11. Heat Transfer, Species Transport and Multiphysics CFDIntroduction and contextComputational fluid dynamics is most valuable when it represents the coupled physics that determine an engineering system’s behaviour. In many practical devices, momentum transport cannot be separated from energy transfer, chemical composition, phase change, porous resistance, structural deformation, or electromagnetic effects. A gas turbine combustor, for example, involves turbulent flow, heat transfer, species mixing, chemical reaction, radiation, and thermal stresses. A boiling channel combines liquid–vapour motion, phase change, interfacial heat transfer, and pressure variation. A battery pack involves conjugate heat transfer, porous electrodes, species or charge transport, and thermal management. These problems are generally called multiphysics CFD problems. Their difficulty is not simply that several equations must be solved. The principal challenge is that the equations are strongly coupled, often nonlinear, and governed by processes operating at widely different length and time scales. A physically credible simulation therefore requires more than selecting models in software. It requires identification of dominant mechanisms, formulation of appropriate conservation equations, careful treatment of interfaces and source terms, numerical stability, and systematic validation. This chapter develops a framework for coupling convection, conduction, radiation, and species transport, and then extends it to reacting flows, combustion, multiphase and free-surface flows, cavitation, porous media, and fluid–structure interaction. Emphasis is placed on model selection: the best model is not the most elaborate one, but the least expensive model that captures the physics relevant to the engineering decision. Learning objectivesAfter studying this chapter, the reader should be able to: 1. formulate the principal equations for conjugate heat transfer and species transport; 2. distinguish diffusion, convection, radiation, reaction, and phase-change source terms; 3. select suitable models for reacting, multiphase, cavitating, porous, and fluid–structure problems; 4. explain the coupling strategies used in multiphysics solvers; 5. assess mesh, time-step, convergence, stability, and validation requirements; 6. evaluate practical trade-offs between fidelity, computational cost, and uncertainty; 7. identify professional, safety, ethical, and governance issues in multiphysics CFD. From a single flow field to coupled conservation lawsFor a Newtonian fluid, the continuity and momentum equations retain their usual forms. The additional equations arise because temperature and composition influence density, viscosity, buoyancy, reaction rates, and phase behaviour. In a general compressible formulation, \[ \frac{\partial \rho}{\partial t}+\nabla\cdot(\rho \mathbf{u})=0, \] \[ \frac{\partial(\rho\mathbf{u})}{\partial t}+\nabla\cdot(\rho\mathbf{u}\mathbf{u})=-\nabla p+\nabla\cdot\boldsymbol{\tau}+\rho\mathbf{g}+\mathbf{S}_m. \] The total energy equation may be expressed in terms of sensible enthalpy, total enthalpy, or internal energy. A representative sensible-enthalpy equation is \[ \frac{\partial(\rho h)}{\partial t}+\nabla\cdot(\rho\mathbf{u}h)=\nabla\cdot(k\nabla T)+S_h, \] where \(k\) is thermal conductivity and \(S_h\) includes viscous dissipation, volumetric heating, radiation exchange, reaction heat, and phase-change contributions. In a solid, the velocity is absent and heat conduction is described by \[ \rho_s c_{p,s}\frac{\partial T}{\partial t}=\nabla\cdot(k_s\nabla T)+\dot q_s. \] At a fluid–solid interface, temperature and normal heat flux are normally continuous: \[ T_f=T_s,\qquad -k_f\frac{\partial T_f}{\partial n}=-k_s\frac{\partial T_s}{\partial n}. \] This simultaneous solution of fluid convection and solid conduction is called conjugate heat transfer. Prescribing a wall temperature is appropriate only when the wall temperature is known or its thermal resistance is negligible. A prescribed heat flux may similarly be unsuitable when wall conduction controls the result. Convection and dimensionless interpretationConvection is the transport of thermal energy by fluid motion. It contains both mean advection and turbulent or unresolved transport. In Reynolds-averaged models, turbulent heat flux is usually represented through an eddy diffusivity, giving an effective conductivity related to turbulent viscosity by a turbulent Prandtl number. This approximation is convenient but may be inaccurate in separated flows, strong buoyancy, swirling flows, and near-wall regions. The Péclet number, \(Pe=UL/\alpha\), compares convection with thermal diffusion. Large values indicate thin thermal boundary layers and increased sensitivity to numerical diffusion and mesh alignment. The Prandtl number, \(Pr=\nu/\alpha\), compares momentum and thermal diffusion. The Rayleigh number, \(Ra=g\beta\Delta T L^3/(\nu\alpha)\), characterizes buoyancy-driven flow and assists in judging whether natural convection is laminar or turbulent. RadiationRadiation is electromagnetic energy transfer and does not require a material medium. At engineering temperatures it may be comparable to convection, especially in furnaces, fires, boilers, re-entry vehicles, and surfaces with large temperature differences. The net radiative exchange between idealized surfaces depends on emissivity, view factors, temperature, and enclosure geometry. Participating gases such as carbon dioxide, water vapour, soot, and combustion products absorb, emit, and sometimes scatter radiation. Common CFD radiation approaches include the surface-to-surface method, discrete ordinates, the discrete transfer method, and radiation models based on angular or diffusion approximations. Surface-to-surface radiation is efficient for nonparticipating media, whereas participating combustion gases require a volumetric radiation model. Radiation properties are wavelength-dependent in reality; grey-gas approximations reduce cost but introduce modelling error. Radiation should be coupled to the energy equation because the radiative source changes temperature, which in turn changes emission. Species transport and reacting flowsFor species \(i\), the general transport equation is \[ \frac{\partial(\rho Y_i)}{\partial t}+\nabla\cdot(\rho\mathbf{u}Y_i) = -\nabla\cdot\mathbf{J}_i+\dot\omega_i+S_i, \] where \(Y_i\) is mass fraction, \(\mathbf{J}_i\) is diffusive flux, \(\dot\omega_i\) is the chemical production rate, and \(S_i\) represents additional sources. The mass fractions must satisfy \(\sum_iY_i=1\). For dilute mixtures, Fickian diffusion is often adequate. In high-pressure, multicomponent, or strongly non-uniform mixtures, mixture-averaged or multicomponent diffusion may be required. Thermal diffusion, or the Soret effect, can cause species migration due to temperature gradients; the Dufour effect is the reciprocal energy flux caused by concentration gradients. A reacting flow couples species equations to energy through the heat of reaction and couples both to momentum through density and transport properties. Chemical reaction rates are frequently Arrhenius functions, \[ k=A T^n\exp\left(-\frac{E_a}{RT}\right), \] so small temperature errors can produce large rate errors. This sensitivity creates stiffness: chemical time scales may be much shorter than flow time scales. Explicit time integration may then require impractically small steps, while implicit methods and robust chemistry solvers become attractive. The mixture fraction is a conserved scalar under idealized nonpremixed combustion and is useful for describing fuel–oxidizer mixing. In premixed combustion, flame-propagation models, progress variables, flame-surface-density models, or finite-rate chemistry may be used. Finite-rate chemistry resolves reaction kinetics but can be expensive and mechanism-dependent. Equilibrium or partially stirred reactor models are cheaper but cannot reliably predict ignition delay, extinction, pollutant formation, or transient chemistry unless their assumptions are satisfied. Turbulence–chemistry interaction is often the dominant modelling uncertainty. RANS models provide mean reaction fields at modest cost but require closures for fluctuations. Large-eddy simulation resolves larger turbulent structures and can improve prediction of unsteady mixing and flame dynamics, but demands finer meshes and smaller time steps. Direct numerical simulation is generally restricted to fundamental research because it resolves all relevant scales. Combustion models must be selected according to the question being asked. A preliminary estimate of furnace temperature may justify a reduced mechanism and an eddy-dissipation model. Prediction of carbon monoxide, nitrogen oxides, flashback, or ignition may require finite-rate chemistry, detailed radiation, and high-fidelity turbulence treatment. A model that reproduces outlet temperature may still predict pollutant emissions incorrectly. Multiphase and free-surface flowsMultiphase CFD represents two or more immiscible or interacting phases. The central modelling decision is whether the interface is resolved, averaged, or represented statistically. The volume-of-fluid method tracks the volume fraction of each phase and is particularly appropriate for a sharp, deforming interface such as a wave, filling process, or sloshing liquid. Level-set methods represent the interface as an implicit surface and provide smooth curvature calculations, although mass conservation requires special attention. The arbitrary Lagrangian–Eulerian approach can follow a moving mesh when interface deformation is moderate and mesh quality can be preserved. The Eulerian multiphase model solves conservation equations for interpenetrating continua and is suitable for dispersed flows with significant phase interaction. The Eulerian–Lagrangian approach solves the carrier fluid on a mesh and tracks droplets, bubbles, or particles as parcels. It is efficient when the dispersed phase occupies a relatively small volume fraction, but two-way coupling, particle collisions, turbulent dispersion, and parcel statistics must be treated carefully. The discrete element method may be coupled to CFD when particle–particle contacts are important. Interphase momentum transfer is commonly represented by drag, but lift, added mass, pressure-gradient, wall lubrication, turbulent dispersion, and virtual mass forces may also matter. Heat and mass transfer between phases require correlations for interfacial area and transfer coefficients. Phase change introduces latent heat and mass sources; these sources must conserve mass and energy simultaneously. A free-surface model must distinguish physical interface motion from numerical smearing. Excessive numerical diffusion can alter wave height, entrainment, impact pressure, and breakup. Interface compression, geometric reconstruction, bounded advection, and mesh refinement near the interface are therefore important. Time-step selection is often governed by a Courant condition and, for capillary flows, a capillary time-scale restriction. CavitationCavitation occurs when local pressure falls below the vapour pressure of a liquid, causing vapour formation. Subsequent condensation can produce strong pressure pulses, noise, vibration, erosion, and performance loss in pumps, turbines, propellers, valves, and fuel systems. Cavitation prediction requires a mass-transfer model between liquid and vapour, an equation of state or saturation relation, and an appropriate treatment of turbulence and nuclei. A cavitation number, commonly based on the difference between reference pressure and vapour pressure divided by dynamic pressure, provides a useful operating indicator. However, cavitation inception also depends on dissolved gas, nuclei population, surface roughness, and transient pressure fluctuations. Homogeneous models assume a shared velocity or equilibrium-like phase mixture; inhomogeneous models permit separate phase velocities and may better represent slip, but cost more. Agreement with a measured cavity length does not by itself establish reliable prediction of erosion or noise, which requires resolution of collapse dynamics and pressure peaks. Porous media and thermal transportPorous materials contain interconnected solid and void regions. When pore-scale resolution is unnecessary, their effect is represented through volume-averaged equations. The Darcy–Forchheimer relation introduces viscous and inertial resistance: \[ \Delta p/L=\mu K^{-1}U+C_F\rho |U|U. \] The permeability tensor may be anisotropic, as in fibrous composites, packed beds, or geological formations. Porous energy models may assume local thermal equilibrium between solid and fluid, or solve separate temperatures when thermal exchange is finite. The latter is important in high-temperature insulation, metal foams, catalytic converters, and packed-bed reactors. Porous media models are sensitive to permeability, porosity, inertial coefficients, dispersion, and boundary conditions. These parameters should be measured, inferred from experiments, or supported by credible literature. A porous region should not be used merely to conceal an unresolved geometry without checking whether the assumed scale separation is valid. Fluid–structure interactionFluid–structure interaction (FSI) occurs when fluid forces deform a structure and the deformation changes the flow. Examples include aeroelastic wings, flexible valves, blood vessels, pipes, membranes, and heat exchangers. In one-way coupling, fluid loads are transferred to the structure but structural deformation is not returned to the fluid. This is acceptable when deformation is small. Two-way coupling is required when deformation significantly changes the flow or when dynamic instability is possible. In partitioned FSI, separate fluid and structural solvers exchange pressure, displacement, velocity, and traction at the interface. Weak coupling exchanges information once per time step; strong coupling iterates until interface residuals are sufficiently small. Strong coupling is more stable for incompressible flow, light structures, large added mass, and strong deformation, but is computationally expensive. Under-relaxation, quasi-Newton schemes, sub-iterations, and conservative interpolation help prevent divergence. Mesh motion may use spring analogy, Laplacian smoothing, algebraic methods, or remeshing. Large deformation can destroy mesh quality, so overset meshes, immersed-boundary methods, or remeshing may be preferable. Structural nonlinearity, contact, plasticity, fatigue, and material uncertainty can be as important as fluid modelling. Coupling strategies and numerical practiceMultiphysics solvers may be monolithic or partitioned. A monolithic method solves all unknowns in one assembled system and can provide strong coupling and consistent convergence, but implementation and memory requirements are substantial. Partitioned methods use established single-physics solvers and are flexible, modular, and easier to integrate with commercial or specialist codes. Their main difficulty is stable exchange of information at interfaces. Coupling may be explicit, implicit, segregated, or fully coupled. Explicit coupling is inexpensive per iteration but may become unstable when source terms are strong. Implicit coupling improves stability but requires linearization, Jacobians, or inner iterations. Segregated algorithms solve pressure, momentum, energy, and species sequentially; under-relaxation is often essential. A coupled algorithm solves several fields together and can be advantageous for strong density, buoyancy, or reaction coupling. A reliable workflow begins with a hierarchy of models. First define the engineering quantity of interest: pressure drop, wall temperature, heat flux, conversion, pollutant concentration, cavity extent, or structural stress. Then identify dominant mechanisms and characteristic scales. Estimate dimensionless groups, select the geometry and boundary conditions, and establish a baseline model. Add complexity only when sensitivity analysis shows that it affects the decision. Verification asks whether the equations have been solved correctly; validation asks whether they represent reality adequately. Verification includes residual monitoring, conservation balances, manufactured solutions, code-to-code comparison, mesh refinement, and time-step studies. Residual reduction alone is insufficient: a solution can have small algebraic residuals and still violate mass or energy conservation or remain physically wrong. Validation should use independent measurements such as temperatures, species concentrations, pressure fluctuations, interface location, or deformation. Uncertainty quantification should distinguish numerical uncertainty, parameter uncertainty, and model-form uncertainty. Illustrative case study: thermal management of a reacting porous catalytic converterBackgroundConsider an illustrative automotive exhaust after-treatment unit containing a ceramic honeycomb coated with a catalytic washcoat. Hot exhaust gas flows through narrow channels. The monolith is porous at the effective scale, chemical reactions convert pollutants, and heat is conducted through the solid walls and exchanged by convection and radiation near the inlet and outlet. ProblemEngineers must determine whether the converter reaches light-off temperature rapidly without exceeding the allowable ceramic temperature gradient. A model based only on gas flow and a prescribed wall temperature would miss solid conduction and could misrepresent ignition. A detailed pore-resolved model, however, would be too expensive for design studies. Analysis and approachThe selected model treats the gas as a reacting compressible mixture, the honeycomb as an anisotropic porous medium, and the ceramic as a conducting solid. Species equations describe reactants and products. A reduced kinetic mechanism represents oxidation reactions, while an effective volumetric source accounts for the washcoat. Conjugate heat transfer is imposed at gas–solid interfaces. Radiation is included at the open ends and external casing because gas temperatures are high, although internal radiation is represented with an effective property rather than a fully resolved angular model. The study begins with a cold-flow calculation to establish pressure drop and residence time. It then introduces energy transport without reaction, followed by reaction and heat release. Mesh refinement is concentrated near the inlet, outlet, and thermal transition region. Time steps are reduced during ignition because the chemical time scale decreases sharply with temperature. Under-relaxation and implicit source treatment are used to avoid divergence. Outcome and interpretationThe model predicts that the inlet region reaches light-off first, generating a heat-release front that travels downstream. The peak solid temperature, rather than the peak gas temperature, controls durability. A design with slightly larger hydraulic resistance improves residence time and conversion but increases pumping work. The final decision therefore balances conversion, thermal stress, pressure loss, and transient warm-up rather than optimizing one output. Learning pointsThe case demonstrates that porous, reacting, conjugate heat-transfer models are useful only when their effective properties are defensible. It also shows why staged model development, conservation checks, sensitivity analysis, and validation against both pressure drop and temperature history are necessary. Matching pollutant conversion alone would not validate the predicted thermal field. Applications and professional decision-makingMultiphysics CFD supports thermal design of electronics, heat exchangers, combustors, furnaces, cooling channels, batteries, fuel cells, and nuclear systems. Species transport is central to ventilation, indoor air quality, membrane separation, drying, electrochemical devices, and environmental dispersion. Multiphase methods are used in sprays, reactors, sediment transport, hydraulic machinery, casting, additive manufacturing, and oil–gas systems. FSI is important in rotating machinery, aerospace structures, biomedical devices, and safety valves. In industry, model credibility must be communicated with assumptions, parameter sources, mesh statistics, convergence criteria, validation evidence, and uncertainty bounds. Engineers should report whether a result is a prediction, a calibrated estimate, or an exploratory scenario. Design decisions involving pressure vessels, combustion safety, toxic releases, emissions, or public infrastructure require documented review and, where applicable, compliance with relevant codes and regulatory requirements. Automation and digital engineering platforms increasingly connect CAD, meshing, solver execution, post-processing, and optimization. Reduced-order models and surrogate models can accelerate design exploration, while machine learning may identify patterns in high-dimensional simulation data. These tools do not remove the need for conservation laws or physical validation. A data-driven surrogate trained only on a narrow operating range can fail dangerously outside that range. Automated workflows should therefore include physical bounds, dimensional checks, outlier detection, version control, and traceability of input data. Limitations, risks, and common mistakesImportant sources of error include inappropriate turbulence–chemistry closure, uncertain reaction mechanisms, inaccurate thermophysical properties, excessive numerical diffusion, poor interface reconstruction, incorrect phase-change sign conventions, inconsistent source terms, and non-conservative data transfer between solvers. Common mistakes include prescribing wall temperature when wall conduction is dominant, using a single-phase model for a strongly separated two-phase flow, treating radiation as negligible without an order-of-magnitude estimate, and interpreting convergence as validation. Multiphysics models can also be over-parameterized. Adding detailed chemistry, fine particles, radiation bands, or structural nonlinearity may increase computational cost without improving the decision. Conversely, excessive simplification may conceal safety-critical phenomena such as ignition, thermal runaway, cavitation collapse, or flutter. Sensitivity studies should identify which assumptions control the output, and model complexity should be increased selectively. Professional practice requires honest communication of uncertainty. Results should not be presented with unjustified precision, and visual agreement between a simulation and an experiment should not replace quantitative comparison. Confidential industrial data, environmental predictions, and safety analyses require secure handling, reproducibility, and independent technical review where consequences are significant. Current developments and best practicesEmerging multiphysics CFD research includes adaptive mesh refinement driven by error indicators, high-order interface methods, GPU-accelerated chemistry, real-fluid and supercritical-fluid models, immersed and overset methods for moving interfaces, and tightly coupled electrochemical–thermal–fluid simulations. Exascale computing is enabling more realistic large-eddy simulations and uncertainty ensembles. Hybrid physics–machine-learning methods are being explored for subgrid closure, surrogate modelling, and parameter estimation. A sound best-practice sequence is to: - define the decision variable and acceptable uncertainty;
- estimate characteristic scales and dimensionless groups;
- choose the simplest physically defensible model;
- verify conservation, mesh independence, and time-step adequacy;
- introduce coupled physics progressively;
- validate against independent measurements;
- perform sensitivity and uncertainty analyses;
- document assumptions, data sources, solver settings, and limitations.
The central principle is model credibility. Multiphysics CFD is not a substitute for physical reasoning; it is a structured means of applying physical reasoning to systems too complex for closed-form analysis. Chapter SummaryHeat transfer, species transport, reacting flows, multiphase flow, cavitation, porous media, and FSI extend CFD from single-field flow prediction to coupled engineering simulation. Energy equations must account for convection, conduction, radiation, reaction heat, and phase change. Species equations require appropriate diffusion, reaction, and turbulence–chemistry closures. Multiphase models differ according to whether interfaces are resolved, averaged, or tracked statistically. Cavitation requires vapour mass transfer and pressure-sensitive modelling; porous media require defensible effective properties; and FSI requires stable exchange of loads and deformation. Monolithic and partitioned coupling offer different balances of robustness, flexibility, and cost. Verification, validation, conservation checks, mesh and time-step studies, and uncertainty analysis are essential. Model selection should be governed by the engineering question, dominant physics, required fidelity, available data, and computational resources. Professional CFD practice also demands transparent assumptions, reproducibility, responsible use of automation, and clear communication of uncertainty. Key TermsConjugate heat transfer: Simultaneous solution of heat conduction in solids and convection in adjacent fluids. Péclet number: Ratio of advective thermal or mass transport to diffusive transport. Radiative heat transfer: Energy transfer by electromagnetic emission, absorption, and scattering. Participating medium: A medium that absorbs, emits, or scatters radiation volumetrically. Species transport: Conservation-based prediction of the concentration or mass fraction of chemical constituents. Mixture fraction: A conserved scalar describing fuel–oxidizer mixing in idealized nonpremixed flows. Arrhenius law: Temperature-dependent expression commonly used to represent chemical reaction rates. Chemical stiffness: Numerical difficulty caused by widely separated chemical and flow time scales. Turbulence–chemistry interaction: Influence of turbulent fluctuations on reaction rates and flame structure. Volume-of-fluid method: Interface-capturing method based on phase volume fractions. Level-set method: Interface representation using an implicit signed-distance-like function. Eulerian–Lagrangian model: Framework in which carrier flow is solved on a mesh and dispersed entities are tracked. Cavitation: Formation and collapse of vapour regions when liquid pressure falls near or below vapour pressure. Permeability: Measure of a porous medium’s ability to transmit fluid under a pressure gradient. Darcy–Forchheimer model: Porous-flow relation including viscous and inertial resistance. Fluid–structure interaction: Two-way or one-way interaction between fluid loads and structural deformation. Partitioned coupling: Multiphysics strategy using separate solvers that exchange interface data. Verification: Demonstration that numerical equations are solved correctly. Validation: Assessment of whether a model represents the physical system adequately. Model-form uncertainty: Uncertainty arising from assumptions and approximations in the governing model. Review QuestionsShort Answer Questions1. What is meant by conjugate heat transfer? 2. Why can chemical reaction source terms make a CFD calculation stiff? 3. Distinguish a participating and a nonparticipating radiative medium. 4. State the principal difference between a volume-of-fluid and an Eulerian multiphase model. 5. What is the purpose of a porous-medium permeability coefficient? Long Answer Questions1. Derive and explain the principal terms in a species transport equation for a reacting mixture. 2. Compare finite-rate chemistry, eddy-dissipation, and reduced-chemistry approaches for combustion CFD. 3. Explain the modelling and numerical issues involved in free-surface and multiphase simulations. 4. Discuss weak and strong partitioned coupling in fluid–structure interaction. 5. Develop a verification and validation plan for a conjugate heat-transfer simulation. Analytical / Application Questions1. A furnace simulation predicts correct outlet temperature but incorrect wall temperature. Identify possible causes and propose a diagnostic sequence. 2. Select and justify a multiphysics model for a pump operating near cavitation inception, considering fidelity, cost, and validation data. 3. A catalytic porous reactor shows numerical divergence immediately after ignition. Analyse the likely physical and numerical causes and recommend remedies. 22. Multiple Choice Questions with AnswersQuestion 1Which condition most directly justifies using a conjugate heat-transfer model instead of prescribing a wall temperature? A. The fluid is incompressible B. Wall conduction and thermal resistance influence the fluid temperature C. The Reynolds number is very high D. The flow contains no species gradients Correct Answer: B. Wall conduction and thermal resistance influence the fluid temperature Question 2In a reacting species equation, the term that represents chemical production or consumption is A. The diffusive flux B. The convective flux C. The reaction source term D. The pressure gradient Correct Answer: C. The reaction source term Question 3Which model is generally most appropriate for tracking a sharp, deforming liquid free surface? A. Volume-of-fluid B. Darcy–Forchheimer C. Mixture-fraction chemistry only D. Rigid-body dynamics Correct Answer: A. Volume-of-fluid Question 4Why can finite-rate combustion calculations become numerically stiff? A. Pressure is always constant B. Chemical and flow time scales may differ greatly C. Radiation eliminates diffusion D. Species mass fractions are independent Correct Answer: B. Chemical and flow time scales may differ greatly Question 5A porous-medium pressure-drop model that includes both viscous and inertial resistance is the A. Navier–Stokes–Fourier model B. Darcy–Forchheimer model C. Level-set model D. Surface-to-surface radiation model Correct Answer: B. Darcy–Forchheimer model Question 6Which statement best distinguishes verification from validation? A. Verification compares with experiments; validation checks coding B. Verification checks numerical solution accuracy; validation checks physical adequacy C. Both terms mean mesh refinement D. Validation is performed only before solving Correct Answer: B. Verification checks numerical solution accuracy; validation checks physical adequacy Question 7In two-way fluid–structure interaction, structural deformation A. Is ignored by the fluid solver B. Is transferred back to modify the fluid domain C. Is used only to calculate radiation D. Can occur only in compressible flow Correct Answer: B. Is transferred back to modify the fluid domain Question 8For a participating combustion gas, a suitable radiation treatment must account for A. Only wall geometry B. Volumetric absorption and emission C. Only liquid volume fraction D. Permeability anisotropy Correct Answer: B. Volumetric absorption and emission Question 9A CFD model predicts pollutant conversion correctly but has not been checked against pressure drop or temperature history. The most appropriate conclusion is that A. The model is fully validated B. The model has no numerical uncertainty C. Validation remains incomplete for other important outputs D. Reaction chemistry is unnecessary Correct Answer: C. Validation remains incomplete for other important outputs Question 10When strong coupling causes a partitioned FSI calculation to diverge, a commonly appropriate remedy is A. Remove all interface exchanges B. Use under-relaxation and interface sub-iterations C. Increase the time step without testing D. Replace structural deformation by a fixed wall Correct Answer: B. Use under-relaxation and interface sub-iterations
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