I'm very glad that I found another guy to come replace the circuit board and put it away from the water, fix the water leak, and also find and fix another impending failure. All of that was for much less than HVAC Service wanted to charge for repair or replacement. The other guy did a great repair, so I'm confident it will not break down again, but if it does, I will not call HVAC Service. Don't get suckered by their Yelp Deal.
Some research suggests that cleaning heating and cooling system components (e.g., cooling coils, fans and heat exchangers) may improve the efficiency of your system, resulting in a longer operating life, as well as some energy and maintenance cost savings. However, little evidence exists that cleaning only the ducts will improve the efficiency of the system.
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All these pro duct cleaners answer with "it's common sense, everything operates better when cleaner" etc. But your explanation is correct. Especially so with flex tube ducting where dust gets "stuck" between the lowest valleys (between wire coil supports) where air flow is drastically reduced -- which is more than 50 pct of the entire interior surface area of the flex ducting. That sounds like a bad thing but also has a good effect of trapping dust from escaping.
The short answer is yes, duct cleaning, done right by a reputable company will help with the smell. It is likely though the smell is coming from another source, ie the crawl space. It could also be that another rodent is dead in the duct work. A visual inspection would be in order to check for any breach in the duct system. A duct pressure test would be able to tell you how much air is leaking from the system over all. A hole large enough for an animal to enter would loses a great deal of air, over 300 CFM. It would be worth looking into having this test done and it should cost around $200. Cleaning the air handler and evaporator coil will greatly improve the performance of the air conditioner. Dirt and dust on the evaporator acts as insulation and reduces the amount of cooling done be the coil. Any quality duct cleaning should include cleaning the air handler and coil, and the tech should allow you to watch him perform the work as it is done.
PickHVAC Tips: Don’t be sold on systems with features you don’t want or need. Called “upselling,” it is rampant in the HVAC industry. Some features are nice – if you want them. If your single-stage furnace was loud and pushed out cold air at the start of the cycle, then a two-stage model will improve those issues. If you didn’t notice them, the upgrade will be a waste of money. That’s just one common example.
Air duct cleaning service providers may tell you that they need to apply chemical biocide to the inside of your ducts as a means to kill bacteria (germs) and fungi (mold) and prevent future biological growth. They may also propose the application of a "sealant" to prevent dust and dirt particles from being released into the air or to seal air leaks. You should fully understand the pros and cons of permitting application of chemical biocides or sealants. While the targeted use of chemical biocides and sealants may be appropriate under specific circumstances, research has not demonstrated their effectiveness in duct cleaning or their potential adverse health effects. No chemical biocides are currently registered by EPA for use in internally-insulated air duct systems (see Should chemical biocides be applied to the inside of air ducts?).