Flow of a micropolar fluid bounded by a stretching sheet

We consider boundary layer flow of a micropolar fluid driven by a porous stretching sheet. A similarity solution is defined, and numerical solutions using Runge-Kutta and quasilinearisation schemes are obtained. A perturbation analysis is also used to derive analytic solutions to first order in the perturbing parameter. The resulting closed form solutions involve relatively complex expressions, and the analysis is made more tractable by a combination of offline and online work using a computational algebra system (CAS). For this combined numerical and analytic approach, the perturbation analysis yields a number of benefits with regard to the numerical work. The existence of a closed form solution helps to discriminate between acceptable and spurious numerical solutions. Also, the expressions obtained from the perturbation work can provide an accurate description of the solution for ranges of parameters where the numerical approaches considered here prove computationally more difficult.

Effect of surface conditions on flow of a micropolar fluid driven by a porous stretching sheet

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Note on similarity solutions for viscous flow over an impermeable and non-linearly (quadratic) stretching sheet

Similarity solutions for flow over an impermeable, non-linearly (quadratic) stretching sheet were studied recently by Raptis and Perdikis (Int. J. Non-linear Mech. 41 (2006) 527–529) using a stream function of the form ψ=αxf(η)+βx2g(η). A fundamental error in their problem formulation is pointed out. On correction, it is shown that similarity solutions do not exist for this choice of ψ

Analytical Solution of a Walters’ Liquid B Flow Over a Linear Stretching Sheet in a Porous Medium

This chapter represents the analytical solution of two-dimensional linear stretching sheet problem involving a non-Newtonian liquid and suction by (a) invoking the boundary layer approximation and (b) using this result to solve the stretching sheet problem without using boundary layer approximation. The basic boundary layer equations for momentum, which are non-linear partial differential equations, are converted into non-linear ordinary differential equations by means of similarity transformation. The results reveal a new analytical procedure for solving the boundary layer equations arising in a linear stretching sheet problem involving a non-Newtonian liquid (Walters’ liquid B). The present study throws light on the analytical solution of a class of boundary layer equations arising in the stretching sheet problem.

Flow modeling in a novel non-perfusion conical bioreactor

We have developed a bioreactor vessel design which has the advantages of simplicity and ease of assembly and disassembly, and with the appropriately determined flow rate, even allows for a scaffold to be suspended freely regardless of its weight. This article reports our experimental and numerical investigations to evaluate the performance of a newly developed non-perfusion conical bioreactor by visualizing the flow through scaffolds with 45° and 90° fiber lay down patterns. The experiments were conducted at the Reynolds numbers (Re) 121, 170, and 218 based on the local velocity and width of scaffolds. The flow fields were captured using short-time exposures of 60 µm particles suspended in the bioreactor and illuminated using a thin laser sheet. The effects of scaffold fiber lay down pattern and Reynolds number were obtained and correspondingly compared to results obtained from a computational fluid dynamics (CFD) software package. The objectives of this article are twofold: to investigate the hypothesis that there may be an insufficient exchange of medium within the interior of the scaffold when using our non-perfusion bioreactor, and second, to compare the flows within and around scaffolds of 45° and 90° fiber lay down patterns. Scaffold porosity was also found to influence flow patterns. It was therefore shown that fluidic transport could be achieved within scaffolds with our bioreactor design, being a non-perfusion vessel. Fluid velocities were generally same of the same or one order lower in magnitude as compared to the inlet flow velocity. Additionally, the 90° fiber lay down pattern scaffold was found to allow for slightly higher fluid velocities within, as compared to the 45° fiber lay down pattern scaffold. This was due to the architecture and pore arrangement of the 90° fiber lay down pattern scaffold, which allows for fluid to flow directly through (channel-like flow).

Engineering cellulose nanofibre suspensions to control filtration resistance and sheet permeability

This study examines and quantifies the effect of adding polyelectrolytes to cellulose nanofibre suspensions on the gel point of cellulose nanofibre suspensions, which is the lowest solids concentration at which the suspension forms a continuous network. The lower the gel point, the faster the drainage time to produce a sheet and the higher the porosity of the final sheet formed. Two new techniques were designed to measure the dynamic compressibility and the drainability of nanocellulose–polyelectrolyte suspensions. We developed a master curve which showed that the independent variable controlling the behaviour of nanocellulose suspensions and its composite is the structure of the flocculated suspension which is best quantified as the gel point. This was independent of the type of polyelectrolyte used. At an addition level of 2 mg/g of nanofibre, a reduction in gel point over 50 % was achieved using either a high molecular weight (13 MDa) linear cationic polyacrylamide (CPAM, 40 % charge), a dendrimer polyethylenimine of high molecular weight of 750,000 Da (HPEI) or even a low molecular weight of 2000 Da (LPEI). There was no significant difference in the minimum gel point achieved, despite the difference in polyelectrolyte morphology and molecular weight. In this paper, we show that the gel point controls the flow through the fibre suspension, even when comparing fibre suspensions with solids content above the gel point. A lower gel point makes it easier for water to drain through the fibre network,reducing the pressure required to achieve a given dewatering rate and reducing the filtering time required to form a wet laid sheet. We further show that the lower gel point partially controls the structure of the wet laid sheet after it is dried. Halving the gel point increased the air permeability of the dry sheet by 37, 46 and 25 %, when using CPAM, HPEI and LPEI, respectively. The resistance to liquid flow was reduced by 74 and 90 %, when using CPAM and LPEI. Analysing the paper formed shows that sheet forming process and final sheet properties can be engineered and controlled by adding polyelectrolytes to the nanofibre suspension.

Integrated lean six sigma approach for patient flow improvement in hospital emergency department

This research aims to develop an Integrated Lean Six Sigma approach to investigate and resolve the patient flow problems in hospital emergency departments. It was proposed that the voice of the customer and the voice of the process should be considered simultaneously to investigate the current process of patient flow. Statistical analysis, visual process mapping with A3 problem solving sheet, and cause and effect diagrams have been used to identify the major patient flow issues. This research found that engaged frontline workers, long-term leadership obligation, an understanding of patients' requirements and the implementation of a systematic integration of lean strategies could continuously improve patient flow, health care service and growth in the emergency departments.

Micropolar flow in a porous channel with high mass transfer

Two dimensional flow of a micropolar fluid in a porous channel is investigated. The flow is driven by suction or injection at the channel walls, and the micropolar model due to Eringen is used to describe the working fluid. An extension of Berman's similarity transform is used to reduce the governing equations to a set of non-linear coupled ordinary differential equations. The latter are solved for large mass transfer via a perturbation analysis where the inverse of the cross-flow Reynolds number is used as the perturbing parameter. Complementary numerical solutions for strong injection are also obtained using a quasilinearisation scheme, and good agreement is observed between the solutions obtained from the perturbation analysis and the computations.