This page calculates the average heat transfer coefficient and chip temperatures for PC Board in free stream flow, with isothermal (constant temperature) components, where the heat is evenly distributed throughout the component. The power levels of all components are assumed equal. The component temperature calculated is the mean case temperature. For purposes of reliability assessment, the junction temperature is of greater interest. This is largely controlled by the components internal structure the manufacturer's internal resistance values can be used for further thermal analysis under most circumstances.
For this analysis, the conductance should be less than 0.03 W/oC. In this model each component and the surrounding PCB area is treated in isolation, the PCB area being the rectangle formed cutting midway between components. It is then assumed that the heat that is dissipated by this isolated component and area of PCB is equal to the component power. The heat path is by convection from the exposed surfaces and conduction through the leads and stand-off gap into the PCB and then convection from the PCB to the air.
The component temperature Tc can be calculated as:
Tc = Tl + q x R
Where q is the heat load on the component, R is the thermal resistance of the component to air, and Tl the local air temperature. The local air temperature is calculated from:
Tl = Ta +Qt / (F x rho x Cp)
Where Ta is the ambient air temperature, Qt is the total heat dissipated upstream of the component, F is the flow rate of the air, rho is the density of the fluid, and Cp is the specific heat of air. The total heat dissipated upstream from the component Qt is calculated as:
Qt = q x M x (N - 1)
Where N is the number of components in the flow direction, and M is the number of components perpendicular to the flow direction. The flow rate F can be calculated as:
F = um x (Nb x a)
Where a is the flow area over the PCB less component obstructions. The flow area a is calculated as:
a = Wb * HF - (M x S x e)
Where Wb is the width of PC Boards, HF is the height of the flow channel above the PCB, M is the number of components in the lateral direction S is the component width (lateral), and e is the height that the component protrudes from the PCB.
R is calculated as:
R = 1 / (h x A1 + 1 / ( Ri + 1/ (A2 x h) ) )
Where h is the heat transfer coefficient, A1 is the exposed surface area of the component, Ri is the interface resistance between the component and the PCB, and A2 is the effective area of the component. The exposed surface area A1 is calculated as:
A1 = S x b + 2e (S + b)
Where b is the component length (streamwise). The area between the component and PCB is not included in this area because the generally small distance between component and PCB inhibits convection. The leads generally inhibit convection from the sides of the chip, therefore the stand-off gap is included in the effective depth package as shown. The thermal interface resistance Ri can be calculated as:
Ri = 1 / ( (1/rc) + (1 / rl) )
Where rc is the resistance across the air gap del, and rl is the lead resistance between the case and the PCB. rc and rl can be calculated as:
rc = del / (ka x S x b)
rl = L / (kl x n x Al)
Where del refers to the air gap between the component and the PCB, ka is the conductivity of air, L is the length of the leads, kl is the conductivity of the leads, n is the number of leads, and Al is the cross-sectional area of one lead.
The d x w rectangles of the PCB are not isothermal and therefore the effective area of the component A2 is calculated as:
A2 = 2 ( d' x w' ) - S x b
Where d' is the effective streamwise pitch and w' is the effective lateral width, which are calculated as:
w' = E1 x w + S ( 1 - E1)
d' = E2 x d + b ( 1 - E2 )
Where d is the component width and E1 and E2 are the two PCB fin efficiencies in the lateral and streamwise directions respectively. These are calculated as follows:
E1 = ( tanh M1 ) / M1
E2 = ( tanh M2 ) / M2
where:
M1 = ( ( w - S ) / 2 ) x ( 2 h / C1 )0.5
M2 = ( ( d - b ) / 2 ) x ( 2 h / C2 )0.5
Where C1 and C2 are the conductances of the PC Board in the lateral and streamwise directions respectively. Both conductances are calculated the same way. The conductance of the PC Board is calculated as:
C1 = kb x t + kc x phi1
C2 = kb x t + kc x phi2
Where kb is the conductivity of the board without copper, kc is the conductivity of the copper used, and phi1 and phi2 are the ratios of the volume of copper on the PC Board in the direction of interest per unit plan area of PCB (lateral and streamwise).
Depending on flow velocity um, the heat transfer coefficient is be calculated using Will's Correlation:
When the flow velocity is between or equal to 0.2 and 8.0 m/s
Where G is 6.2 when no card guides are used at the PCB leading edges and 7.6 when chard guides are not used.
The conductance of the PC Board is calculated as (both lateral as well as streamwise):
C = kb x tb + kc * phi
Where kb is the conductivity of the board without copper, tb is the thickness of the board without copper, kc is the conductivity of the copper used, and phi is the ratio of the volume of copper on the PC Board in the direction of interest per unit plan area of pcb.
References
Thermal Analysis of Air Cooled PCB's, Electronic Production, Parts 1 - 4, May - August 1983.
Rajaram, Dr. S., Thermal Design of Electronic Equipment For Reliability & Performance, AT&T Bell Laboratories, Whippany USA. Sess. 3 p 20 - 42.