Heat Ux Research Articles

A numerical simulation of MHD ow and radiation heat transfer of nano uids through a porous medium with variable surface heat ux and chemical reaction

In this paper, the problem of MHD ow and radiation heat transfer of nanouids against a at plate in porous medium with the eects of variable surface heat ux and rst-order chemicalreaction is investigated numerically. Three dierent types of nanoparticles, namely Cu, Al2O3 andAg are considered by using water as a base uid with Prandtl number Pr = 6:2. The governingpartial dierential equations can be written as a system of nonlinear ordinary dierential equationsover a semi-innite interval using a similarity transformation. A new eective collocation methodis proposed based on exponential Bernstein functions to simulate the solution of the resultingdierential systems. The advantage of this method is that it does not require truncating ortransforming the semi-innite domain of the problem to a nite domain. In addition, this methodreduces the solution of the problem to the solution of a system of algebraic equations. Graphicaland tabular results are presented to investigate the inuence of the solid volume fraction, types ofnanoparticles, radiation and suction/blowing, magnetic eld, permeability, Schmidt number andchemical reaction, on velocity, temperature and concentration proles. The obtained results ofthe current study are in excellent agreement with previous works.

Experimental estimation heat flux and heat transfer coefficient by using inverse methods

The purpose of this paper is to present experimental applications of the inverse heat transfer methods (conjugate gradient method and sequential method). Three experiments are designed to estimate the heat ux and the heat transfer coecients. In the third experiment, convective heat transfer coecient is estimated directly and indirectly. In direct estimation, the conjugate gradient method with adjoint equation is used. The results show that inverse heat transfer methods are able to estimate the desired parameters with good accuracy in experimental state when mathematical model and boundary condition are correct and appropriate with experimental model.

SOLUTION OF SLIP FLOW OVER A PERMEABLE PLATE (WITH SUCTION) EMBEDDED IN A POROUS MEDIUM USING THE ADOMIAN DECOMPOSITION METHOD-PADE APPROXIMANTS

In recent years, the study of the boundary-layer  ow behavior and heat transfer characteristics of a Newtonian  uid over a plate embedded in a porous medium has attracted considerable attention because of its extensive applications in engineering processes, especially in the enhanced recovery of petroleum resources and packed bed reactors (Pal and Shivakumara, 2006; Ishak et al., 2007). Recently, Aziz (2010) studied the boundary-layer slip  ow over a  at plate with a constant heat  ux condition at the SOLUTION OF SLIP FLOW OVER A PERMEABLE PLATE (WITH SUCTION) EMBEDDED IN A POROUS MEDIUM USING THE ADOMIAN DECOMPOSITION METHOD–PADE APPROXIMANTS

Uncertainty Analysis of Reaction Rates in a Finite-Rate Surface-Catalysis Model

The implementation of a nite-rate-catalytic wall boundary condition easily incorporated into generic hypersonic ow solvers is described in detail. Simulations of hypersonic ow over a cylinder are presented using the nite-rate-catalytic model parameterized with a test air-silica chemical model comprising the gas-surface reaction mechanisms and their associated rates. It is demonstrated that backwards recombination rates should not be arbitrarily set but must be consistent with the gas-phase thermodynamics, otherwise a drift from the equilibrium state may occur. The heat ux predicted by the nite rate model lies between non-catalytic and super-catalytic limits depending on the surface temperature. It is found that even for a constant surface temperature, the oxygen recombination eciencies determined by the model are not only a function of temperature, but also a function of the surface coverage, where recombination eciencies are seen to rise as coverage decreases. Monte Carlo uncertainty analysis is performed to correlate the inuence of individual mechanisms to the stagnation point heat ux. The expected progression of dominant mechanisms is found as the surface temperature is raised, and the uncertainty in heat ux is highly correlated to the reaction rate of the dominant mechanism at a specied surface temperature. It is found that increased surface reactivity increases the chemical heat ux while also altering the boundary layer in a manner that decreases the convective heat heat ux.

Existence, uniqueness and exponential decay: An evolution problem in heat conduction with memory

A rigid linear heat conductor with memory conductor is considered. An evolution problem which arises in studying the thermodynamical state of the material with memory is considered. Specically, the time evolution of the temperature distribution within a rigid heat conductor with memory is investigated. The constitutive equations which characterize heat conduction with memory, involve an integral term since the temperature’s time derivative is connected to the heat ux gradient. The integro-dierenti al problem, when initial and boundary conditions are assigned, is studied to obtain existence and uniqueness results. Key tools, turn out to be represented by suitable expressions of the minimum free energy which allow to construct functional spaces which are both meaningful under the physical as well as the analytic viewpoint since therein the existence and uniqueness results can be established. Finally, conditions which guarantee exponential decay at innity are obtained.

Large-Eddy Simulation of Flame-Turbulence Interactions in a Shear Coaxial Injector

Various state-of-the-art Computational Fluid Dynamics (CFD) approaches are currently being evaluated by NASA for the modeling of combustion chambers in liquid rocket engines. This evaluation is performed through the simulation of a laboratory-scale chamber equipped with a single-element gaseous hydrogen-gaseous oxygen GH2-GO2 shear-coaxial injector. While a joint paper 1 compares the dierent steady and unsteady simulations of this chamber, this paper focuses on the three-dimensional Large Eddy Simulations (LES) performed at the Georgia Institute of Technology. The goal here is to nd a compromise between accuracy and computational cost while accurately capturing the unsteady ame physics thanks to the full 3D formulation. The solver employed in this study includes a hybrid central-upwind scheme used to solve the compressible, multi-species Navier-Stokes equations with a thermally perfect formulation. From a resolution point of view, priority was given to the near-eld resolution rather than the near-wall resolution. Yet, the seemingly correct modeling of the ame anchoring and dynamics provides a satisfactory estimate of the wall heat ux. The unsteady and three dimensional features of the ow are discussed in length and the implications of the unique features of this shear-coaxial GH2-GO2 injector for turbulent combustion modeling are also analyzed.

Transport Studies Using Perturbative Experiments

By inducing a small electron temperature perturbation in a plasma in steady state one can in principle determine the conductive and convective components of the electron heat ux, and the associated thermal diffusivity and convection velocity. The same can be done for other plasma parameters, like density or ion temperature.In this paper experimental and analysis techniques are briey reviewed. The fundamental question whether the uxes are linear functions of the gradients or not is discussed. Experimental results are summarized, including so-called ‘non-local’ phenomena.

Integral Equation for the Heat Transfer with the Moving Boundary

Although the heat conduction problem in cooling Ž ns is usually consideredto haveone steady-statesolutionfor givenboundaryconditions, two solutions may exist when nonstandard, yet physically admissible, boundary conditions are applied. In particular, the situation inwhich the cooling Ž n has Ž xed temperatureat both ends and speciŽ ed heat  ux at the root is examined. The analysis shows that, depending on the value of the heat  ux at the Ž n root, the problem may have no solutions, one solution, or two solutions for the Ž n length. The results can Ž nd practical applications in the design of passive safety devices for chemical or nuclear plants.

Is There a Difference Between Aeroacoustics and Aerodynamics? An Aeroelastician's Viewpoint

Nomenclature a = speed of sound c = undisturbed speed of sound, a1 cp = speciŽ c heat coefŽ cient at constant pressure D = strain rate tensor Dc=Dt = material time derivative deŽ ned in Eq. (33) Di j = 1 2 .vi; j C v j;i / DW =Dt = material time derivative deŽ ned in Eq. (28) d = dissipative term vector; Eq. (41) E.x/ = domain function;Eq. (10) F = three-dimensionalFourier transform G = fundamental solution for Laplacian; Eq. (7) G A = fundamental solution for acoustics; Eq. (15) GQC = quasi-potentialcompressible fundamental solution; Eq. (35) GQS = quasi-potential subsonic fundamental solution; Eq. (36) GVC = viscous compressible fundamental solution; Eq. (49) H .t/ = Heaviside step function h = enthalpy hS = slab thickness J = Jacobian of transformation k = kkk k = Fourier transform frequency vector L = linear operator L = Laplace transform L¤ = linear operator adjoint of L ` = characteristic length M = undisturbedMach number, v1=c n = outward normal to S Pr = Prandtl number,1cp=· p = pressure q = heat  ux vector R = ideal gas constant RS = slab radius

Modified Collapsed Dimension Method for Radiative Heat Transfer Problems

Introduction C OLLAPSED dimensionmethod (CDM) is one of the ray tracing methods used for the solution of radiative transfer problems. Development of this method is partly based on the works of Shih and Chen1 and Shih and Ren2 on the discretized intensity method. Some light on the method was thrown by Blank. Subsequent developmentof the method was made by Blank andMishra.4 Detailed description of this method is available in Ref. 5. In CDM, three-dimensionalradiative information is mapped into a two-dimensionalsolutionplane in terms of effective intensity (EI) andoptical thicknesscoefŽ cient (OTC). Thus, unlikeothermethods, analysis and computations in this method are performed in a twodimensional solution plane instead of three-dimensionalspace. CDMhas beenused for the solutionof radiativetransferproblems with highaccuracy.4;5 Thismethodhasbeenfoundtowork for awide rangeof optical thickness (very low to high optical thickness). Furthermore, CDM has also been found to work well for the conjugate mode heat transfer problems. In CDM, for determinationof heat  ux and temperature information, at each point of interest EIs have to be integrated over planar angle in the solutionplane.Theseangularintegrationsareperformed by dividing the planar angle into intervals of equal sizes. In each subinterval, EI is assumed isotropic. Hence, for higher accuracy, CDM requiresmore EIs and, thus, higher computational time. In the presentwork,with the objectiveofmakingCDMmore economical, the method is modiŽ ed. In the modiŽ ed CDM (MCDM), angular integrations of the EIs are performed differently. The discretizationand integrationsperformed in thismethod originatefrom the concept of the discrete ordinate method (DOM). Here, the planar angle is divided into a Ž nite number of subintervals according to the number of Gaussian quadraturepoints considered.Hence, in MCDM, angular subintervals are unequal and instead of considering average values of interval, the weighted mean corresponding to the Gauss points is considered. With this, the method becomes more realistic, and it derives computational efŽ ciency with a more realistic representationof the radiative transfer process. In the present work, improvements in MCDM over CDM are tested by solving radiative transfer problems in oneand twodimensional Cartesian enclosures with gray and homogeneous, absorbing, emitting, and anisotropically scattering medium. Both radiative and nonradiative equilibrium situations are considered. MCDM and CDM results are compared with results from the exact method and DOM.

Regression-Rate and Heat-Transfer Correlations for Hybrid Rocket Combustion

A series of static engine Ž rings, thermal pyrolysis experiments, and gas chromatograph/mass spectrometer tests were conducted to investigate the solid-fuel regression rate and heat-transfer behavior in a lab-scale hybrid rocket motor burning hydroxyl terminated polybutadiene/gaseous oxygen. A real-time, X-ray radiography system was used to determine the local, instantaneousregression rates. A dataanalysisprogramwas developedto help correlate the experimental data. The semi-empirical regression-rate correlation showed that, in addition to convection, radiation from soot and variable  uid properties across the boundary layer had signiŽ cant effects on regressionrate behavior. The radiant heat  ux from sootwas relativelymore signiŽ cant under lowmass  ux and low oxidizerto-fuel ratio conditions. Radiation from CO2 , H2O, and CO was quite small compared to convection and soot radiation. The nondimensional regression-rate correlation agreed with the experimental data to within § 3%. Stantonand Nusselt-number correlations were also developed and found to depend on both  ow regime and radiant heat  ux. The regression-rate correlations predicted independent data from both a lab-scale tube burner and the 11-in. (28 cm) JIRAD motor to very reasonable accuracy.

Minimum Safe Distance from Pool Fires

Radiation heat transfer is a primary reason for Ž re growth. Experimental data are needed to clarify the ignition potential and time required to ignite a particular target second item. The concepts of critical heat  ux and thermal response parameter are important to the material ignition problem. The objective of the present contribution is to clarify these important radiant ignition concepts and to exemplify a range of realistic calculations related to real-world situations.

Conduction and Radiation Heat Transfer in High-Porosity Fiber Thermal Insulation

Nomenclature a, b = partial wave coefŽ cients C = radiative cross section F = orientation distribution function fv = Ž ber volume fraction G k = asymmetry scattering factor; Eq. (23) Ib = black-body radiation Ib k = Planck function i k = Ž ber-scattering intensity distribution K k = extinction coefŽ cient kr = radiative conductivity k0 = propagation constant L = specimen thickness M = number of Ž ber polar orientations mg = molecularmass of gas-phasematerial ms = molecularmass of solid-phasematerial N = number of Ž ber sizes n = real part of complex refractive index P = size of the equivalent pore spaces inside aerogel pk = scattering phase function q = heat  ux r = radius of Ž ber T = temperature xi = fractional volume of Ž bers of radius ri a = size parameter, 2p r / k C k = modiŽ ed extinction coefŽ cient; Eq. (22) c = ratio of speciŽ c heats at constant pressure and constant volume d s = solid fraction of matrix medium g = scattering angle

Numerical Thermal Model of NASA Solar Electric Propulsion Technology Application Readiness Ion Thruster

A thermal computer model of the 30-cm NASA solar electric propulsion technology application readiness (NSTAR) xenon ion thruster has been produced using a lumped-parameter thermal nodal-network scheme. This model contains 104 nodes on the thruster and was implemented using SINDA and TRASYS on various UNIX workstations. The model includes the radiation and conduction heat transfer, the effect of plasma interaction on the thruster, andan account for Ž nely perforated surfaces. Themodelwasdeveloped in conjunctionwith anNSTAR thruster outŽ tted with approximately 20 thermocouples for thermal testing at the JohnH. Glenn Research Center. The results of these experiments were used to calibrate and conŽ rm the computer model Ž rst without and then with the plasma interaction. The calibrated model was able to predict discharge chamber temperatures to within 10±C of measured temperatures. To demonstrate the ability of the model under various circumstances, the heat  ux was examined for a thruster operating in a deep-space environment.

Analysis of Galileo Probe Heatshield Ablation and Temperature Data

The Galileo Probe deceleration module contained instrumentation to measure heatshield ablation and temperatures during its hypersonic entry into the atmosphere of Jupiter. The ablation data reduction and analysis were reported previously; therefore, only a brief review is provided. One-dimensional transient analyses of the heatshield ablation, pyrolysis, and heat conduction were performed at the thermometer locations. These calculations were coupled with an axisymmetric heat conduction model to predict the thermometer temperature response. Near the end of the frustum, the temperature and recession data are very consistent. The measured recession is 3.63 § 0.15 cm, and the estimated peak heat  ux and heat load are 13.4 § 0.5 kW/cm2 and 161 § 6 kJ/cm2, respectively. At the aft cover, the material response analyses do not match the low magnitude and slope of the temperature data, which seem to indicate that heat conduction into the heatshield was lower than expected.

Dynamic Oxidation Performance of NARloy-Z with Cu-30 Volume Percent Cr Coating

The copper alloyNARloy-Z (Cu-3Ag-0.5Zrwt%)has goodpotential for high heat  ux structural applications in hypersonic vehicles because of its high thermal conductivity and high-temperature strength. However, it is subject to severe oxidationat temperatures where it might be used. A Cu-30 vol%Cr protective coating produced by lowtemperature arc vapor deposition was evaluated under dynamic oxidation in an electric arc-heated wind tunnel. The emittance of the coating is greater than the emittance of the alloy, and the recombination efŽ ciency of the coating is typical of values encountered with metal alloys and metallic oxides. The coating protects the alloy under dynamic oxidation conditions, with specimens gaining less than 1 mg/cm2 over a 10-h exposure period. Protection of the alloy from oxidation results from a continuous layer of Cr2O3 that it is partially shielded from the hostile dynamic oxidation/atomic oxygen environment by a layer of CuO.

Truss Structure Effects on International Space Station Global Positioning System Antenna Performance

because the wall temperature remains in the diffusion-controlled regime through the trajectory, and the surface oxidation reaction results in heat release to the  ow near the surface. When the wall temperature reaches the sublimation regime, the convectiveheating rate is signiŽ cantly reduced. In the  ight regime of peak stagnation heating, the heat  ux augmentation due to the surface oxidation is much smaller than that due to the catalyticrecombination.However, the difference becomes smaller at lower altitudes. The temporal variations of the wall temperature and the surface mass loss rate alongthe trajectoryare presentedin Fig. 4.After the peakconvective heating, the surface mass loss rate decreases gradually because it is not sensitive to the wall temperature in the diffusion-controlled regime, as shown in Fig. 1. Consequently, the wall temperature for the ablatingwall becomes higher than that for the nonablatingwall at lower altitude.

Modeling and Experiments of Laser-Induced Ignition of Nitramine Propellants

The objective of the work is to develop and experimentally verify a model for CO2 laser-induced ignition of nitramine-based propellants. The one-dimensional model considers heat conduction in the condensed-phase coupled to heat and mass transport with global chemical kinetics of a heterogeneous propellant in the gas-phase region. The highly nonlinear model was solved numerically. Experimentally, increases in heat  ux [125– 375 W/cm (193– 578 cal/s-in.)] lowered the ignition delay time, but changes in pressure [1.38–3.79 MPa (200–550 psia)] had very little effect. This supports the assumption that cyclotrimethylenetrinitramine decomposition is primarily temperature controlled. These trends are correctly predicted by the model. Predictions of ignition delay time match the experimental data within the measurement uncertainty. Sensitivities of the numerical solution to the material properties and kinetic rate constants are addressed.

Improvements to Steady-State Combustion Modeling of Cyclotrimethylenetrinitramine

Many improvements have been made to models of cyclotrimethylenetrinitramine combustion in the past few years. The one-dimensional model presented in this paper models the solid, two-phase, and gas regions using complex kinetics and concentrationand temperature-dependent thermophysical properties. Calculated values agree well with experimentally determined burning rate sp, melt layer thickness, surface temperature, and species concentration proŽ les. When including laser-assisted burning in the model, a dark zone appeared that was similar to that seen experimentally. With the laser-assisted case, the chemistry controlling the burning rate is signiŽ cantly different from cases without the laser heat  ux. Calculations show that the melt-layer thickness is determined primarily by the liquid thermal conductivity and the surface temperature is controlled by the vapor pressure correlation. All other model predictions are relatively insensitive to these parameters. The condensed-phase decomposition and evaporation/condensation submodel are the weakest areas of the model.

Large-Scale Roughness Influence on Turbulent Hypersonic Boundary Layers Approaching Compression Corners

The in uence a short stretch of large-scale regular surface roughness on a Mach 5 turbulent boundary layer approaching a compression corner was investigated on axisymmetric wind-tunnel models. Roughnesses were of sawtooth and cavity shape with typical dimensions up to a full boundary-layer thickness. The effects of roughness on  ow parameters compared to an equivalent smooth surface differed signiŽ cantly for each measured quantity. Velocity proŽ les downstream of the roughness were found to be less full, and skin friction was reduced. Surface heat  ux was increased for a short distance. Surface pressures remained unchanged. Little in uence was noted on the  ow in the compression corner. Upstream in uence was increased in some cases but no large-scale separation due to the additionaleffects of roughnesswas observed. Roughnesses of sawtooth shapewere found to cause greater disturbance to the  ow than square cavities.