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# Accepted Manuscripts

BASIC VIEW  |  EXPANDED VIEW
research-article
John H. Lienhard V
J. Heat Transfer   doi: 10.1115/1.4042912
Shape factors for steady heat conduction enable quick and highly simplified calculations for heat conduction within bodies having a combination of isothermal and adiabatic boundary conditions. Many shape factors have been tabulated and most undergraduate heat transfer books cover their derivation and use. However, the analytical determination of shape factors for any but the simplest configurations can quickly come to involve complicated mathematics, and, for that reason, it is desirable to extend the available results as far as possible. In this paper, we show that known shape factors on the interior of two-dimensional objects are identical to the corresponding shape factor for the exterior of the object. The canonical case for the interior and exterior of a disk is examined first. Then, conformal mapping is used to relate known configurations for squares and rectangles to the solutions for the disk. Both a geometrical and a mathematical argument are introduced to show that shape factors are invariant under conformal mapping. Finally, the general case is demonstrated using Green's functions. In addition, the ``Yin-Yang'' phenomenon for conduction shape factors is explained as a rotation of the unit disk prior to conformal mapping.
research-article
J. Heat Transfer   doi: 10.1115/1.4042905
Turbulent natural convection in a large-scale cavity has taken a great attention due to its importance in many engineering applications such as building heating. In the present work, the lattice Boltzmann method (LBM) is used to simulate heat transfer by turbulent natural convection in a small room of housing heated from below by means of a heated floor. The celling and the four vertical walls of the room are adiabatic except of a portion of one vertical wall. This portion simulates a glass door with a cold temperature ?c=0. The cavity of side H is filled by air (Pr=0.71) and heated from below with an uniformly imposed temperature ?h=1. The effect of length ratio of heated floor, which varies from 20% to 80% of the total length H and of Rayleigh number, which varies from 5Ã—106 to 108 on thermal field characterized by temperature and isotherms, and on dynamic field characterized by air velocity streamlines. The heat transfer is examined in term of local and mean Nusselt number. The results show that, an increase in Rayleigh number or in heat source length increases the temperature in the core of cavity. Some correlations of the impact of heat source length on the temperature at the center of cavity and on the average Nusselt number are obtained.
TOPICS: Modeling, Natural convection, Cavities, Turbulence, Lattice Boltzmann methods, Temperature, Heat transfer, Heat, Rayleigh number, Engineering systems and industry applications, Doors, Glass, Heating
research-article
J. Heat Transfer   doi: 10.1115/1.4042904
In hot-forming die-quenching (HFDQ) boron manganese steel blanks are heated within a roller hearth furnace, and then simultaneously quenched and formed into fully-martensitic body-in-white components. Industry has a need for models that can predict the instantaneous temperature and austenite phase fraction within the roller furnace to diagnose problems (e.g. incomplete austenitization), forecast costs, and optimize process settings. This paper introduces a thermometallurgical model for Al-Si coated 22MnB5, consisting of coupled heat transfer and austenitization submodels. Two candidate austenitization submodels are considered: an empirical first-order model and a model based on the detailed austenitization kinetics. In the case of the first-order model, a detailed Monte Carlo procedure is used to construct 95% credibility intervals for the blank temperature and austenite phase fraction that accounts for uncertainties in the furnace temperature and model parameters. The models are first assessed using temperature and austenite phase fractions from Al-Si coated 22MnB5 coupons heated in a laboratory-scale muffle furnace, and then used to simulate austenitization of patched blanks within an industrial roller hearth furnace. The results show that the empirical first-order model provides a more robust estimate of austenite phase fraction compared to the detailed model.
TOPICS: Furnaces, Metal stamping, Temperature, Rollers, Blanks, Hearths, Boron, Uncertainty, Heat transfer, Steel, Quenching (Metalworking)
research-article
J. Heat Transfer   doi: 10.1115/1.4042840
Heat transfer from a cylinder of square cross section placed near a plane wall under the incidence of Couette- Poiseuille flow based nonuniform linear/nonlinear velocity profile is studied numerically. The cylinder is either dissipating constant heat flux (qW ) or maintaining at a constant temperature (TW). The conventional fluids are chosen as water, and ethylene glycol and water mixture. The nanoparticle materials are selected as Al2O3 and CuO. The flow field and heat transfer are computed through a finite volume method on a staggered grid system using QUICK scheme for convective terms and SIMPLE algorithm. Roles of pressure gradient P, temperature of base fluids, thermal conditions (TW or qW ) and parameters governing the nanofluids on the heat transfer (Nusselt number (NuM)) of the cylinder is investigated here. The heat transfer enhancement from the cylinder together with its drag coefficient reduction/increment due to addition of nanomaterials in both base fluids at two different temperature is assessed under the Couette flow. The classical fluid dynamics relationship among NuM, Re and Pr is discussed through Colburn j-factor, and hence the utility of proposed correlation between j-factor and Re towards engineering problems is also explored. The observations of dependency of NuM on the aforesaid parameters (from its graphical representation of computed data) are reconfirmed by proposed functional forms of NuM = NuM(P), NuM = NuM(f) and hence NuM = NuM(P,f). An effort is made to examine the effectiveness of the aforementioned parameters on the heat transfer enhancement rate.
TOPICS: Temperature, Heat transfer, Fluids, Cylinders, Nanofluids, Pressure gradient, Heat flux, Water, Flow (Dynamics), Fluid dynamics, Finite volume methods, Drag (Fluid dynamics), Nanoparticles, Algorithms, Nanomaterials, Poiseuille flow
research-article
J. Heat Transfer   doi: 10.1115/1.4042841
In internal cooling passages in a turbine blade, rib structures are widely applied to augment convective heat transfer by the coolant passing through over the ribbed surfaces. This study concentrates on perforated 90Âº ribs with inclined holes in a cooling duct with rectangular cross section, aiming at improving the perforated holes with additional secondary flows caused by inclined hole arrangements. Two sets of perforated ribs are used in the experiments with the inclined angle of the holes changing from 0Âº to 45Âº and the cross-sections are, respectively, circular and square. Steady-state Liquid Crystal Thermography (LCT) is applied to measure the ribbed surface temperature and obtain corresponding convective heat transfer coefficients (HTCs). Two turbulence models, i.e., k-? Shear Stress Transportation (SST) model and Detached Eddy Simulation (DES) model, are used in the numerical studies to simulate the flow fields. All inclined cases have slightly larger overall averaged Nusselt number (Nu) than straight cases. The enhancement ratio is approximately 1.85 % - 4.94 %. The averaged Nu in the half portion against the inclined direction is enlarged for inclined hole cases. The inclined hole cases usually have smaller averaged Nu in the half portion along the inclined direction. For the straight hole case and small inclined angle case, the penetrated flows mix with the mainstream flows at the perforated regions. When the inclined angle is larger, the penetrated flows are pushed to the inclined direction and mixing with the approaching flows occurs just at the side of the inclined direction.
TOPICS: Heat transfer, Turbulence, Flow (Dynamics), Cooling, Convection, Transportation systems, Ducts, Steady state, Shear stress, Liquid crystals, Temperature, Eddies (Fluid dynamics), Thermography, Simulation, Coolants, Turbine blades, Cross section (Physics)
research-article
Bengisen Pekmen Geridonmez
J. Heat Transfer   doi: 10.1115/1.4042782
In this study, free convection in a cavity with differentially heated wavy walls is numerically investigated in presence of a magnetic source. Polyharmonic spline radial basis function is utilized to discretize the governing dimensionless equations formulated by stream function-vorticity. The effects of dimensionless numbers Hartmann number, the number of undulations, amplitude of wave and the location of magnetic source are visualised in streamlines and isotherms as well as calculating average Nusselt number through the heated wall. Results show that primary vortex in streamlines is altered with the impact of magnetic source. The augmentation of undulations and amplitude causes convective heat transfer to decrease if \$Ra=10^5\$. The impact of location of magnetic source is noted close to the top wall.
TOPICS: Natural convection, Cavities, Dimensionless numbers, Vortices, Waves, Splines, Vorticity, Convection
research-article
J. Heat Transfer   doi: 10.1115/1.4042785
Pulse thermography is a nondestructive testing method in which an energy pulse is applied to a surface while the surface temperature evolution is measured to detect sub surface defects and estimate their depth. This nondestructive test method was developed on the assumption of instantaneous surface heating, but recent work has shown that relatively long pulses can be used to accurately determine defect depth in polymers. This paper examines the impact of varying input pulse length on the accuracy of defect depth quantification as a function of the material properties. Simulations using both thermoplastics and metals show that measurement error is dependent on a nondimensionalized pulse length. The simulation results agree with experimental results for 3D printed Acrylonitrile butadiene styrene (ABS) and Polylactic acid (PLA) components. Analysis and experiments show that defects can be accurately detected with minor modification to the standard methods as long as the pulse ends before the characteristic defect signal is detected.
TOPICS: Thermography, Nondestructive evaluation, Materials properties, Engineering simulation, Polymers, Errors, Signals, Simulation results, Heating, Additive manufacturing, Simulation, Temperature, Metals
research-article
J. Heat Transfer   doi: 10.1115/1.4042777
This study investigates the combined effects of blowing ratio and density ratio on flat plate film cooling effectiveness from two-row of compound angled cylindrical holes. Two arrangements of two-row compound angled cylindrical holes are tested: the first row and second row are oriented in staggered but same compound angled direction (ÃŸ = +45Â° for the first row, +45Â° for the second row); the first row and second row are oriented in inline but opposite direction (ÃŸ = +45Â° for the first row, -45Â° for the second row). Each cooling hole is 4 mm in diameter with an inclined angle 30Â°. The streamwise distance between the two rows is fixed at 4d and the spanwise pitch between the two holes (p) is 4d, 6d, and 8d, respectively. The experiments are performed at four blowing ratios (M = 0.5, 1.0, 1.5, 2.0) and three density ratios (DR = 1.0, 1.5, 2.0). The free stream turbulence intensity is kept at 6%. Detailed film cooling effectiveness distributions are obtained using the steady state pressure-sensitive paint (PSP) technique. The detailed film cooling effectiveness contours are presented and the spanwise averaged film effectiveness results are compared over the range of flow parameters. Film cooling effectiveness correlations are developed for both inline and staggered compound angled cylindrical holes. The results provide baseline information for the flat plate film cooling analysis with two-row of compound angled cylindrical holes.
TOPICS: Film cooling, Flat plates, Density, Pressure, Flow (Dynamics), Cooling, Turbulence, Steady state
research-article
J. Heat Transfer   doi: 10.1115/1.4042784
Forced convection heat transfer is investigated from a thin disk in power-law fluids over wide ranges of conditions as: Reynolds number, 1 = Re = 100, Prandtl number, 1 = Pr = 100, power-law index, 0.4 = n = 1.8 and disk thickness to diameter ratio, t/D = 0.01, 0.025, 0.05 and 0.075. The wide range of values of the power-law index spanned here covers both shear-thinning as well as shear-thickening fluid behavior. These results also elucidate the influence of the type of thermal boundary conditions, i.e., constant wall temperature condition (CWT) and constant heat flux condition (CHF) prescribed on the disk surface. Extensive results are presented in terms of the local and average Nusselt numbers to delineate the effect of each of the influencing parameters, Re, Pr, n, t/D for each thermal boundary condition. Limited results are also included here at vanishingly small values of the Peclet number to understand the behavior in the creeping flow condition. Finally, the present numerical results on the average Nusselt number have been consolidated in the form of a predictive equation to facilitate the interpolation of the present data for intermediate values of the parameters and/or a priori estimation of the average Nusselt number in a new application.
TOPICS: Forced convection, Disks, Fluids, Shear (Mechanics), Reynolds number, Boundary-value problems, Creeping flow, Interpolation, Prandtl number, Wall temperature, Heat flux, Thermal boundary layers, Critical heat flux, Heart failure
research-article
J. Heat Transfer   doi: 10.1115/1.4042812
Numerical investigations have been carried out to predict the near-wall dynamics in indirect natural convection for air (Pr = 0.7) and water (Pr = 5.2). Near-wall flow structures appear to be line plumes. Three-dimensional laminar, steady-state model was used to model the problem. Density was formulated using the Boussinesq approximation. Flux scaling, plume spacing and plume lengths obtained numerically are found to have the same trend with the results available in the literature. Plume length and Nusselt number, Nu exhibits an increasing trend with an increase in Rayleigh number, Ra for both Pr fluids. The plume spacing is found to have an inverse relationship with Ra. The cube root of Rayleigh number based on plume spacing is found to have a slight dependence on the dimensionless plume spacing. Nu scales as Nu ~ C Ra^n, n=0.26 for air and n= 0.3 for water. Heat transfer is thus found to be dominated by near wall phenomenon. Nu shows a non-linear relationship with L_p H/A and is found to be an accurate representation of heat transfer
TOPICS: Fluids, Plumes (Fluid dynamics), Numerical analysis, Rayleigh number, Heat transfer, Water, Natural convection, Approximation, Steady state, Density, Dynamics (Mechanics), Flow (Dynamics)
research-article
J. Heat Transfer   doi: 10.1115/1.4042781
Two biomimetic synthetic jet actuators were designed, manufactured, and tested under conditions of a jet impingement onto a wall. Nozzles of the actuators were formed by a flexible diaphragm rim, the working fluid was air, and the operating frequencies were chosen near the resonance at 65 Hz and 69 Hz. Four experimental methods were used: phase-locked visualization of the oscillating nozzle lips, jet momentum flux measurement using a precision scale, hot-wire anemometry, and mass transfer measurement using the naphthalene sublimation technique. The results demonstrated possibilities of the proposed actuators to cause a desired heat/mass transfer distribution on the exposed wall. It was concluded that the heat/mass transfer rate was commensurable with a conventional continuous impinging jets at the same Reynolds numbers.
TOPICS: Heat, Mass transfer, Actuators, Biomimetics, Nozzles, Visualization, Experimental methods, Resonance, Momentum, Fluids, Reynolds number, Wire, Diaphragms (Mechanical devices), Diaphragms (Structural), Jets
research-article
J. Heat Transfer   doi: 10.1115/1.4042780
Numerical simulations are used to analyze the thermal performance of turbulent flow inside heat exchanger tube fitted with cross-cut twisted tape with alternate axis (CCTA). The design parameters include the Reynolds number , cross-cut width ratio , cross-cut length ratio , and twist ratio . The objective functions are the Nusselt number ratio , the friction factor ratio , and the thermal performance . Response surface method (RSM) is used to construct second-order polynomial functions to study the 3D surfaces and sensitivity of the system to the different geometrical parameters of CCTA. The regression analysis shows that heat transfer ratio decreased with increasing both the Reynolds number and the width to diameter ratio of the twisted tape. This means that the twisted tape has more influence on heat transfer at smaller inlet fluid velocities. Sensitivity analysis reveals that among the effective input parameters, the sensitivity of to and is positive at . This indicates that an increment in Reynolds number led to an enhancement in friction factor ratio. Results reveal that thermal performance enhances with increasing the width to diameter ratio of the twisted tape . The maximum thermal performance factor of 1.531 is obtained for the case of , and .
TOPICS: Heat exchangers, Optimization, Sensitivity analysis, Reynolds number, Friction, Heat transfer, Fluids, Turbulence, Computer simulation, Polynomials, Regression analysis, Response surface methodology, Design
research-article
J. Heat Transfer   doi: 10.1115/1.4042778
It is important to understand the stress induced by phase transformation for cracks during the laser drilling of yttria-stabilized zirconia (YSZ). In this paper, a thermomechanical model is presented to investigate what happened in laser trepan drilling of YSZ. The thermal part involving the interaction between laser and YSZ is developed to obtain the transient temperature. While the mechanical part is to calculate the stress caused by the phase transformation based on the temperature results. The goal of the computational study combined with experimental work reported in this paper is to explore the intrinsic mechanism of cracking from the aspect of phase transformation in laser drilling of YSZ.
TOPICS: Lasers, Drilling, Thermomechanics, Phase transitions, Temperature, Stress, Transients (Dynamics), Cracking (Materials), Fracture (Materials), Fracture (Process)
research-article
J. Heat Transfer   doi: 10.1115/1.4042779
In the present work, Direct Contact Condensation (DCC) was studied using a mathematical and com- putational model with an eulerian approach. The homemade code MFSim was used to run all the computational simulations in the cluster of the Fluid Mechanics Laboratory from the Federal University of Uberlandia (UFU). The computational model was validated and showed results with high accuracy and low differences compared to previous works in the literature. A complex case study of DCC with cross-flow was then studied and the computa- tional model provided accurate results compared to experimental data from the literature. The jet centerline was well represented and the interface dynamic was accurately captured during all the simulation time. The investiga- tion of the velocity field provided information about the deeply transient characteristic of this flow. The v-velocity component presented the most large variations in time since the standard deviation was subjected to a variation of about 45% compared to the temporal average. In addition, the time history of the maximum resultant velocities observed presented magnitude from 29 m/s to 73 m/s. The importance of modelling 3D effects was confirmed with the relevance of the velocity magnitudes in the third axis component. Therefore, the eulerian phase change model used in the present study indicated the possibility to model even complex phenomena using an eulerian approach.
TOPICS: Condensation, Computational fluid dynamics, Cross-flow, Simulation, Transients (Dynamics), Fluid mechanics, Flow (Dynamics), Modeling
Technical Brief
Chembai Ganesh Subramaniam
J. Heat Transfer   doi: 10.1115/1.4042813
A generalized effective medium theory is proposed to account for the fractal structure of the dispersed phase in a dispersing medium under the dilute limit. The thermal conductivity of nanofluids with fractal aggregates is studied using the proposed model. Fractal aggregates are considered as functionally graded spherical inclusions and its effective thermal conductivity is derived as a function of its fractal dimension. The results are studied for self-consistency and accuracy within the limitations of the analytical approximations used.
TOPICS: Thermal conductivity, Fractals, Nanofluids, Approximation, Dimensions
Discussion
Asterios Pantokratoras
J. Heat Transfer   doi: 10.1115/1.4042783
The present comment concerns some doubtful results in the above paper.
research-article
J. Heat Transfer   doi: 10.1115/1.4042810
An experimental investigation of fluid flow friction and heat transfer coefficient in simultaneously developing flow through a multiport microchannel flat tube (MMFT) was presented. The cross-sectional geometries of five tubes were rectangular with hydraulic diameters of 0.8 mm to 1.33 mm and aspect ratio of 0.44 to 0.94. The working fluid was water, and the Reynolds number was in the range 150-4500. The experiment result showed that friction factor was successfully predicted by classical correlation in laminar regime, whereas the laminar-turbulent transition in the developing flow was not as obvious as in the completely developed flow. The greater aspect ratio produced stronger heat transfer capacity in the developing flow, although the effect of the aspect ratio decreased at increased Reynolds numbers for heat transfer characteristics. Moreover, the scale effect improved the heat transfer performance of MMFTs, especially at high Reynolds numbers.
TOPICS: Convection, Microchannels, Flow (Dynamics), Heat transfer, Reynolds number, Friction, Fluids, Turbulence, Fluid dynamics, Water, Heat transfer coefficients
research-article
J. Heat Transfer   doi: 10.1115/1.4042770
In this paper, a lattice Boltzmann (LB) model is established to simulate the gaseous fluid flow and heat transfer in the slip regime under the curved boundary condition. A novel curved boundary treatment is proposed for the LB modeling, which is a combination of the non-equilibrium extrapolation scheme for the curved boundary and the counter-extrapolation method for the macroscopic variables on the curved gas-solid interface. The established numerical model can accurately predict the velocity slip and temperature jump of the micro-scale gas flow on the curved surface, which agrees well with the analytical solution for the micro-cylindrical Couette flow and heat transfer. Then, the slip flow and heat transfer over the single micro cylinder are numerically studied in this work. It shows that the velocity slip and temperature jump are obviously influenced by the Knudsen number and Reynolds number, and the local Nusselt number depends on which gas rarefaction effect (velocity slip or temperature jump) is dominant. An increase in the Prandtl number leads to a decrease in the temperature jump, which enhance the heat transfer on the micro cylinder surface. The numerical simulation of the flow and heat transfer over two micro cylinders in tandem configuration are carried out to investigate the wake interference effect. The results show that the slip flow and heat transfer characteristics of the downstream micro cylinder are influenced by the wake region behind the upstream cylinder as the spacing is small.
TOPICS: Heat transfer, Computer simulation, Cylinders, Slip flow, Lattice Boltzmann methods, Temperature, Flow (Dynamics), Wakes, Knudsen number, Phase interfaces, Microscale devices, Modeling, Boundary-value problems, Reynolds number, Gas flow, Equilibrium (Physics), Fluid dynamics, Prandtl number
research-article
Michael J. Bluck
J. Heat Transfer   doi: 10.1115/1.4042776
This article considers the convective heat transfer processes in fully developed laminar magnetohydrodynamic (MHD) flows in rectangular ducts of the kind proposed in some nuclear fusion blanket designs. Analytical solutions which incorporate the non-uniformity of peripheral temperature and heat flux and the effect of volumetric heating, are developed as functions of magnetic field strength and duct aspect ratio. A distinct feature of these MHD problems, not yet addressed in the literature, is that unlike the conventional characterisation of heat transfer by a Nusselt number, it is necessary to generalise the concept to vectors and matrices of Nusselt coefficients, due to the extreme anisotropy of both the flow and heating. The new analytical results presented here capture more complex heat transfer behaviour than non-MHD flows and in particular chracterize the importance of aspect ratio. The importance of these new results lie not only in the improved understanding of this complex process, but also in the provision of characterisations of convective heat transfer which underpin progress toward systems scale simulations of fusion blanket technology which will be vital for the realisation of practical fusion reactors.
TOPICS: Heat transfer, Flow (Dynamics), Magnetohydrodynamics, Ducts, Heating, Convection, Engineering simulation, Temperature, Nuclear fusion, Fusion reactors, Magnetic fields, Simulation, Anisotropy, Underpinning, Heat flux
research-article
J. Heat Transfer   doi: 10.1115/1.4042811
The coupled phenomena of radiative-magnetohyrodynamic natural convection in a horizontal cylindrical annulus is numerically investigated. The buoyant flow is driven by the temperature difference between the inner and outer cylinder walls, while a circumferential magnetic field induced by a constant electric current is imposed. The hybrid approach of finite volume and discrete ordinates methods (FV-DOM) is developed to solve the nonlinear integro-differential governing equations in polar coordinate system, and accordingly, the influences of Hartmann number, radiation-convection parameter, and optical properties of fluid and wall on thermal and hydrodynamic behaviors of the 'downward flow', originally occurring without consideration of radiation and magnetic field, are mainly discussed. The results indicate that both the circulating flow and heat transfer are weakened by the magnetic field, but its suppression effect on the latter is rather small. Under the influence of magnetic field, the 'downward flow' pattern has not been obtained from zero initial condition even for the case of weak radiation of NR=0.1. Besides, the variation of radiative heat transfer rate with angular positions diminishes for the fluid with strong scattering or weak absorption.
TOPICS: Magnetohydrodynamics, Natural convection, Annulus, Magnetic fields, Flow (Dynamics), Radiation (Physics), Fluids, Absorption, Temperature, Heat transfer, Radiative heat transfer, Electric current, Scattering (Physics), Radiation scattering, Electromagnetic scattering, Convection, Cylinders