The performances of the heat transfer due to dissipative heat likely magnetic dissipation is a challenging field of research because of it's diversifies applications in industries and engineering. Particularly, nowadays, in biomedical field of research the implementation of dissipation along with thermal radiation is vital. Based upon the current scenario, the present investigation leading to the role of magnetic dissipation vis‐à‐vis thermal radiation on the water‐based hybrid nanofluid past an electro‐magnetized elongating surface associated with melting boundary conditions. The adaptation of the transformed rule particularly, similarity rules are useful to convert the proposed set of problems in to ordinary. Further, shooting‐based numerical technique is proposed to handle the governing equations. The interesting and novel approach in this topic is the use of robust statistical technique, that is, response surface methodology for the optimizing Nusselt number for the use of various factors. Moreover, the validation is obtained by conducting a hypothetical testing using analysis of variance (ANOVA) which conforms a best output model for appropriate response. Further, the major outcomes of the study are depicted as; the unsteadiness parameter decelerates the velocity profile of the hybrid nanofluid for the interaction. However, the increasing particle concentration favours in enhancing the heat transport phenomenon.