Evaluation of temperature difference models for heat transfer analysis in tube-in-tube heat exchangers for energy-efficient thermal systems: a CFD-based comparison

This study presents a comparative thermal analysis of a tube–in–tube counterflow heat exchanger under steady–state operating conditions, relevant to engine oil cooling applications, with water and engine oil serving as the working fluids in the inner tube and outer annular region, respectively. An analytical framework was developed to evaluate the logarithmic mean temperature difference (LMTD) and four alternative thermal averages – arithmetic mean temperature difference (AMTD), geometric mean temperature difference (GMTD), harmonic mean temperature difference (HMTD), and root mean square temperature difference (RMSTD) – using outlet temperatures obtained from energy balance relations and regime–appropriate heat transfer correlations. The analytical model accounts for laminar developing flow in the annular region and turbulent flow in the inner tube using appropriate Nusselt correlations, with temperature–dependent viscosity considered for engine oil. In parallel, a computational fluid dynamics (CFD) model was established in ANSYS Fluent to predict outlet temperatures and resolve flow development and near–wall effects. The analytical results demonstrate that GMTD consistently provides the closest approximation to LMTD under moderate operating conditions when analyzed in terms of the dimensionless temperature ratio, while HMTD and RMSTD exhibit larger deviations. The CFD predictions show qualitative agreement with the analytical trends.