AbstractThe objective of the current article is to explore the unsteady flow and heat transfer of magnetohydrodynamics tangent‐hyperbolic fluid flow over a stretching sheet. The governing flow model is transformed into a nonlinear set of ordinary differential equations by utilizing the appropriate similarity techniques. A new modification is introduced into the traditional Legendre wavelet method to obtain the results of the model mentioned above. The classic wavelet scheme is unable to find the solution for an infinite domain. Hence, we successfully extended it for an infinite domain and used it to attain the significant findings of the fluid problem. Additionally, the study of emerging parameters on temperature and velocity profiles is reported graphically. The velocity behavior is decreasing for the physical parameters, namely, power‐lax index, unsteadiness, Hartmann number, and Weissenberg number. The temperature profile is an increasing function for power‐law index and Eckert number while the behavior is the opposite for the Prandtl number. Moreover, a tabular form comparison of outcomes with existing literature, convergence, and error analysis is provided in our study, which confirms the credibility of the suggested method. The obtained results endorse the credibility and reliability of the proposed method; therefore, it could be extended for other nonlinear problems of complex nature.