Axial heat conduction effects within the fluid can be important for duct flows if the Prandtl number is relatively low (liquid metals). In addition, axial heat conduction effects within the flow might also be important, if the heating zone is relatively short in length. The present paper shows an entirely analytical solution to the extended Graetz problem with piecewise constant wall temperature boundary conditions. The solution is based on a selfadjoint formalism resulting from a decomposition of the convective diffusion equation into a pair of first order partial differential equations. The obtained analytical solution is as simple to compute as the one without axial heat conduction. The analytical results are compared to available numerical calculations and good agreement is found.

A combined experimental and numerical investigation of the heat transfer characteristics inside an impingement cooled combustor liner heat shield has been conducted. Due to the complexity and irregularity of heat shield configurations, standard correlations for regular impingement fields are insufficient and detailed investigations of local heat transfer enhancement are required. The experiments were carried out in a perspex model of the heat shield using a transient liquid crystal method. Scaling of the model allowed to achieve jet Reynolds numbers of up to Rej=34,000 without compressibility effects. The local air temperature was measured at several positions within the model to account for an exact evaluation of the heat transfer coefficient. Analysis focused on the local heat transfer distribution along the heat shield target plate, side rims, and central bolt recess. The results were compared with values predicted by a standard correlation for a regular impingement array. The comparison exhibited large differences. While local values were up to three times larger than the reference value, the average heat transfer coefficient was approximately 25% lower. This emphasized that standard correlations are not suitable for the design of complex impingement cooling pattern. For thermal optimization the detailed knowledge of the local variation of the heat transfer coefficient is essential. From the present configuration, some concepts for possible optimization were derived. Complementary numerical simulations were carried out using the commercial computational fluid dynamics (CFD) code ANSYS CFX. The motivation was to evaluate whether CFD can be used as an engineering design tool in the optimization of the heat shield configuration. For this, a validation of the numerical results was required, which for the present configuration was achieved by determining the degree of accuracy to which the measured heat transfer rates could be computed. The predictions showed good agreement with the experimental results, both for the local Nusselt number distributions as well as for averaged values. Some overprediction occurred in the stagnation regions, however, the impact on overall heat transfer coefficients was low and average deviations between numerics and experiments were in the order of only 5–20%. The numerical investigation showed that contemporary CFD codes can be used as suitable means in the thermal design process.

As part of an industrial gas turbine research program, the present study provides the results of a basic investigation of the heat transfer in an impingement cooled combustor heat shield. Because of the complexity and the irregularity of the impingement pattern of the heat shield, standard correlations for regular impingement fields are insufficient and the investigation of local heat transfer enhancement is required therefore. The model to represent a simplified heat shield is made out of perspex, and heat transfer experiments are performed using a transient liquid crystal method. The local air temperature is measured at several positions within the model. The distributions of the Nusselt number on the impingement target plate as well as on the side rims and along the central bolt recess of the heat shield are shown for different impingement Reynolds numbers. The results are compared with respect to the local and overall heat transfer.

In this paper the convective heat transfer in a rectangular dimpled channel with an aspect ratio of six is studied. Applications could be for gas turbine vanes, vane shrouds, ring segments and hot components in the combustor. Basic heat transfer experiments have been performed using heater foils and a steady-state method with liquid crystals. The cooling effect is achieved by a dimple configuration combined with rib turbulators. The specific subject of this study is to focus on the heat transfer enhancement in the corner regions of the dimpled large aspect ratio channel. Different configurations of rib turbulators are investigated at different Reynolds numbers. Detailed heat transfer distributions are presented for the different configurations, showing the local effect of turbulator placement and angle with respect to the main flow direction. They are complemented by pressure drop measurements and compared with numerical simulations. It is shown that locally implemented rib configurations can enhance the heat transfer in these critical regions without large pressure loss penalties.

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