Seeking advice on the temperature difference correction coefficient

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I was working on a project recently, and since I had no prior experience in heat exchanger design, I couldn’t figure out the approach to take. The task was to design an air heater (a box-type heat exchanger) that uses hot flue gas to heat cold air. Hot side (flue gas): inlet temperature of 700°C; outlet temperature to be determined. Flue gas flow rate: 6400 Nm3/h. Cold side (air): inlet temperature of 20°C; outlet temperature of 470°C. Air volume: 5900 Nm3/h. 1. Based on heat balance calculations, the outlet temperature on the flue gas side is 333°C, with a heat transfer load of 912 kW. 2. The logarithmic mean temperature difference calculated is 298°C. 3. Using the calculated values of P and R, an attempt was made to determine the temperature difference correction factor; however, this could not be done as the logarithm in the formula came out to be negative. I would like to ask whether it is impossible to achieve the desired heat transfer temperature if the temperature difference correction factor cannot be calculated ? The outlet temperature needs to be adjusted. I have no experience in doing this as I’ve never done it before, so I’m seeking advice from everyone