PCB Component Array

PCB Component Array — Forced Convection

Calculates the mean case temperature of surface-mounted components on a PCB cooled by a forced-air flow channel. The model accounts for:

1. Convection coefficient from Will's empirical correlation.
2. Local air temperature rise due to upstream component heating.
3. Component exposed surface area (top and side faces).
4. PCB fin efficiency distributing heat laterally and streamwise through the board copper.
5. Interface resistance via the standoff air gap and leads in parallel.

Will's Correlation

$$h=G\cdot u_m^{0.8}$$

where G = 6.2 (no card guides) or G = 7.6 (card guides at PCB leading edges). Valid for air at near-ambient conditions, u_m = 0.2 – 8 m/s.

Local Air Temperature

Heat dissipated by all components upstream of row N raises the local air temperature:

$$T_l=T_a+\frac{q\cdot M\cdot (N-1)}{u_m\cdot N_b\cdot a\cdot \rho \cdot C_p}$$

where $a=W_b\cdot H_F-M\cdot S\cdot e$ is the free-flow area.

Thermal Resistance

The component-to-air resistance combines convection from the exposed top/side faces ($A_1$) and a conduction path through the PCB ($A_2$, corrected for fin efficiency) in parallel with the interface resistance:

$$A_1=S\cdot b+2e(S+b)$$ $$R=\frac{1}{h{A}_1+\frac{1}{R_i+\frac{1}{h{A}_2}}}$$

PCB Fin Efficiencies

$$M_1=\frac{w-S}{2}\sqrt{\frac{2h}{C_1}},E_1=\frac{\tanh M_1}{M_1}$$ $$C_1=t_b(k_b+k_c{\varphi }_1),C_2=t_b(k_b+k_c{\varphi }_2)$$

where ${\varphi }_1$, ${\varphi }_2$ are the fraction of the board cross-section that is copper (dimensionless, e.g. 0.05 = 5 % copper). The copper equivalent thickness $\varphi t_b$ converts the volume fraction to the length scale required by the conductance.

Interface Resistance

The air-gap conduction and lead conduction act in parallel:

$$r_c=\frac{\delta }{k_{a}Sb},r_l=\frac{L_{\text{lead}}}{k_l{n}_{\text{leads}}{A}_l}$$ $$R_i=\frac{1}{1/r_c+1/r_l}$$

Component Temperature

$$T_c=T_l+q\cdot R$$

References

• Thermal Analysis of Air-Cooled PCBs, Electronic Production, Parts 1–4, May–August 1983.
• Rajaram, S., Thermal Design of Electronic Equipment for Reliability & Performance, AT&T Bell Laboratories, Session 3, pp. 20–42.