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A two-dimensional heat conduction model was developed to determine the transient temperature distribution within a flat substrate that was exposed to the impingement of a cold spray hot air jet during the deposition process. The credibility of employing average heat transfer coefficient in mathematical modelling and prediction of the surface temperature profile of a substrate was studied. Moreover, the condition under which the effect of the presence of the in-flight particles on the heat transfer coefficient of the underexpanding air jet can be neglected was investigated. In this regard, a cold spray unit was used to generate a supersonic air jet. A twodimensional heat conduction model was developed and solved by using Green’s functions to determine the temperature distribution within the substrate. By applying a surface integral to the analytically-estimated spatially-varying heat transfer coefficient of an underexpanding cold spray air jet, the average heat transfer coefficient was determined. Both the average and spatially-varying heat transfer coefficients were used separately in the model to predict the transient surface temperature profile of the substrate. It was shown that when the Stokes number of the particles is sufficiently small, the effect of the presence of the particles on the heat transfer coefficient of the impinging dilute air-particle jet can be neglected. It was further found that the surface temperature that was predicted by using the average heat transfer coefficient, unlike the spatially-varying heat transfer coefficient, produced large errors, especially at higher distances from the stagnation point of the air jet on the substrate surface.

Heat Transfer Coefficient of an Under-Expanding Cold Spray Air Jet on a Flat Substrate