The present paper emphasizes the impacts of the compliant wall and variable liquid properties on the peristaltic stream of a Rabinowitsch liquid in an inclined channel. The viscosity of the liquid differs over the thickness of the channel, and temperature-dependent thermal conductivity is considered. The perturbation strategy is utilized to solve the governing nonlinear temperature equations. The expressions for the velocity, skin friction coefficient, pressure rise, frictional force, streamline, temperature and coefficient of heat transfer are obtained. The consequences of pertinent parameters on the velocity, temperature, streamline and coefficient of heat transfer for the dilatant, Newtonian and pseudoplastic liquid models are analysed graphically. The results obtained for velocity and temperature reveal that an expansion in the estimation of variable viscosity results in diminishing the velocity and temperature fields for shear thickening liquid. Furthermore, it is noticed that for a large value of thermal conductivity the temperature profile decreases for dilatant, Newtonian and pseudoplastic fluid models.

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The MHD peristaltic motion of Bingham fluid through a uniform channel is examined under the influence of long wavelength and small Reynolds number. The impact of variable thermal conductivity, convective heat transfer, porous boundaries, and wall properties are considered. The semi-analytical technique is utilized to solve the governing nonlinear temperature equation. The effects of different parameters on the physiological quantities of interest are captured with the assistance of MATLAB programming. The assessment reveals that an ascent in a magnetic parameter reduces the velocity field. Further, an increment in the estimation of variable thermal conductivity upgrades the temperature profiles. Besides, the trapped bolus is a function of a porous parameter, and an increase in porous parameter will have the proportional increment in the other parameter.

Variable properties play a prominent role in analyzing the blood flow in narrow arteries. Specifically, considering the variation of thermal conductivity and viscosity helps in the understanding of the rheological behavior of blood and other biological fluids, such as urine, spermatozoa, and eye drops. Inspired by these applications, the current study incorporates the impact of variable thermal conductivity and viscosity for modeling the peristaltic flow of a Ree–Eyring liquid through a uniform compliant channel. The governing equations are nondimensionalized with the assistance of similarity transformations. The long‐wavelength and small Reynolds wide variety approximation are utilized for solving the governing differential equations. Furthermore, the series solution method (perturbation technique) is utilized for solving the nonlinear temperature equation. The obtained results show that the velocity is greater in the case of the Newtonian liquid than that of the non‐Newtonian liquid.

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