Heat transfer and flow analysis over a linearly stretching sheet with constant wall temperature: Novel local non-similar solutions in the presence of viscous heating

Flow over a linearly stretching sheet having constant temperature is examined in this article. The effects of frictional heating (viscous dissipation) and Ohmic heating (Joule dissipation) are also studied. As evidenced by the literature, energy equations are not always self-similar when viscous dissipation is considered. It strongly depends on the form of stretching velocity and the surface temperature of the sheet. To facilitate the similarity transformations in these cases, one must find a constraint between the sheet velocity and the surface temperature. It is also observed that for the linearly stretching sheet with constant wall temperature, it is not possible to achieve self-similar equations because in this case, a local variable appears in the viscous dissipation parameter. Hence, this problem corresponds to the non-similar flow. In this analysis, pseudo-similarity transformation is employed, and the viscous dissipation parameter is selected as a non-similarity variable. Governing equations are transferred into non-similar forms then a method known as Sparrow-Quack-Boerner (SQB) local non-similarity (LNS) is used to derive the equations up to the second level of truncations which are then solved numerically. The slope linear regression (SLR) technique is used to compare the solutions obtained from the equations of the first and second levels of truncation.

Automated summary

This article investigates flow over a linearly stretching sheet with constant temperature. The effects of frictional heating and Ohmic heating are studied. It is found that energy equations are not self-similar when considering viscous dissipation, depending on the stretching velocity and surface temperature. A constraint between sheet velocity and surface temperature is needed for similarity transformations. In this analysis, a pseudo-similarity transformation is employed and the viscous dissipation parameter is used as a non-similarity variable.