Intake manifolds can be heated in several ways.
1) Engine water being circulated through jackets where ever the designer decides it needs heat.
2) Exhaust gas being passed through jackets in a similar manner to the water.
3) The manifiold being placed so that engine oil splashes on the bottom of the manifold such as over the valley in V type engines.
4) Air being preheated by passing it over an exhaust pipe before it enters the manifold.
All these methods are for several reasons.
1) To aid in evaporation of the fuel, especially in cold starts and low speed. This is most critical on an engine with a central carby over a low mounted plenum with runners running up and off in various directions and is less critical on multi carby, IR manifolds with direct downhill run from the carby fuel discharge nozzle to the inlet valve. It is hardly required at all with fuel injection with nozzles spraying at the valve.
2) to reduce the need to use rich mixture to start a cold engine for the reasons in 1)
3) To reduce hydrocarbon emissions.
4) To improve response.
5) To reduce the need for accelerator pump shot with carbies.
5) To improve fuel distribution with a central carby.
6) To reduce throttle plate icing.
The various methods impose different costs in manufacture.
The various methods have different impacts on maintenance and durability.
The various methods have different warm up or response rates.
The various methods have different levels of accuracy to which they hold the desired temperature.
Manifold warming is necessary in cold climates but reduces power in warm climates, at high speed and after the engine warms up.
Manifolds designed for maximum power rather than easy starting, emission control, low speed response and economy such as used for racing go to some lengths to insulate or isolate inlet manifolds from heat.
Of course all the above statements are relative.
Regards
Pat
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