Question was answered!
Edited by SCOTTRR, 04 September 2019  01:58 AM.

Posted 03 September 2019  02:34 PM
I'm not sure what sort of explanation you are looking for. We know that heat always flows from high temperature to low temperature. Among all of the other variables, the rate of heat flow is related to the temperature difference.
Perhaps this tutorial will provide a refresher of the basics of heat transfer: https://www.physicsc...fHeatTransfer
Posted 03 September 2019  02:43 PM
I'm not sure what sort of explanation you are looking for. We know that heat always flows from high temperature to low temperature. Among all of the other variables, the rate of heat flow is related to the temperature difference.
Perhaps this tutorial will provide a refresher of the basics of heat transfer: https://www.physicsc...fHeatTransfer
Posted 03 September 2019  03:00 PM
I'm not sure that I have the expertise to give you a definitive answer. From what I know of heat transfer coefficients (basically this page: https://www.engineer...ientd_434.html), heat transfer coefficients are functions of several different variables  some of which (like thermal conductivity) can be functions of temperature. How much a heat transfer coefficient might change in a scenario where one side's temperature is constant and the other side is approaching that temperature, I cannot say. The math seems a lot simpler if I can assume it doesn't change (and I wouldn't be surprised if there are many simple scenarios where engineers make that assumption). You would need to know enough about your heat exchanger to know if it is safe to assume a constant heat transfer coefficient or if you need to vary the coefficient as the cold side warms up.
Posted 03 September 2019  03:23 PM
Asides from the issues that Pilesar and MrShorty already mentioned: How large is the heat exchanger and how much water is inside it? Even if the heat flow was known and constant (which it probably will not be) and you used the formulas correctly (which you didn't) you couldn't calculate the time it takes to heat up the system, because you don't know how large the system is.
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