<p>A study is made to determine the similarity solutions for steady mixed convection flow of tangent hyperbolic fluid and heat transfer over a permeable shrinking sheet. The Lie scaling group of transformation technique is used to find the new form of similarity transformations, effectively transforming the governing momentum and energy equations into a new form of coupled ordinary differential equations (ODEs). The resultant system is then numerically solved using the shooting technique for various values of the governing parameters. Dual solutions are found only for the opposing flow case, and a temporal stability analysis is performed to determine the physically reliable solution branch. It is found that the numerical values of the skin friction coefficient and the local Nusselt number in the case of assisting flow are higher than that in the opposing flow case. The momentum and thermal boundary layer thicknesses for the upper branch solutions are smaller than those of the lower branch solutions. It is observed that the suction parameter increases the fluid velocity but decreases the temperature in the upper branch solution, whereas the non-Newtonian parameter diminishes the fluid velocity but enhances the temperature.</p>