiveness of three different methods to apply closed-cell polyurethane foam to single-wythe concrete masonry wall panels, namely, surface spray-on, filled formwork, and grouting the cores of the concrete blocks. Foams with two densities were applied at three different thicknesses. Two-dimensional heat flow simulations were conducted using THERM to determine the overall thermal resistance of the insulated masonry wall panels. Filled formwork application using normal-density foam yielded the highest thermal resistance. Hygrothermal analysis using WUFI Plus revealed that exterior application of the foam is preferred to avoid durability issues and take advantage of the thermal mass and fire resistance of masonry walls.

Computation of thermal condition in an induction motor during reactor starting

Induction machines transient thermal analysis has been a subject of interest for machine designers in their effort to improve machine reliability. The stator being static is prone to high temperature. Therefore, the study of transient thermal behavior in the stator is useful to identify causes of failure in induction machines. The paper presents a two-dimensional transient heat flow in the stator of an induction motor using arch shaped elements in the r–θ plane of the cylindrical co-ordinate system. A temperature–time method is employed to evaluate the distribution of loss in various parts of the machine. Using these loss distributions as an input for finite element analysis, more accurate temperature distributions can be obtained. The model is applied to one squirrel cage Totally Enclosed Fan Cooled (TEFC) machine of 7.5kW. Finally the temperatures obtained by this two-dimensional approximation at different location of stator have been compared for different stator currents considering the time required for each stator current during the transient in reactor starting.

Thermophoresis particle deposition on unsteady two-dimensional forced convective heat and mass transfer flow along a wedge with variable viscosity and variable Prandtl number

In this paper, the effects of thermophoresis particle deposition on an unsteady two dimensional forced convective heat and mass transfer flow past a wedge taking into account the variation of fluid viscosity and fluid Prandtl number with temperature are studied. The local similarity equations are derived and solved numerically using Nachtsheim–Swigert shooting iteration technique along with the sixth order Runge–Kutta integration scheme. Comparisons with previously published work are performed, and the results are found to be in excellent agreement. Results for the non-dimensional velocity, temperature, concentration, Prandtl number and thermophoretic velocity are displayed graphically whereas thermophoretic deposition velocity is shown in the tabulated form for various values of the pertinent parameters. The obtained numerical results show that in modeling the thermal boundary-layer flow with a temperature-dependent viscosity, consideration of the Prandtl number as a constant within the boundary layer produces unrealistic results, and therefore, it must be treated as a variable rather than a constant within the boundary layer. The results also show that the thermophoretic particle deposition velocity decreases as the thermophoretic coefficient increases.

Interdendritic Strain and Macrosegregation-Coupled Phenomena for Interdendritic Crack Formation in Direct-Chill Cast Sheet Ingots

In a study of the early stages of dendritic solidification in the direct-chill cast sheet ingots, the coupled effect of interdendritic strain and macrosegregation on the interdendritic cracks formation in dendritic equiaxed structure has been investigated by the metallographic study of ingot samples and by performing a set of mathematical analyses for AA-6061 and AA-1050 aluminum alloys. The metallographic investigation contains microstructure examinations and macrosegregation measurements of collected samples from plant trials. The mathematical analysis consists of a two-dimensional (2-D) fluid flow, heat flow, interdendritic strain, and macrosegregation-coupled model. Also, a simple approach to measure interdendritic crack has been developed based on the accumulative interdendritic strain criterion, local dendritic phases, and the crystal distortion correlation factor resulting from steep positive local segregation. The model predications have clarified the effect of high positive macrosegregation on the surface and subsurface interdendritic crack formation. It has been revealed that interdendritic strain starts to generate just below the liquidus temperature, resulting from shrinkage of liquid→solid phase transformation and contraction of dendritic solid in the incoherent mushy region. In this region, the coupled effect of the shrinkage/contraction mechanism increases the interdendritic distances between equiaxed crystals and the interdendritic crack begins to nucleate. Subsequently, in the coherent mushy region, the different interdendritic strain sources start to affect significantly the distances between equiaxed crystals in a diverse way, and therefore, the final morphology of interdendritic crack begins to form. The mechanism of interdendritic crack formation during dendritic equiaxed structure solidification and the possible solutions to this problem are discussed.

Effect of fire-induced damage on the uniaxial strength characteristics of solid timber: A numerical study

The advent of the structural Eurocodes has allowed civil engineers to be more creative in the design of structures exposed to fire. Rather than rely upon regulatory guidance and prescriptive methods engineers are now able to use such codes to design buildings on the basis of credible design fires rather than accepted unrealistic standard-fire time-temperature curves. Through this process safer and more efficient structural designs are achievable. The key development in enabling performance-based fire design is the emergence of validated numerical models capable of predicting the mechanical response of a whole building or sub-assemblies at elevated temperature. In such a way, efficiency savings have been achieved in the design of steel, concrete and composite structures. However, at present, due to a combination of limited fundamental research and restrictions in the UK National Annex to the timber Eurocode, the design of fire-exposed timber structures using numerical modelling techniques is not generally undertaken.The 'fire design' of timber structures is covered in Eurocode 5 part 1.2 (EN 1995-1-2). In this code there is an advanced calculation annex (Annex B) intended to facilitate the implementation of numerical models in the design of fire-exposed timber structures. The properties contained in the code can, at present, only be applied to standard-fire exposure conditions. This is due to existing limitations related to the available thermal properties which are only valid for standard fire exposure. In an attempt to overcome this barrier the authors have proposed a 'modified conductivity model' (MCM) for determining the temperature of timber structural elements during the heating phase of non-standard fires. This is briefly outlined in this paper. In addition, in a further study, the MCM has been implemented in a coupled thermo-mechanical analysis of uniaxially loaded timber elements exposed to non-standard fires. The finite element package DIANA was adopted with plane-strain elements assuming two-dimensional heat flow. The resulting predictions of failure time for given levels of load are discussed and compared with the simplified 'effective cross section' method presented in EN 1995-1-2.

Two-dimensional turbulent heat and fluid flow model to study effect of working gas and other process parameters on heat transfer in plasma furnace

A two-dimensional heat and fluid flow model was used to simulate the plasma arc furnace, where the flow is governed by the steady state incompressible Navier–Stokes equations. The flow has been taken as turbulent and the standard k-epsilon model was used to simulate the turbulence in the flow. The coupled non-linear differential equations were solved with suitable boundary conditions and temperature dependent plasma properties at atmospheric pressure by employing an efficient finite volume method. The calculations and heat transfer to various parts of the furnace were calculated for argon, nitrogen and hydrogen plasmas. The voltage–current characteristic for the different types of plasma and the effect of other process parameters on heat transfer are discussed.

Heat pulse propagation studies around magnetic islands induced by the Dynamic Ergodic Divertor in TEXTOR

Since the efficiency of the tearing mode suppression by heating depends on the electron heat diffusivity it is important to know if the electron heat transport coefficients inside the island are reduced compared with the ambient plasma. With that aim, modulated ECRH has been employed for heat pulse propagation studies in and around magnetic islands at the TEXTOR tokamak. The combination of its special hardware tools of the Dynamic Ergodic Divertor to generate tearing modes, the ECRH system for producing heat pulses and the electron cyclotron emission imaging (ECE-Imaging) diagnostic for its analysis offered a direct view of the perturbed two-dimensional heat flow in around the magnetic island. Inside m/n = 2/1 and m/n = 3/1 islands with a flattened temperature profile, the electron heat transport is shown to be strongly reduced with respect to the surrounding plasma. Inside the islands a heat pulse diffusion coefficients χe ∼ 0.4 m2 s−1 was derived, while outside the island it is an order of magnitude larger χe > 3 m2 s−1. In contrast, power balance calculations of strongly heated islands show that the electron transport is similar to the surrounding plasma. These results suggest that the heat transport inside a magnetic island is also governed by a critical gradient-like behaviour, similar to the bulk plasma.

Some aspects of modelling the energy balance of a room in regard to the impact of solar energy

The architecture of a building is crucial in determining its thermal energy balance and indoor comfort conditions. Knowledge of solar radiation availability and its transmission through a building envelope to the interior of the building helps an architect to design the building in an energy efficient way. Nowadays, in highly populated urban areas, attics are used as living spaces and the building envelope includes inclined external walls and windows in roofs. This paper presents some aspects of modelling the energy balance of rooms with different orientations and with vertical or inclined surfaces of building envelope, with stress on the impact of solar energy. The dynamics of energy flow through windows is analysed in more detail. One dimensional energy flow through the centre of glass area (based on a thermal resistance model), two-dimensional energy flow through the edge of glass area and two-dimensional heat flow through the opaque frame are analysed. The third dimension is also considered in a simplified way by taking into account the specific perimeter of the edge or frame. Stress is put on modelling the solar energy input. Solar radiation is modelled as short wave radiation that is transmitted directly to the room through glazing and as energy absorbed by the building envelope (glass panes, frame and opaque external walls) that becomes internal heat sources and is transferred indirectly to the room. The model developed has been used for numerical simulation using MATLAB as the programming language. This model predicts (amongst other things) the solar energy impact on the energy balance of a room in a building. It allows many cases of rooms and their envelopes to be run and evaluated and as a result both general and detailed conclusions can be drawn. Some results are presented in both graphical and tabular form.