What is the purpose of measuring the exergy efficiency of flat plate collector? There is multiple ways to express efficiency, with different boundary condition assumptions that may lead to different results.
Is it is just for expressing the performance? Optimizing the design options? Comparing and contrasting with other technologies?
There is alternative expression with "Internal boundary condition" assumption (helps to normalize the results with other heat production systems) Article Exergy-based approaches for performance evaluation of buildi...
The expression using detailed design parameters that is useful if looking for optimization Article Exergetic optimization of flat plate solar collectors
There is definitions as universal and functional efficiency expressions that may produce different results.
Hope that this information helps to find right solution and understand additional aspects that may influence your results.