- #1

FEAnalyst

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recently I got interested with practical applications of Newton's law of cooling. Its main disadvantage is that one has to measure temperature at some point of time (other than ##t=0##) to obtain solution for any other ##t##. However I've found an online calculator (https://www.omnicalculator.com/physics/Newtons-law-of-cooling). It features the standard equation from this law: ##T=T_{amb}+(T_{0}-T_{amb}) \cdot e^{-k \cdot t}##. However there's also a formula for approximate constant ##k##: $$k=\frac{hA}{C}$$ where: ##h## - heat transfer coefficient, ##A## - area of heat exchange, ##C## - heat capacity. If this formula is correct then it makes Newton's law of cooling much more useful since no measurement is needed to obtain approximate results. However my question is -

**do you know how this formula is derived, what is the reason for such relationship and, what's even more important, where else can I find it (so far I've only seen it on this single website) ? Do you know any books with this equation ? I need some reliable source.**

Thanks in advance for your help