Iterative Calculation Issue Involving Heat Transfer

Hello,

I apologize in advance for the long post but believe it to be important so that any reader can fully understand.

I am attempting to solve for the internal temperature of a steak when cooked via skillet and induction cooker. The goal is to determine how long it will take the center of the steak to reach a temperature of 70C. In order to do this, the skillet was assumed to be a steady state fin and the steak a transient fin. In order to solve for the nodal temperatures in the steak I first had to solve for the temperature distribution (using 1 dimensional heat transfer) in the skillet. The "top" nodal temperature was then used for the "bottom" nodal temperature of the steak. By using the equations derived for this particular situation (see "Inventory" tab in attached spreadsheet) I successfully solved for the temperature distribution in the cookware and steak for 4 nodes and 10 nodes. For 4 nodes, the time required for the middle node is ~200 seconds and the time for 10 nodes is ~240 seconds However, when I go to 20 nodes, excel provides an error in the values it calculates. It is giving me values that are in the E+40 seconds range. I have used much more calculation intensive spreadsheets in the past, so I am unsure why excel seems to be choking on these. I copied the equations into the 10 node worksheet from the 4 node worksheet and added additional interior nodes to add up to 10. When I adjusted the cell references and copied the equations to "later" times, the calculations copied correctly and the time value I attained was correct. However, when I repeated this process for the twenty nodes, I got erroneous data. I am curious if others have experienced similar problems when using multiple iterative calculations and they have done to fix the issues?

As you can see from the spreadsheet, each nodal temperature depends on the surrounding nodes or the ambient temperature for the top node. The equations referenced in "Equations" I have confirmed are accurate. The same equations were used for the 4 node solution, the 10 node solution, and the 20 node solution.

I'm sure I have left out a detail or two so please feel free to ask any questions you may have.

Thank you in advance for any help you can provide!!

Brandon