R = L / (k x A) governs thermal resistance. In space, convection is unavailable, so heat moves by conduction through the structure and radiation from surfaces. Fixed radiator area makes each conduction path critical. The bus must also carry launch and deployment loads, so its topology serves thermal and structural roles.
This challenge is acute for small satellites in the 3U to 16U CubeSat range and for compact propulsion units mounted on them. Electronics and propulsion components generate heat, while radiator panels on the outer structure reject it. Heat must travel through the members connecting those locations. Those same members carry mechanical loads, making independent thermal and structural tuning impractical. A path that is useful for heat may be poor for stiffness, and a mechanically efficient member may leave a hot component isolated from its radiator.
Conduction Path Design Basics
For aluminum 6061 (k = 167 W/m/K), a 10 cm strut with 2 cm^2 cross-section has a thermal resistance of approximately 0.003 K/W. At 1 W, its temperature drop is only 0.003 degrees Celsius, and at 10 W it is 0.03 degrees Celsius. The larger concern is often the joints. Interface resistances 0.1 to 0.5 K/W per bolted interface can exceed the resistance of the metal members themselves. Preliminary models that focus only on bulk material can therefore understate the source-to-radiator temperature difference.
With three bolted interfaces between a source and radiator, the interfaces alone can create 3 to 15 degrees Celsius temperature drop per watt. An on-board computer dissipating 5 W = 15 to 75 degrees Celsius rise above the radiator temperature, before structural conduction is included. A 70 degrees Celsius operating temperature limit can be consumed quickly when that rise is combined with component and radiator temperatures. The practical design question is not simply whether the material conducts heat, but whether the complete route preserves enough temperature margin.
A source-to-sink member is rarely just a strut. It is part of the bus, which must carry launch loads, support deployment forces, and connect to the launch vehicle adapter. Its shape is usually set by those mechanical duties rather than by heat flow. Structural efficiency often favors thin-walled closed sections and hollow members that provide stiffness per unit mass. Thermal conduction generally favors solid sections with more material along the heat path. The geometry must balance those opposing preferences instead of optimizing either discipline in isolation.
Topology Changes Heat Flow
The coupling exists in the design variable itself. A topology parameter can alter structural compliance and thermal resistance at the same time. As a result, a combined structural and thermal optimization can produce a different geometry from sequential optimization. Optimizing thermal performance first and structure second, or reversing that order, cannot fully capture how one geometry change affects both results.
In a lattice spacecraft bus, diagonal compression members often carry substantial structural load. They can also be short, direct routes through the structure. When they connect a heat source to a radiator, the same members can provide low-resistance thermal paths. Aligning heavily loaded members with high heat flux therefore improves material use across both objectives. Finding that alignment requires a shared objective and simultaneous topology search, rather than separate discipline-by-discipline passes.
In our analysis of a 12U CubeSat bus, sequential optimization placed the main structural load path along two diagonal members. A multi-bolt interface thermally isolated those members from the main electronics board. The coupled result redirected material to create a direct path from the board to the zenith-facing radiator panel while retaining structural compliance. The mass difference was 7 grams on a 220 gram bus structure. Thermal resistance from the board to the radiator fell by 34%, producing a 12 degree reduction in maximum component temperature at full power. For the board's thermally marginal components, the 12-degree margin improvement was the difference between passing and not passing the thermal design requirement.
Radiator Area Constraint
External geometry fixes radiator area. A CubeSat's six faces may be occupied by solar panels, antennas, or deployment mechanisms. The remaining area is constrained, not a free design variable, so conduction must reach the available faces.
At radiator temperature T_rad and emissivity epsilon, heat rejection follows Q = epsilon x sigma x A x (T_rad^4 - T_sink^4). Here, sigma is the Stefan-Boltzmann constant and T_sink is the effective orbital sink temperature. The sink is about 2.7 K in deep space, while Earth albedo and infrared emission raise it in LEO to a 200-250 K effective temperature in LEO. For a 1U face at 0.01 m^2, epsilon = 0.85, T_rad = 340 K, 240 K effective thermal environment = approximately 7 W radiated. A bus with 10 W total power, three available radiator faces, total heat rejection capacity roughly 21 W. That apparent margin can shrink with eclipse view factors and attitude modes that make some faces unavailable.
Thermal architecture leaves little room for error in compact space systems. The path from source to radiator is one of the main controllable variables. A 20% improvement in thermal resistance = 20% more temperature headroom for heat-sensitive components. That margin can determine whether commercial-grade parts remain usable or whether space-grade alternatives, often several times more costly, are required.
Interface Engineering Designers Miss
Bolted metallic interfaces are frequent sources of error in early thermal models. Bulk resistance is straightforward to estimate and is often small. Contact resistance is more difficult to predict, yet it may dominate the complete route from source to radiator.
Contact conductance at a bolted metal joint depends on pressure, roughness, the softer material's hardness, and any thermal interface material. For aluminum-to-aluminum dry contact: 2,500 to 25,000 W/m^2/K. At fixed area, that tenfold conductance range creates a tenfold resistance range. A 4-bolt interface with a 50 mm x 50 mm interface area, dry contact 0.3 to 3 K/W. Those values depend on torque, finish, pressure, and flatness, so the interface assumption should be visible in the model rather than hidden inside a nominal material property.
Choosing the optimistic contact value in analysis can leave inadequate margin when hardware behaves near the pessimistic end. A metallic phase-change thermal interface material (TIM) reduces interface resistance by a factor of three to five. It fills surface asperities, but it must be specified before fabrication rather than added later. The material also brings process and torque-down requirements that belong in the assembly procedure.
When Coupled Topology Pays
The coupled approach is not necessary for bus designs with well-characterized heritage geometry operating within a known envelope. Sequential analysis can be sufficient in that setting. Coupling becomes valuable when radiator area is tight, the component temperature budget is nearly used, or mass limits require smaller structural sections whose thermal effects need characterization. These are the conditions where a modest geometry change can affect both stiffness and heat flow.
These conditions are common in new commercial small satellite programs. Heritage data is limited for unusual bus layouts and new propulsion architectures, requirements tighten, and teams are small. Coupled analysis across enough topology variants can identify feasible designs before testing. It is most useful when late thermal surprises are expensive to correct. In reviews, we check that the selected path and every bolted interface preserve required component temperature margin before hardware testing.