hello
I have some problem modeling an approximate model of natural cooling of a cup of tea/coffee left in a closed and controlled room.
I attached a detailed PDF document (called 01.10.19) that describes all the details regarding the questions I am going to ask below.
1st questions: when I tried to take in account all the heat transfer mechanisms besides radiation (convection from the free upper surface + conduction and afterwards convection through the cup peripheral wall) I got an expression in which I have an extra variable (Tw) that makes my equation become partial differential equation rather than ordinary differential equation. The equation appears in an attached photo called Capture1.
I tried to check what happens when assuming that conduction and afterwards convection through the cup peripheral wall are negligible, but got a horrible typical time constant, 186.6 days.
The solution I got appears in an attached photo called Capture2.
Thanks a lot!
I have some problem modeling an approximate model of natural cooling of a cup of tea/coffee left in a closed and controlled room.
I attached a detailed PDF document (called 01.10.19) that describes all the details regarding the questions I am going to ask below.
1st questions: when I tried to take in account all the heat transfer mechanisms besides radiation (convection from the free upper surface + conduction and afterwards convection through the cup peripheral wall) I got an expression in which I have an extra variable (Tw) that makes my equation become partial differential equation rather than ordinary differential equation. The equation appears in an attached photo called Capture1.
I tried to check what happens when assuming that conduction and afterwards convection through the cup peripheral wall are negligible, but got a horrible typical time constant, 186.6 days.
The solution I got appears in an attached photo called Capture2.
Thanks a lot!
Attachments

251.1 KB Views: 17

24.5 KB Views: 18

24 KB Views: 11