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Conducting surfaces

A conducting_surface represents the thermal resistance of a thin layer through a zero-thickness cuboid. Typical uses include a thermal interface material (TIM) between solids or a coating over a prescribed thermal boundary. The surrounding regions retain their volumetric cells, while the layer contributes resistance to heat flow normal to its plane.

Resistance and temperature jump

The model takes a positive thickness \(\delta\) in meters and a positive scalar conductivity \(\kappa_{\mathrm{s}}\) in \(\mathrm{W/(m\,K)}\). Its resistance per unit area is

\[ R^{\prime\prime} = \frac{\delta}{\kappa_{\mathrm{s}}}. \]

Here, \(R^{\prime\prime}\) has units of \(\mathrm{m^2 K/W}\). For normal heat flux \(q^{\prime\prime}\) from side 1 toward side 2, the temperature jump is

\[ T_1 - T_2 = q^{\prime\prime} R^{\prime\prime}. \]

Heat leaving one side enters the other. A thicker layer or lower conductivity gives a larger temperature jump for the same heat flux. For uniform heat flow through area \(A\), the total resistance is \(R = \delta/(\kappa_{\mathrm{s}}A)\) in \(\mathrm{K/W}\).

Heat transfer through a conducting surface Two conducting regions meet at a surface with no meshed thickness. Normal heat flux passes from interface temperature T1 to T2 through the resistance per unit area R double prime equals thickness divided by conductivity. Conducting region 1 Conducting region 2 Normal heat flux q″ T₁ T₂ Surface: no meshed thickness T₁ T₂ R″ = δ / κₛ
A conducting surface joins two thermal regions through a resistance. The two sides share a geometric plane but can have different interface temperatures. The resistance network is schematic; there is no meshed layer thickness.

Between solved thermal regions

At an ordinary fluid–conducting or conducting–conducting interface, heat flows through a continuous thermal domain without an additional contact resistance. A conducting surface adds \(R^{\prime\prime}\) at the selected faces while retaining heat transfer between the neighboring cells.

The model thickness does not replace any of the neighboring material or move the component faces apart. It adds resistance at their existing contact. Wherever the surface touches fluid, it also acts as an impermeable, no-slip wall; thermal conduction through the sheet remains possible.

Surfaces over thermal boundaries

A conducting surface can cover an existing thermal boundary on a domain wall or an insulating component. The boundary is adjusted only over the covered area to include the layer’s resistance.

Original boundaryEffect of the surface
fixed_tempThe prescribed temperature applies beyond the layer. The solved side exchanges heat with it through the layer’s resistance.
fixed_htcThe layer’s resistance is added in series with the original heat-transfer resistance; ambient_temperature is retained.
heat_fluxThe prescribed heat flux is retained. The layer changes the associated temperature drop.
AdiabaticThe boundary remains adiabatic.

For fixed_temp, the resulting condition is equivalent to an HTC of \(1/R^{\prime\prime}\) with the prescribed temperature as its ambient value. For an existing HTC \(h\), the combined coefficient is

\[ h_{\mathrm{effective}} = \frac{h}{1 + h R^{\prime\prime}}. \]

This includes \(h=0\), which remains adiabatic. Radiative boundary conditions are not supported beneath a conducting surface.

Surfaces on compact thermal models

A conducting surface can sit directly between a compact thermal model and an adjacent conducting solid or fluid. It adds resistance outside the package; the CTM’s resistance_jc, resistance_jb, and resistance_js retain their original meanings.

The case and board faces of both two-resistor and STAR CTMs support these layers. Conducting surfaces on the other four STAR faces are rejected. Each layer that overlaps a supported CTM face must cover that complete face; partial coverage is rejected. A layer may extend beyond the face or cover several complete CTM faces. Inactive two-resistor faces remain adiabatic.

During meshing, Vanellus adds the layer resistance \(R_{\mathrm{TIM}} = \delta/(\kappa_{\mathrm{s}} A)\) to the corresponding junction-to-case or junction-to-board resistance, using the CTM face area \(A\). The original request’s package resistances remain unchanged. The covered surface footprint is absorbed into the CTM; any overhang retains ordinary conducting-surface behavior, including acting as a wall where it touches fluid.

The solver uses the combined resistance to calculate junction temperature. Its CTM boundary temperature is on the outside of the TIM; the intermediate package-side temperature is not resolved. The active CTM face must still completely touch fluid or conducting cells; an insulating surface cannot block it.

Restrictions

The layer models conduction normal to its plane. It does not resolve lateral heat spreading, internal temperature variation, heat storage, or heat generation within the layer. Use a volumetric conducting component when internal temperature variation, heat spreading, or the layer’s physical geometry matter.

The surface occupies no volume cells, so it has no separate temperature field in the output VTUs. Temperatures in neighboring cells include the temperature variation through the surrounding material as well as the layer’s effect.

See also