"The long-term goal of this research is to contribute to the development of mathematical models and numerical solution methods for use as cost-effective tools in procedures for designing the next generation of compact and ultra-compact heat exchangers (core heat transfer area density exceeding 700 m^2/m^3 and 3000 m^2/m^3, respectively). Such heat exchangers are expected to play a major role in ongoing worldwide efforts to propose novel energy conversion systems. The desire to participate in such efforts is the main motivation for this work. Attention in this work was focused on rectangular offset strip-fin plate-fin core configurations. Over the last 50 years, there have been many efforts to increase the compactness of such cores. However, increasing compactness reduces the hydraulic diameter and (hence) the Reynolds number, for the same average velocity, which can lead to turbulent-to-laminar transition. These consequences of increasing compactness bring up the issue of its effect on the rate of heat transfer for a fixed pumping power. The rectangular offset strip-fin plate-fin configuration causes starting, interrupting, and restarting of both velocity and thermal boundary layers, and also possible unsteadiness and vortex shedding; and these thermofluid features bring up the issue of maximizing heat transfer for specified heat transfer surface area and fixed pumping power.The main goal of this research was to contribute to the resolution of the first of the aforementioned two issues, in a highly cost-effective manner. Thus, fins of negligible thickness and flow passages of large cross-sectional aspect ratio were assumed, and attention was limited to steady two-dimensional fluid flow and heat transfer phenomena. Air was the fluid of choice, and it was assumed that its thermophysical properties remained essentially constant. Furthermore, the Eckert number was much less than one in the problems considered here, so viscous dissipation could be ignored.Elliptic and parabolic mathematical models of developing fluid flow and heat transfer in continuous parallel-plate channels and arrays of regular staggered plates were considered. Three different low-Reynolds-number turbulence models (all capable of predicting turbulent-laminar transition with reduction in Reynolds number) were selected for comparative assessment. These mathematical models were solved using two-dimensional elliptic (2DE) and parabolic (2DP) finite volume methods (FVMs): the 2DE FVM was an adapted version of an in-house code; the 2DP FVM was specially formulated and implemented for this work, retaining the momentum equation in the direction transverse to the main flow (a novel feature of the proposed method). Mathematical models of fully developed fluid flow and heat transfer in pipes and parallel-plate channels were also considered and solved using one-dimensional FVMs. The results were compared to those yielded by available empirical correlations and also experimental data. Finally, one of the three low-Reynolds-number turbulence models and the 2DP FVM were used to simulate fluid flow and heat transfer in three actual rectangular offset strip-fin plate-fin cores of compact heat exchangers.For fully developed flows, all three low-Reynolds-number turbulence models considered in this work gave results that showed excellent agreement with those yielded by available empirical correlations and also experimental data. For developing fluid flow and heat transfer, the 2DP results compared very well with the 2DE results; however, the 2DP FVM executed 700 to 12,000 times faster than the 2DE FVM for comparable computational grids. In simulations of developing fluid flow and heat transfer in continuous-plate channels and regular arrays of staggered plates, only one of the three low-Reynolds-number turbulence models gave good results. The details of the models, numerical methods, and results, and also some recommendations, are presented and discussed in this thesis." --