HOMOTOPY ANALYSIS OF MAGNETOHYDRODYNAMIC CONVECTION FLOW IN MANUFACTURE OF A VISCOELASTIC FABRIC FOR SPACE APPLICATIONS

Aerospace electro-conductive polymer materials are a new family of “smart” materials being deployed in many complex applications. The precision manufacturing of such processes to manipulate properties and enhance performance can exploit magnetohydrodynamic (MHD) control and simultaneous heat transfer (thermal processing). Motivated by these applications, we develop a model for laminar free convective flow of an incompressible and electrically-conducting viscoelastic fluid (Walters’ liquid B) over a continuously moving stretching surface embedded in a porous medium in the presence of strong radiative heat flux, as a simulation of magnetic smart fabric sheet processing. A heat generation/absorption term is included in the model. Darcy’s law is used to simulate porous media bulk drag effects. The stretching is assumed to be a linear function of the coordinate along the direction of stretching. Using similarity transformations, the governing partial differential equations are converted to nonlinear ordinary differential equations. The energy equation is further rendered into confluent hypergeometric form and then solved analytically for the prescribed surface temperature (PST) case and also for the Prescribed Boundary Surface Heat Flux (PHF) case, using Kummer’s function, subject to physically realistic boundary conditions. The momentum and energy equations are also solved using the semi-numerical homotopy analysis method (HAM), which contains the auxiliary parameter , permitting relatively easy adjustment and control of the convergence region of the series solution. This method provides an efficient approximate analytical solution with high accuracy, minimal calculation, and avoidance of physically unrealistic assumptions. HAM solutions are benchmarked with robust numerical shooting quadrature and found to correlate well. The influence of magnetic field on velocity and temperature profiles is studied via the Chandrasekhar number (Q). Furthermore detailed simulations are conducted for the influence of viscoelastic parameter (k1), Eckert number (E), radiation-conduction parameter (NR), Grashof number (Gr) and heat source/sink parameter (α) on the flow variables. The study finds applications in electro-conductive polymeric materials processing for aerospace fabric covers and other a pplications with demanding safety and protection requirements in smart materials synthesis.

Magnetohydrodynamics, Viscoelasticity; Homotopy, Radiation; Semi-numerical, Electro-conductive polymer materials processing; Heat Transfer; Chandrasekhar number