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The present analytical study reports the effect of fin spacing, mass flow rate and isolation on exergy performance of triangular fin attached SAH. The primary objective of the work is to manifest the condition and parameter combinations that yield high values of exergy efficiency. A computer code has been developed in MATLAB R2016a. The numerical results of triangular fin SAH obtained are compared with that of plain SAH as a measure to evaluate the effectiveness of former over the latter. It is found that lower values of mass flow rate and fin spacing yields maximum exergy efficiency. Exergy efficiency drops continuously thereafter and at higher values of mass flow rate, the exergy efficiency drops even below the exergy efficiency of plain SAH.