NOVELTY - The heat exchanger comprises: a first channel (810) having a flowpath, a first wall, a second wall opposite to the first wall, an inlet manifold (812) at a first end, and an outlet manifold (814) at a second opposite end, where the inlet manifold and the outlet manifold orthogonally run to the flowpath; a second channel (820) having a flowpath parallel to the flowpath of the first channel; and a fin (845) extending from the second channel into the first channel, where the fin passes through the first wall and extends to the second wall.    USE - The heat exchanger is useful in a reactor usable in connection with fuel cells e.g. proton-exchange membrane fuel cell and solid oxide fuel cell to generate electricity.    ADVANTAGE - The heat exchanger has reduced heat loss and size, is easy to manufacture, affordable and less sensitive to carbon formation, and provides lateral heat transfer between reactant gases and combustion gases to enhance thermal flow and overall efficiency of the fuel cells, thus improving electricity production of the solar cells in an effective and economical manner.    DETAILED DESCRIPTION - The heat exchanger comprises: a first channel (810) having a flowpath, a first wall, a second wall opposite to the first wall, an inlet manifold (812) at a first end, and an outlet manifold (814) at a second opposite end, where the inlet manifold and the outlet manifold orthogonally run to the flowpath; a second channel (820) having a flowpath parallel to the flowpath of the first channel; and a fin (845) extending from the second channel into the first channel, where the fin passes through the first wall and extends to the second wall. The first channel and the second channel are separated by the first wall. The first channel has micro-channels, and the second channel has micro-channels. The ratio of a first micro-channel width to a first micro-channel height is 2:1-20:1. The heat exchanger is formed from a channel shim and a separator shim. The channel shim defines the first channel. The separator shim includes the fin. The ratio of a channel shim height to a separator shim height is 0.125-8. The channel shim comprises a micro-channel extending from a first end of the channel shim to a second end of the channel shim. The micro-channel comprises a mixing manifold. The separator shim further comprises slots that align with the micro-channel of the channel shim, a mixing manifold, a central slot at the return end, two recesses at the entry end that align with the micro-channels of the channel shim, and an alignment slot that aligns with the alignment slot of the channel shim. The micro-channel of the channel shim is formed from two longitudinal walls joined together by at least one transverse support. The micro-channel is separated into a series of chambers. The chamber at a first end of the micro-channel is shorter in length than the other chambers. The channel shim further comprises: alignment tabs arranged on opposite corners; notches on opposite ends; an entry end and a return end; two outer walls and a central wall that define two micro-channels; and an alignment slot in the central wall. The reaction channel includes a catalyst. The catalyst is inserted into the reaction channel as a catalyst insert. The catalyst insert comprises a corrugated center piece coated on at least one side with the catalyst. The corrugated center piece is sandwiched between two flat shims, and an inner surface of each flat shim is coated with the catalyst. The channel shim and the separator shim are stacked in a regular alternating pattern to form a shim stack, operate to form the first channel, the second channel and the fin, and are diffusion bonded together. The heat exchanger further comprises a top plate above the shim stack, and a bottom plate below the shim stack.    DESCRIPTION OF DRAWING(S) - The diagram shows a schematic view of a heat exchange assembly.    First channel (810)    Inlet manifold (812)    Outlet manifold (814)    Second channel (820)    Fin. (845)