Wheel graphs can be constructed by adding an additional vertex on the center of a cycle graph and then joining this vertex with all other surrounding vertices. A 𝑘 −labeling of type (𝛼, 𝛽, 𝛾) in a wheel graph is a labeling from graph elements into the set of positive integers. Face irregularity strength of a wheel graph 𝑊𝑛 with respect to 𝑘 −labeling of type (𝛼, 𝛽, 𝛾) is the minimum integer 𝑘 on which the face weights of the graph are distinct. We investigate the exact value for the face irregularity strength with respect to vertex 𝑘 −labeling, edge 𝑘 −labeling and total 𝑘 −labeling of wheel graphs. Some real life applications on face irregularity strength of graphs are discovered and their models are discussed which will be helpful in practical situations.