Could homeless people in a dystopian world, where combustion is illegal (to reduce particulates) and electricity strictly rationed, cook food by harvesting human warmth using a back-pack with a battery that runs a heat pump that takes heat from the back of a human and pumps it into a slow cooker that hangs on the persons front?
Since the cooker is on the chest, let's assume we're pumping heat from both the back and the chest
Average adult human body surface: 1.8 m2
Average waste heat of an average adult human: 18.4 BTU/hr/0.09m2 (Source)
The chest and back equal 27% or .486m2 (Source)
That's 99.36 BTU/hr that could be used to heat food
For the sake of argument, we'll assume perfect transference of heat from the skin surface to the food. This is certainly NOT true, but the result is a best-case measurement of what this technology could do. So, what can we do with 99.36 BTU/hr?
1 Btu = amount of heat required to increase temperature of 1 pound (1 pint) of water by 1 DEGREE F
- The average adult human needs four pounds of food each day. (Source)
Let's assume only 2 pounds of food must be cooked. It must be raised to 350℉. For convenience we'll assume we don't need to hold it there. Cooking food during the heat-raising time is not as efficient as pre-heating the cooking apparatus and has the potential of causing botulism, so it's not the best solution, but it's a simplification that's useful for this exercise. How many BTUs are needed to heat 2 pounds of food from room temperature (75℉) to 350℉?
- (350 - 75) * 2 = 550 BTU, which would be generated in about 5.5 hours.
The above analysis is assuming the human is resting. If the human is working, they'll generate more waste heat, but they'll also need more food. I can't prove it, but my spidey senses suggest food will be needed at a greater rate than heat will be generated.
The inefficiencies ignored in this analysis would lengthen the time needed to cook food. 10 hours to cook 2 pounds of food would be more believable.
The ambient conditions were completely ignored by this analysis and it's important that they be considered. In high summer, "room temperature" would be higher but heat pumps work much less efficiently. In deep winter "room temperature" would be quite a bit lower, but the heat pump would work more efficiently. Consequently, cooking during the summer might be hard-to-impossible (but, then, you could cook eggs on surrounding rocks, n'est pas?) However, adding to the improved efficiency of heat pumps in the winter is the benefit to having all the apparatus under insulating clothing — Except the homeless are usually a bit short of insulating clothing and the loss of waste heat might compromise their ability to stay warm at all during the winter.
Therefore, while I conclude this is believable, I wouldn't focus too much on it. I wouldn't be surprised that a rigorous review of physics would demonstrate this solution would barely work, at best, and be so susceptible to botulism that it wouldn't be worth the effort.