Approximate analytical solutions to nonlinear peristaltic flow with temperature-dependent viscosity parameters: Application of multi-step differential transform method (MsDTM)

Abstract

This paper investigates the influence of temperature-dependent viscosity on peristaltic flow of a Newtonian fluid past a vertical asymmetric channel through a porous medium in the presence of heat and mass transfer. A mathematical model is analyzed under assumptions of long wavelength and small Reynolds number. The resulting system of coupled nonlinear differential equations with corresponding boundary conditions is computed in two different cases. In the first case (labeled as system I), all non-dimensional parameters, which are functions of viscosity, have been considered as constants within the flow (as treated in previous peristaltic flow problems). In the second case (labeled as system II), these mentioned parameters are then assumed to vary with temperature. Solutions in each case have been obtained using an easy and highly accurate series-based method called the multi-step differential transform method (MsDTM). The effects of the pertinent physical parameters on the longitudinal velocity, temperature, concentration, longitudinal pressure gradient, and pressure rise per wavelength are analyzed graphically and through tables for both systems I and II. The results reveal that the longitudinal pressure gradient and the pressure rise per wavelength in the case of system II are of lower magnitude than the equivalent values of system I. Another interesting observation is that the temperature field in the case of system II, increases with a decrease in the fluid viscosity, which is in accordance with physical observations, whereas the opposite behavior appears in the case of system I. A detailed comparison between system I and system II demonstrates that in modelling fluid problems with variable viscosity, treating the viscosity-dependent parameters as constants leads to unrealistic results. Such a model is applicable for the transportation of physiological flows (blood flow models) in the arteries with heat and mass transfer.

Modulated Viscosity-Dependent Parameters for MHD Blood Flow in Microvessels Containing Oxytactic Microorganisms and Nanoparticles

“…Since viscosity is assumed to vary across the flow, then these mentioned parameters will vary, too. Ignoring such phenomena will lead to unrealistic results [28].…”

“…Therefore, from the above discussions, we conclude that the CP-Model case leads to unrealistic results, whereas the VP-Model shows real outcomes. Discussion on Some Previous Works Elogail and Elshekipy [28] caught sight of the necessity of treating the non-dimensional parameters that rely on viscosity in their definitions in the set of governing equations to be variables too. Consequently, this extra step has modified the set of governing equations (as in the VP-Model).…”

“…In these studies, the authors did not recognize that the non-dimensional parameters defined in terms of viscosity should be considered variables. Recently, Elogail and Elshekhipy [28] investigated the effect of temperature-dependent viscosity on the peristaltic flow in two different cases. In the first case, the authors treated the non-dimensional parameters that depend on viscosity in the non-dimensional governing equations as constants inspired by previously analogous works in the literature.…”

Letter to the editor regarding “Hall current effect on the peristaltic motion of synovial nanofluid with magnetohydrodynamics” by Wahed M. Hasona

“…The condition presented in eq. (7) of Reference (p. 4) is wrong and its correct form is as follows For more details see References …”

Mutual effects of chemical reaction and thermal radiation on MHD peristaltic transport of Jeffrey nanofluids: Tumor tissues treatment

“…19,20 After considering the abovementioned studies, the vital role of this study is to present an original model for the influence of thermal radiation and temperature-dependent viscosity on peristaltic pumping of nanofluid models. It is worth mentioning that Elogail and ElShekhipy 29 have introduced the idea of the variable nondimensional parameters in a base fluid in peristaltic transport of a Newtonian fluid. We develop that idea in nanofluid models with a non-Newtonian fluid flow in a tapered asymmetric channel.…”