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The processes of hydrodynamics and heat transfer during the flow of a non-Newtonian polymeric medium in a plane channel have been investigated with boundary conditions of the first kind. Consideration was given to a steady-state nonisothermal process with low values of the Reynolds number and high values of the Péclet number, which made it possible to neglect gravity and inertial forces, and also longitudinal thermal conductivity. The Ellis model with a viscosity dependent on temperature, pressure, and the degree of chemical transformation was used as the rheological model. A high-viscosity medium was investigated. Therefore, it is the dissipative term that was taken account of in the energy equation. With the above rheological model, an expression in explicit form was obtained from the equation of motion of such a medium for the velocity profile of its flow. It has been established that the dependence of the viscosity of a medium on its temperature, pressure, and the degree of transformation has an appreciable effect on the distribution of the temperature of the medium and the velocity of its flow along the channel's length. Taking account of the temperature dependence of the viscosity of the medium leads to a decline in the role of dissipation in the process of its warmup. The dependence of the medium's viscosity on pressure, conversely, considerably enhances the dissipative effect, which appreciably accelerates the course of a chemical reaction. [ABSTRACT FROM AUTHOR]

• MHD non-Newtonian fluid flow with CNTs and heat transfer across a linearly shrinking sheet. • An exact solutions are extracted for the governing equations of the aforesaid flow. • Two types of non-Newtonian fluids like second grade fluid and Walters' liquid B. • The existence of unique and dual solutions domains are traced by physical parameters. • Dual solutions exist for second grade fluid for both slip and no-slip restrictions. The present paper focuses on electrically driven magnetohydrodynamic non-Newtonian fluid flow (viscoelastic fluid)with CNTs and heat transmission across a linearly shrinking sheet. The flow is urged with the partial slip conditions, radiation and heat source/sink. Single walled and multi walled CNTs are considered in this analysis. An exact solution is extracted for the governing equations of the aforesaid flow of two types of non-Newtonian fluids like second grade fluid and Walters' liquid B with CNTs using similarity transformations. The flow velocity is pretentious due to many physical parameters like magnetic force, visco-elasticity, slip parameter, whereas the energy profile is pretentious due to Prandtl number, Biot number, heat sink/source parameter and radiation parameter. The existence of unique and dual solutions domains are traced by combining the above parameters and velocity, energy profiles and skin friction are explained using graphs. The results reveal that the dual solutions exist for both types of viscoelastic fluids under specific flow restrictions. In particular, dual solutions exist for second grade fluid for both slip and no-slip restrictions. And similar observations are found for Walters' liquid B fluid for unique slip flow when viscoelastic parameter value increases above a definite value. Inclusion of magnetic field terminates the ambiguity of existence of solution for different λ 1 values for both viscoelastic fluids. [ABSTRACT FROM AUTHOR]