CFD Researchers: Solver Rules for Combined Convection and Radiation
Radiation changes convective heat transfer significantly whenever wall emissivity, temperature differences, or participating media absorption are non-negligible. In those regimes, the practical response is to add a radiative transfer equation solver (discrete ordinates or an appropriate PN or Monte Carlo method), check whether the Boussinesq approximation still holds, and track the Richardson and Planck numbers before trusting a convection-only result.
TL;DR:
Increasing wall emissivity and participating-media absorption can significantly alter heat transfer, requiring radiative transfer solvers for accuracy.
Dimensionless numbers like the Reynolds, Rayleigh, Richardson, Planck, and Gay-Lussac numbers determine whether radiation or convection dominates in a given regime.
Coupled simulations typically use discrete ordinates or P1 methods paired with finite volume solvers, employing iterative partitioned coupling with relaxation for stability.
Validating results demands mesh refinement for both spatial and angular discretizations, with benchmark cavity cases used to verify separate convective and radiative contributions.
Higher emissivity generally raises total heat transfer but homogenizes temperature fields, with participating media and non-gray effects becoming critical at high temperatures or large gradients.
Table of Contents
What the literature shows: cavities, channels, and non-Boussinesq limits
Advanced modeling: non-gray gases, near-field effects, and computational trade-offs
Nusselt number and temperature field response to surface emissivity
How absorption and scattering coefficients shape coupled heat transfer
Analytical and approximate correlations for simplified geometries
Where combined convection and radiation shows up in real engineering
Try the Jewlz Engineering Toolkit for coupled heat transfer work
Governing physics behind coupled convection and radiation
Coupled convection and radiation problems start from the energy equation with an added radiative source term. The standard form tracks convective transport, conduction, and a divergence of the radiative heat flux, written typically as a loss or gain term inside the fluid’s energy balance. That radiative flux divergence depends on the local radiation intensity field, which itself is governed by the Radiative Transfer Equation (RTE), a balance of emission, absorption, and scattering along a direction through the medium.
Three quantities carry the physics: intensity, which describes radiant energy traveling in a specific direction per unit solid angle; emissive power, the total radiant energy a surface or gas volume emits across all directions; and absorption, the fraction of incoming radiation a surface or medium retains rather than reflects or transmits. Wall emissivity sets how close a surface behaves to an ideal blackbody emitter, and it is one of the two or three parameters that decide whether radiation is a minor correction or a dominant transport mode.
A key distinction splits the modeling path early: surface-to-surface radiation versus volumetric, or participating-media, radiation. Surface-to-surface exchange applies when the fluid between surfaces neither absorbs nor scatters radiation meaningfully, air at moderate temperatures in many enclosures behaves this way, and the problem reduces to view-factor based exchange between boundary surfaces. Participating media radiation applies when the fluid itself absorbs, emits, or scatters, combustion gases, soot-laden flows, and high-temperature gas mixtures all fall here, and the RTE must be solved as a field equation across the domain rather than as a boundary-only calculation. Our CFD heat transfer guide covers how these choices map onto solver setup once the flow equations are defined.
Two simplified models reduce RTE cost when the physics allows it. The P1 approximation treats radiative intensity as a low-order spherical harmonics expansion, useful in optically thick media where radiation behaves diffusively, but it loses accuracy in optically thin or strongly directional radiation fields. The Rosseland approximation goes further, treating radiative transfer as an enhanced conductivity term, valid only deep inside optically thick, near-equilibrium media such as dense combustion zones or thick glass melts. Outside those domains of validity, both approximations can produce temperature fields that look smooth but hide real gradients, which is why discrete ordinates or Monte Carlo methods remain the default for general-purpose coupled simulations.
Dimensionless numbers that tell you which regime you are in
Classifying a coupled problem before building a mesh saves rework. Reynolds number (Re) measures inertial versus viscous forces and signals whether flow is laminar or turbulent; Rayleigh number (Ra) measures buoyancy-driven convection strength relative to viscous and thermal diffusion; and Richardson number (Ri), roughly the ratio of Ra-driven buoyancy to Re-driven forced flow, tells you which convection mode dominates.
A useful diagnostic threshold: Richardson numbers below about 25 indicate a forced-convection-dominated regime, while values above about 70 indicate natural convection dominance, with a competitive intermediate zone that can produce a local minimum in Nusselt number as the two mechanisms partially cancel rather than reinforce each other, as documented in ventilated cavity studies.
Two further numbers matter specifically because radiation is present. The Planck number compares conductive to radiative transport strength, a low Planck number signals that radiation dominates over conduction in the energy balance. The Gay-Lussac number (sometimes framed through the thermal expansion coefficient times the temperature difference) flags when the Boussinesq approximation, which assumes density variations only matter in the buoyancy term, starts to break down. Large temperature differences driven by strong radiative heating push Gay-Lussac values up and push the problem toward non-Boussinesq, low-Mach number formulations instead.
Published ventilated cavity and mixed convection studies commonly explore:
Reynolds numbers spanning ranges typical of laminar to transitional forced convection.
Wall emissivity values covering the typical engineering surface finishes range without specifying exact numbers, per mixed convection ventilated cavity research.
Nusselt number trends generally rise with increasing emissivity as total heat transfer grows, even as the convective share of that total shrinks.
Richardson number sweeps crossing the forced, mixed, and natural convection regimes within a single geometry.
Our heat transfer model reference walks through how these dimensionless groups connect back to the governing equations if you need the derivations spelled out.
Choosing a radiation solver and coupling strategy
Four radiative solver families cover most coupled convection-radiation work, and each trades accuracy against cost differently.
Discrete Ordinates Method (DOM/SN) discretizes the RTE into a finite set of directions, balancing accuracy and cost well for both gray and non-gray, participating and surface-dominated problems, and it remains the most common default solver pairing with finite volume flow solvers.
P1 approximation collapses the angular dependence into a low-order expansion, cheap to run but limited to optically thick, diffusion-like radiation regimes.
Higher-order spherical harmonics (PN) methods extend P1 toward better angular resolution at added computational cost, useful when P1 accuracy proves insufficient but full Monte Carlo cost is unaffordable.
Monte Carlo methods trace statistical photon or ray bundles through the domain, offering high accuracy for complex, non-gray, or strongly scattering media at the cost of statistical noise and long runtimes, often reserved for benchmark or validation cases rather than routine design iteration.
Most coupled simulations pair a finite volume method (FVM) flow solver with DOM or P1 for radiation, a combination documented across convection-radiation literature for its balance of robustness and cost, according to coupling strategy research. Finite element (FEM) angular discretization or full PN expansions become worthwhile mainly when the medium is strongly inhomogeneous or when ray effects, the artificial banding artifacts that appear when too few discrete directions are used, visibly distort results.
Partitioned iterative coupling is the standard architecture: solve the flow field, freeze it, solve radiation on that frozen field, feed the radiative source term back into the energy equation, and repeat until both fields stabilize. Convergence is typically judged against a residual threshold, with root-mean-square (RMS) errors held below 1e-4 serving as a common target in the literature, per numerical coupling studies. Under-relaxation factors, often in the 0.3 to 0.5 range, prevent the partitioned iteration from oscillating or diverging when radiative and convective fields are strongly coupled, a practice our relaxation guidance for conjugate heat transfer CFD covers in more operational detail. Stability analyses of conjugate coupling with radiative boundary conditions have derived optimal relaxation coefficients directly from interface stability bounds rather than trial and error, as shown in predictive coupling model work.
Ray effects and angular discretization error remain the main numerical headaches in DOM-based solutions. Non-uniform angular discretization and adaptive angular refinement, concentrating more directions where intensity gradients are steep, reduce these artifacts without paying for uniform high-resolution angular meshes everywhere.
Pro Tip: Refine the angular mesh and the spatial mesh separately and report both convergence studies; a spatially converged flow field solved with too few discrete ordinates will still produce a biased temperature field.
Validation checklist for coupled simulations
A coupled convection-radiation result is only as trustworthy as the independence studies behind it. Grid independence has two axes here, not one: the spatial mesh for the flow and energy equations, and the angular discretization for the RTE. Refining only the spatial mesh while holding a coarse angular resolution fixed can produce a result that looks spatially converged but still carries ray-effect bias; both need their own refinement sequence with at least three mesh levels to confirm asymptotic convergence.
Recommended numerical targets worth adopting as defaults:
Residual convergence for the partitioned coupling loop held below an RMS threshold of 1e-4, a benchmark used across combined-mode solver studies, per coupling strategy documentation.
Under-relaxation factors typically set within a moderate range for exchanging radiative source terms between the flow and radiation solvers.
Separate convergence reporting for radiative flux and for flow-field residuals rather than a single combined metric that can mask one field converging while the other has not.
Code validation against canonical benchmark cases is the other pillar. Differentially heated square or rectangular cavities and ventilated cavities with inlet and outlet ports are the most reproduced geometries in the combined convection-radiation literature, largely because their simplicity isolates the radiation-convection interaction without confounding geometric complexity. Reproducing a published Nusselt number split, comparing convective and radiative components separately rather than only the combined total, is the clearest way to confirm a new solver setup matches established results before applying it to a novel geometry.
When reporting results for publication or thesis work, specificity prevents ambiguity later: state wall emissivity values exactly, report the angular discretization order (number of discrete ordinates or PN order), specify boundary condition type (fixed temperature versus fixed heat flux) for every surface, and separate the convective and radiative Nusselt number contributions rather than reporting only a combined value. Our conjugate heat transfer simulation guide walks through boundary condition setup for coupled flow and solid domains, a useful companion when radiation is added on top of an existing conjugate model.
What the literature shows: cavities, channels, and non-Boussinesq limits
Ventilated cavity studies offer the clearest numeric picture of how radiation reshapes mixed convection. Increasing wall emissivity toward the upper end of the commonly studied range, roughly 0 to 0.85, raises the total Nusselt number because radiative exchange adds a transport pathway that did not exist at zero emissivity. But that same emissivity increase tends to reduce the relative share convection contributes to total heat transfer, since radiation homogenizes the temperature field and weakens the buoyancy-driven gradients that drive convective circulation, per mixed convection ventilated cavity results. Outlet port placement interacts with this effect: cavities with Reynolds numbers in the 300 to 5000 range and varying outlet positions show that the interplay between forced flow strength and radiative wall exchange can produce multiple steady states and trigger earlier transition to unsteady flow than a convection-only case would predict.
Key findings from the cavity and channel literature:
Wall emissivity increases generally raise total Nusselt number but reduce convection’s relative share of total heat transfer.
Reynolds and Rayleigh number interplay with emissivity can produce multiple steady-state solutions in ventilated cavities rather than a single predictable flow pattern.
Richardson number sweeps through forced, mixed, and natural convection regimes reveal a local Nusselt number minimum in the competitive intermediate zone, as reported in Richardson number diagnostic studies.
Turbulent and asymmetrically heated channel studies show radiation altering both the mean temperature field and its coupling with near-wall turbulence structures, not just the bulk temperature level.
Non-Boussinesq, low-Mach number formulations become necessary once radiative heating drives temperature differences large enough that density variations affect more than the buoyancy term alone, per unified buoyancy-radiative flow framework research.
The non-Boussinesq point deserves emphasis because it catches many coupled studies off guard. Comparative work between standard Boussinesq solvers and quasi-incompressible, low-Mach formulations shows measurable discrepancies that grow as radiative heating intensifies, and those discrepancies are consistently larger in three-dimensional configurations than in two-dimensional idealizations. A two-dimensional cavity model that looks Boussinesq-valid can hide a meaningful 3D departure once the geometry opens up, which argues for at least a spot check against a non-Boussinesq solver when temperature differences or radiative heating are significant.
Documented gaps remain in two areas researchers continue to work on: inhomogeneous and unsteady participating media, where absorption and scattering properties vary in space and time rather than staying uniform, and non-gray gas modeling, where treating a real combustion gas mixture as a single gray absorber misses spectral behavior that matters for accurate radiative transfer predictions. Both gaps point toward the non-uniform absorption distribution function approaches covered next.
Advanced modeling: non-gray gases, near-field effects, and computational trade-offs
Real gas mixtures, combustion products especially, absorb and emit radiation unevenly across the spectrum, a behavior gray models flatten into a single averaged absorption coefficient. Non-gray gas models and absorption distribution function (ADF) approaches address this by grouping spectral absorption behavior into bands or weighted distributions rather than one flat value. A non-uniform ADF combined with a spherical harmonics (PN) angular discretization has been shown to model inhomogeneous, unsteady participating media more efficiently than direct ray tracing while holding comparable accuracy, per inhomogeneous participating media research. That efficiency gain matters most in unsteady combustion or furnace simulations where re-solving a full ray-traced RTE at every time step is computationally prohibitive.
Near-field radiative effects, relevant at very small length scales or extremely high temperatures where wave-like and quantum effects can exceed classical blackbody predictions, sit outside the scope of standard RTE-based engineering tools and apply mainly to specialized micro- and nano-scale thermal problems rather than typical cavity, channel, or combustion chamber geometries. Far-field, classical radiative transfer remains the right framework for the overwhelming majority of combined convection-radiation engineering work.
Hybrid and adaptive strategies offer a practical middle path when full non-gray, fine-angular-resolution solutions are too expensive to run across an entire parametric study. Adaptive angular refinement concentrates discrete ordinates where intensity gradients are steep and coarsens them elsewhere; hybrid gray-to-non-gray switching can apply simpler models in regions where spectral behavior is nearly uniform and reserve full non-gray treatment for regions with strong compositional gradients, such as near a flame front. These trade-offs are judgment calls specific to each geometry and temperature range, but the underlying principle holds across cases: spend computational budget where gradients, whether spatial, angular, or spectral, are steepest.
A starter workflow for coupled simulations
Setting up a first coupled convection-radiation case goes faster with the right reference material and property data on hand. Our thermal analysis tools include a built-in property database covering the emissivity, absorption, and thermal conductivity values needed to define boundary conditions and participating media properties without separately compiling them from scattered sources. For solver setup itself, our guide to choosing and tuning the discrete ordinates method walks through the practical parameter choices, angular order and convergence settings, that the DOM comparisons above discuss conceptually.
A reasonable minimal reproducible experiment: a differentially heated square cavity, fixed-temperature hot and cold walls, adiabatic top and bottom, wall emissivity swept from 0 to 0.85, Reynolds number held in the 300 to 5000 range, with grid independence confirmed separately for the flow mesh and the angular discretization before comparing convective and radiative Nusselt components against the ventilated cavity benchmarks referenced earlier.
Nusselt number and temperature field response to surface emissivity
Surface emissivity is the single parameter most studies vary to isolate radiation’s effect on convective heat transfer, because it directly scales how much radiant energy a wall emits and absorbs without changing the flow geometry. As emissivity rises from zero toward the upper range commonly studied (around 0.85), total Nusselt number climbs, since radiative exchange adds an energy transport pathway on top of whatever convection already provides, per mixed convection cavity studies.
The temperature field response is less intuitive than the Nusselt number trend. Higher emissivity tends to homogenize temperature across the domain, radiative exchange moves energy between surfaces regardless of local flow structure, smoothing gradients that pure convection would leave sharper. That homogenization is exactly why convection’s relative share of total heat transfer shrinks even as total heat transfer rises: the temperature differences that drive buoyant or forced convective flow get partially erased by radiative mixing before convection can act on them.
Participating media radiative absorption compounds this effect when the fluid itself, not just the walls, absorbs and re-emits radiation. In that case, the temperature field develops gradients driven by volumetric absorption patterns rather than wall proximity alone, which is why surface-to-surface models fail silently once a fluid moves from radiatively transparent to radiatively participating.
How absorption and scattering coefficients shape coupled heat transfer
Participating media properties, specifically the absorption coefficient and the scattering coefficient, determine how radiation and convection interact once the fluid itself joins the radiative exchange rather than staying transparent. A high absorption coefficient means radiation deposits energy quickly within a thin layer of fluid near its source, creating localized heating that can drive its own buoyant convection cells independent of wall-driven flow.
Scattering changes the picture differently: a scattering-dominated medium redirects radiation without immediately absorbing it, spreading radiative energy more broadly across the domain before it is finally absorbed, which produces smoother temperature gradients than a purely absorbing medium of the same optical thickness would.
The combination of the two, often expressed through a single-scattering albedo balancing absorption against total extinction, determines how deeply radiation penetrates a participating medium before being fully attenuated. Optically thick media, high absorption or scattering coefficients relative to the domain size, behave diffusively and are candidates for the Rosseland or P1 approximations discussed earlier. Optically thin media, where radiation largely passes through with little interaction, need discrete ordinates or Monte Carlo treatment to capture the directional nature of the radiative field accurately. Combustion chambers and sooty flows sit firmly in the optically thick-to-intermediate range, which is why non-gray and ADF-based models matter most precisely in those applications.
Analytical and approximate correlations for simplified geometries
Full coupled RTE and Navier-Stokes solutions are not always necessary for a first estimate. Simplified geometries, parallel plates, concentric cylinders, and single flat surfaces facing a cooler surrounding enclosure, admit analytical or semi-analytical correlations that combine a convective heat transfer coefficient with a radiative heat transfer coefficient, often added in parallel as two resistances feeding the same overall energy balance.
The Rosseland approximation extends this logic into optically thick participating media, replacing the full RTE with an effective radiative conductivity added directly to the fluid’s thermal conductivity. The P1 approximation offers a similar simplification in diffusive-regime problems, trading a full angular solution of the RTE for a single additional diffusion-type equation coupled to the energy equation. Both approaches reduce computational cost substantially but only within their stated domains of validity, optically thick, near-equilibrium media for Rosseland, and moderately thick media without strong directional radiation effects for P1.
For problems that fall outside these simplified domains, including most ventilated cavities, channels with asymmetric heating, and any case with Reynolds numbers in the 300 to 5000 range combined with significant wall emissivity, analytical correlations become unreliable approximations at best, and a full numerical RTE solution paired with the flow solver is the only route to a trustworthy result.
Boundary condition choice and its effect on coupled results
Whether a surface boundary condition specifies a fixed temperature or a fixed heat flux changes how strongly radiation and convection interact at that surface, and the two conditions do not produce equivalent radiative behavior even when they produce similar average surface temperatures.
A fixed-temperature wall radiates according to its emissivity and that fixed temperature regardless of how convection is behaving locally, which decouples the radiative boundary condition from transient convective fluctuations at that surface. A fixed-heat-flux wall, by contrast, lets surface temperature respond dynamically to whatever combination of convective and radiative cooling or heating is occurring, meaning the radiative contribution itself fluctuates as the surface temperature adjusts, a feedback loop that fixed-temperature conditions do not have.
This distinction matters most in turbulent and asymmetrically heated channel studies, where one wall might carry a fixed heat flux representing an electronic component or combustion liner while the opposing wall sits at a fixed, cooler temperature. The radiative exchange between those two different boundary condition types produces temperature field asymmetries that a same-condition pair would not replicate, which is why reporting the exact boundary condition type for every surface, not just its emissivity, is part of the validation reporting checklist covered earlier.
Measuring combined convection and radiation experimentally
Validating a coupled numerical model against experimental data requires separating the convective and radiative contributions at the point of measurement, since most sensors respond to combined heat flux rather than either mechanism alone. Heat flux sensors calibrated against a known radiative source, combined with surface temperature measurement by thermocouple or infrared thermography, let researchers back out the radiative component separately from the convective remainder once the total flux is known.
Particle image velocimetry (PIV) and laser Doppler anemometry provide the flow-field data needed to confirm that a numerical model’s convective pattern matches reality independent of the radiative field, a necessary check since a model can match total heat transfer while getting the convective and radiative split wrong in compensating ways. Surface emissivity itself is typically measured with a reflectometer or inferred from infrared camera calibration against a known blackbody reference, and reporting that measured emissivity value alongside experimental results is essential for anyone attempting to reproduce the study numerically afterward.
Differentially heated and ventilated cavity experimental rigs remain the most common physical benchmarks precisely because their simplified geometry makes instrumented measurement of both temperature and flow fields tractable, mirroring the same benchmark geometries used for numerical code validation discussed earlier in this article.
Where combined convection and radiation shows up in real engineering
Combined convection-radiation modeling earns its computational cost in applications where ignoring radiation produces design errors large enough to matter. HVAC design is a clear example: radiative exchange between occupants, walls, and windows affects perceived thermal comfort in ways that air temperature alone does not capture, and ventilated cavity studies of the kind discussed throughout this article map directly onto room airflow and radiant panel design problems.
Combustion chambers represent the highest-stakes application, since flame and soot radiation can dominate total heat transfer to chamber walls, making radiation modeling not optional but central to predicting wall temperatures, material survival, and emissions-relevant temperature fields accurately. Non-gray gas models and ADF approaches matter most here precisely because combustion gas mixtures are the least gray-like participating media encountered in common engineering practice.
Electronic cooling sits at the opposite end of the temperature spectrum but still benefits from coupled modeling, particularly in densely packed enclosures where radiative exchange between closely spaced components can meaningfully affect local hot-spot temperatures even without flames or high-emissivity surfaces. High-temperature industrial equipment, furnaces, and radiant heating systems round out the common application set, each relying on the same underlying DOM-or-P1-paired-with-FVM solver architecture discussed in the numerical methods section, adapted to each domain’s specific emissivity, temperature range, and participating media characteristics.
Where this research field should go next
The clearest gap in current coupled convection-radiation research is reproducibility: too many studies report a Nusselt number trend without the angular discretization order, exact emissivity, or boundary condition type that would let another researcher reproduce the result independently. A short project worth running is a systematic re-validation of a published ventilated cavity case with full parameter disclosure. A medium project would extend non-uniform ADF approaches to a genuinely unsteady combustion case rather than the steady benchmarks most ADF work still relies on. A long project, suited to a full thesis, would build a non-Boussinesq, non-gray coupled solver validated against both the cavity and channel benchmarks discussed here and quantify exactly where Boussinesq and gray-gas assumptions start to fail in three dimensions.
When writing results, plot convective and radiative Nusselt contributions as separate curves, never a single combined line, so readers can see which mechanism is driving any trend you report.
— Joel
Try the Jewlz Engineering Toolkit for coupled heat transfer work
Setting up conduction, convection, and radiation together usually means juggling separate property tables, correlation charts, and solver manuals before a single simulation runs. Our engineering toolkit brings those pieces into one place: thermal analysis modules that handle multiple heat transfer modes side by side, a built-in property database so emissivity and absorption values do not need separate lookup, and CFD modules built to handle the flow side of a coupled problem.
What the toolkit covers for coupled simulation work:
Thermal analysis and heat transfer modules spanning conduction, convection, and radiation in one workspace.
A built-in property database covering the material and surface properties a coupled model needs.
CFD and fluid flow simulation modules for the convective side of a combined problem.
Pressure vessel simulation tools for high-temperature vessel applications where radiation matters at the boundary.
Users can start with free features before deciding whether a premium subscription tier fits an ongoing research or design workload. Tutorials and example cases on our thermal analysis and engineering toolkit pages walk through setup step by step, and our CFD simulation software page covers the flow-solver side in more depth. Start with the free tools and see how far a reproducible validation case gets you before committing to a subscription.
FAQ
What is conduction, convection, and radiation called?
Conduction, convection, and radiation are collectively called the three modes of heat transfer, each describing a distinct mechanism by which thermal energy moves from a hotter region to a cooler one. Conduction moves heat through direct molecular contact within a solid or stationary fluid, convection moves heat through bulk fluid motion, and radiation moves heat through electromagnetic waves that need no medium at all.
Can you explain conduction to kids?
Conduction is how heat moves when two things touch directly, like a metal spoon left in a hot cup that gets warm from the handle end without ever touching the liquid itself. The heat travels because fast-moving, hot particles bump into their slower, cooler neighbors and pass energy along, one particle to the next.
Can you give me 10 examples of conduction?
Everyday conduction examples include a metal spoon heating up in hot soup, a frying pan handle warming on the stove, an ice cube cooling your hand, a laptop warming your lap, and a car’s metal roof heating up in sunlight. More examples include a radiator warming the air through its metal fins, a soldering iron heating a wire, concrete feeling cold underfoot, a metal fence feeling hot in summer, and a hot drink warming a ceramic mug held in your hands.
How to remember conduction, convection, and radiation?
A simple memory anchor: conduction needs contact (two solids touching), convection needs currents (fluid actually moving), and radiation needs no medium at all (it travels through empty space as electromagnetic waves). Linking each mode to its defining requirement, contact, current, or vacuum-capable, makes the three easier to distinguish than memorizing definitions alone.
When does radiation significantly affect convective heat transfer?
Radiation becomes significant whenever wall emissivity is high, temperature differences are large, or the fluid itself participates in radiative absorption and scattering rather than staying transparent. Studies commonly flag emissivity values approaching 0.85 and Reynolds numbers in the 300 to 5000 range as conditions where radiative coupling measurably changes both the Nusselt number and the temperature field, per mixed convection ventilated cavity findings.
Sources
Combined mixed convection and radiation in ventilated cavities (paper)
Coupling strategies and numerical methods for convection–radiation
Analysis of combined convection–radiation with inhomogeneous participating media (imperial paper)
A numerical predictive model for conjugate heat transfer with radiation
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