Note that as of 2004, ASME is the primary design code for heat exchangers. TEMA is no longer valid for new construction. TEMA is approved for use on repair of existing vessels/HTX under the rules of R stamp.
you can use asme sec viii for some part of heatexchenger such as tubesheet or sylinder of hex under pressure
otherwise TEMA is only for the shell and tube hex.
TEMA also has some very helpful information such as suggested good practice for the design of saddle supports for horizontal exchangers, how to adjust flange calculations to include the pass partition gaskets, etc.
The design of tubesheet in accordance with ASME is very economical compared to TEMA. TEMA calls for minimum tubesheet thickness based on size of tubes, where in case of ASME this requirement is not mandatory.