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I am familiar with using $\dot{Q}=c_p\cdot\dot{m}\cdot\Delta T$ to calculate the heat transfer rate of a fluid given a singular value for specific heat capacity (such as with water), but how do I go about calculating heat transfer rate for an aequeous solution such as $MgCl_2 (aq)$? Do I somehow use the heat capacities of both water and salt together?

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  • $\begingroup$ I'd be amazed if there's no expermintal resarch into taht. What did you find so far? $\endgroup$ – mart Sep 29 '20 at 14:52
  • $\begingroup$ Check out solar systems - think some tried salt solutions but the disadvantage was corrosion iirc. $\endgroup$ – Solar Mike Sep 29 '20 at 18:46
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The formula you are quoting is for estimating the heat exchange rate of a fluid that enters a control volume with rate $\dot m$ and has a change in temperature $\Delta T$.

If you know

  • the mass rate of the solution
  • the precise per weight ratio of your solution
  • the heat capacity of the elements
  • the temperature difference

And provided there are not endothermal or exothermal reactions, then its basically a pretty straight forward sum of the parts.

$$\dot{Q}_{total} = \dot{Q}_{water} + \sum _{i=1}^n \dot{Q}_{sub.1} $$ $$\dot{Q}_{total} = \dot{m}_{water}c_{p,water}\Delta T + \sum _{i=1}^n \dot{m}_{sub.i}c_{p,sub.i}\Delta T $$

However, you will find that in most cases, because $c_p$ of water is so much greater that most other substances and the weight percentage in most solutions is much greater, you probably don't need to bother.

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