New methods to provide exact solutions for some unidirectional motions of rate type fluids

Abstract

Based on three immediate consequences of the governing equations corresponding to some unidirectional motions of rate type fluids, new motion problems are tackled for exact solutions. For generality purposes, exact solutions are developed for shear stress boundary value problems of generalized Burgers fluids. Such solutions, for which the shear stress instead of its differential expressions is given on the boundary, are lack in the literature for such fluids. Consequently, the first exact solutions for motions of rate type fluids induced by an infinite plate or a circular cylinder that applies a constant shear f or an oscillating shear fsin(wt) to the fluid are here presented. In addition, all steady-state solutions can easily be reduced to known solutions for second grade and Newtonian fluids.

Numerical study of unsteady axisymmetric flow and heat transfer in Carreau fluid past a stretched surface

“…The main focus of present investigation is the study of the unsteady axisymmetric boundary-layer flow and heat transfer characteristics of Carreau fluid over a permeable time dependent radially stretching sheet. The system of non-linear ODE (10) and (11) subject to the boundary conditions (12) and (13) are solved numerically by an effective numerical technique namely bvp4c function in MATLAB. The comprehensive numerical results are computed for different values of the physical pertinent parameters of flow and heat transfer namely, unsteadiness parameter, A, power law index, n, Prandtl number, local Weissenberg number (We), mass transfer parameter, S, and Eckert number.…”

“…The bvp4c function is an effective solver of the boundary value problems which employs a collection method for determining the solution of boundary value problems of the form y′ = f(x, y, p), a ≤ x ≤ b with boundary conditions g[y(a), y(b), p] = 0 where p denotes a vector of unknown parameters. The transformed non-linear ODE (12) and (13) along with boundary conditions (14) and 15are solved numerically by employing the MATLAB boundary value problems solver bvp4c function. For this, we convert the given ODE as a system of first order ODE.…”

“…For this, we convert the given ODE as a system of first order ODE. As a result, the non-linear ODE (12) and 13 A comprehensive discussion of this method is explained in [22].…”

“…Pantokratoras [11] conducted the comparative study of Blasius and Sakiadis flows of Carreau fluid. Fetecau et al [12] presented the exact solutions for unidirectional flow of rate type fluids. Khan et al [13] demonstrated a numerical study to examine the melting heat transfer in Carreau nanofluid flow over a wedge in the presence of heat generation/absorption.…”

Rotational motion of fractional Maxwell fluids in a circular duct due to a time-dependent couple

“…As we have to solve a motion problem with shear stress on the boundary, we follow [41] and eradicate the velocity field between Eqs. (3) and (4).…”