A tubular heat exchanger having a plurality of shell-side and tube-side fluid passes. The heat exchanger includes an elongated cylindrical shell, a head coupled thereto, and a tube bundle positioned in the shell and supported in part by a tube sheet attached to the head. The shell of the heat exchanger may include a plurality of vertically stacked shell-side compartments each defining a shell-side pass. The head of the heat exchanger may have a plurality of tube-side compartments each defining a tube-side pass. A tube-side fluid enters the head and flows through the tube bundle progressively through a series of tube-side passes to heat the fluid with a shell-side fluid. Each shell-side pass contains multiple tube-side passes. The tube-side fluid may perform a plurality of horizontally arranged tube-side fluid passes in each vertically stacked shell-side fluid pass before cascading vertically to a next shell-side fluid pass.