Printed circuit heat exchangers (PCHE) and the similar formed plate heat exchangers (FPHE) offer highly attractive economics due to their higher power densities when compared to more conventional shell-and-tube designs. However, their complex geometry makes them more vulnerable to damage from thermal stresses during transient thermal hydraulic conditions. Transient stresses far exceed those predicted from steady state analyses. Therefore, a transient, hydraulic, thermal, and structural analysis is needed to accurately simulate and design high performing PCHE. The overall length of the heat exchanger can be thousands of times larger than the characteristic length for the heat transfer and fluid flow. Furthermore, simulating the thermal hydraulics of the entire heat exchanger plate is very time consuming and computationally expensive. The proposed methodology mitigates this by using a multiscale analysis with local volume averaged (LVA) properties and a novel effective porous media (EPM) approach. This method is implemented in a new computer code named the compact heat exchanger explicit thermal and hydraulics (CHEETAH) code which solves the time-dependent, mass, momentum, and energy equations for the entire PCHE plate as well as hot and cold fluid streams using finite volume analysis (FVA). The potential of the method and code is illustrated with an example problem for a Heatric-type helium gas-to-liquid salt PCHE with offset strip fins (OSF). Given initial and boundary conditions, CHEETAH computes and plots transient temperature and flow data. A specially developed grid mapping code transfers temperature arrays onto adapted structural meshes generated with commercial FEA software. For the conditions studied, a multiscale stress analysis reveals mechanical vulnerabilities in the HX design. This integrated methodology using an EPM approach enables multiscale PCHE simulation. The results provide the basis for design improvements which can minimize flow losses while enhancing flow uniformity, thermal effectiveness, and mechanical strength.