# Estimating heat transfer coefficients

Previously we have discussed ways to complete a feasibility thermal management analysis. For a given thermal budget, we want to determine whether the junction temperature will meet specifications for reliability and thermal runaway.

In electronic systems that rely on air flow for cooling, convection is of paramount importance.

Power dissipation due to convection is given by q = hA(ΔT), where q is the power dissipated (W), h is the heat transfer coefficient in

W/(m2K), A is the surface area exposed to the flow (m2) and ΔT = Tsurface – Tambient (⁰C).  The largest degree of uncertainty lies with Tsurface and h, so in the feasibility analysis we can solve for temperatures given a value for h.

Obtaining a heat transfer coefficient a priori is difficult, we suggest using a range of values representative of different conditions. Ultimately if high values of h are selected it suggest that the thermal behavior may need to be redesigned.

The table below provides approximate heat transfer coefficients for different conditions.  [H.S. represents Heat Sink.]

 Case Electronics Environment Heat transfer model Thermal solution over component Approximate Heat Transfer Coefficient (in W/m2K) Approximate thermal resistance (⁰C/W) A Handheld device with up to 2 mm air gap, operates when horizontal Conduction through air (worst case) None Treat as conduction in gap 50 – 100 B Small module, no fan, orientation controlled (always vertical). Open top & bottom, chimney style convection Natural convection h also depends on ΔT & height Optimized plate fin heat sink (vertical base & fins) For plate fin heat sinks, correlations are readily available* 3 – 6 (based on H.S. area) 1 – 5 C Laptop Single small fan Optimized heat sink 25 – 100 (based on H.S. area) 1 – 20 D Desktop Multiple fans Optimized heat sink 50 – 150 (based on H.S. area) 0.25 – 5

* White, Frank M., Heat and Mass Transfer, Adison-Wesley © 1991, p. 408-9.

With heat sinks it is important to remember that simply increasing the number of fins does not automatically lead to increased heat dissipation, as the fins approach each other the resistance to flow also increases, causing h to drop.  This is why in case B above, the systems cannot be optimized further.

For cases C and D, further effort may be needed to select an appropriate heat sink.  Some suppliers can provide an estimate of the thermal resistance associated with the heat sink based on a representative airspeed in Linear Feet per Minute (LFM). So you may be able to complete your system-level feasibility analysis by simply using a network of thermal resistances, without having to explicitly assume a heat transfer coefficient value.