Fourier Heat Transfer Calculation
This page performs a Fourier heat transfer calculation to give an output temperature based on a known heat exchanger surface area. You can't do this analytically because you can't split the Log Mean Temperature Difference algebraically so you have to iterate. The heat transfer calculator displays a graph showing the temperature of the product at any point along the length of the heat exchanger in terms of the surface area, you can back calculate the actual position along the length based on the geometry of your device.