Although the advent of fast and inexpensive parallel computers has rendered numerous previously intractable calculations feasible, many numerical simulations remain too resource-intensive to be directly inserted in engineering optimization efforts. An attractive alternative to direct insertion considers models for computational systems: the expensive simulation is evoked only to construct and validate a simplified input-output model; this simplified input- output model then serves as a simulation surrogate in subsequent engineering optimization studies. We present here a simple 'Bayesian-validated' statistical framework for the construction, validation, and purposive application of static computer-simulation surrogates. As an example, we consider dissipation-transport optimization of laminar-flow eddy-promoter heat exchangers: parallel spectral element Navier-Stokes calculations serve to construct and validate surrogates for the flowrate and Nusselt number; these surrogates then represent the originating Navier-Stokes equations in the ensuing design process. Numerical analysis, Fluid dynamics, Optimization, Surrogates, Monte Carlo Method, Modelling.