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/^{o}C. 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 *T _{c}* can be
calculated as:

T_{c} = T_{l} + q x R

Where * q* is the heat load on the component, *R* is the thermal
resistance of the component to air, and *T _{l}* the
local air temperature. The local air temperature is calculated from:

T_{l} = T_{a} +Q_{t }/ (F x rho x C_{p})

Where *T _{a}* is the ambient air temperature,

Q_{t} = 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 = u_{m} x (N_{b} x a)

Where *a* is the flow area over the PCB less component
obstructions. The flow area *a* is calculated as:

a = W_{b} * *H** _{F }* - (M x S x e)

Where *W _{b}* is the width of PC Boards,

*R* is calculated as:

R = 1 / (h x A_{1} + 1 / ( R_{i} + 1/ (A_{2}
x h) ) )

Where * h* is the heat transfer coefficient, *A _{1}*
is the exposed surface area of the component,

A_{1} = 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 *R _{i}* can be calculated
as:

R_{i} = 1 / ( (1/r_{c}) + (1 / r_{l}) )

Where *r _{c}* is the resistance across the air
gap

r_{c} = del / (k_{a} x S x b)

r_{l} = L / (k_{l} x n x A_{l})

Where * del* refers to the air gap between the component and the
PCB, * k _{a} * is the conductivity of air,

The *d x w* rectangles of the PCB are not isothermal and
therefore the effective area of the component *A _{2}*
is calculated as:

*A _{2}*
= 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' = E_{1} x w + S ( 1 - E_{1})

d' = E_{2} x d + b ( 1 - E_{2} )

Where *d* is the
component width and *E _{1}* and

E_{1} = ( tanh M_{1} ) / M_{1}

E_{2} = ( tanh M_{2} ) / M_{2}

where:

M_{1} = ( ( w - S ) / 2 ) x ( 2 h / C_{1} )^{0.5}

M_{2} = ( ( d - b ) / 2 ) x ( 2 h / C_{2} )^{0.5}

Where C_{1} and C_{2} 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:

C_{1} = k_{b} x t + k_{c}
x phi_{1}

C_{2} = k_{b} x t + k_{c}
x phi_{2}

Where *k _{b}* is the conductivity of the board
without copper,

Depending on flow velocity *u _{m}*,
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 = k_{b} x t_{b} + k_{c} * phi

Where *k _{b}* is the conductivity of the board
without copper,

**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.