Can the same CNN architecture be used for different data sets?
One way is to redesign your CNN architecture to fit your new data input. However, if you want to use the current model you have, you should: 

(1) Retraining: Re-train the model with new data set images

(2) Reshape new images: You should add a pre-processing layer to convert 28x28x1 images to 32x32x3 images. This could be done by replicating a single channel in other two channels and adding boundaries to your images. This deformation process should be the same on all new input images.