First, search this forum for MUA as a topic.
Second, read or skim the relevant references at my My Clippings.

Now, once warmed up, you will see what a can of worms this can be without some study or some funds sent the way of a knowledgeable commercial HVAC company.

The answer will depend on:
a) your ambient temperature range, which drives your potential need for heating and/or cooling of the MUA.
b) the need for filtering the MUA to keep out insects, if not eagles.
c) how the MUA is to be introduced to the kitchen -- directly or indirectly
d) beyond providing enough MUA so that your hood actually has the performance you want, what is the situation with respect to combustion appliances using the same household air, other exhaust fans such as in a bathroom, fireplaces?

Some of these questions will inform whether a passive or active MUA is needed. (Active MUA uses a fan or blower to make up for the pressure loss in the MUA system due to filtration, heat-exchangers, and ducting. It will generally require a control circuit that may have to be fairly sophisticated under some conditions -- more sophisticated than large buildings that can afford to run fan motors 24/7.)

kas