A mathematical model for entropy generation in a Powell-Eyring nanofluid flow in a porous channel.

The continuous generation of entropy leads to exergy destruction which reduces the performance of a physical system. Hence, entropy minimization becomes necessary. New applications of nanofluids due to their enhanced thermo-physical properties has spurred new studies into the heat transfer and entropy generation rate in nanofluids in the last decade. In this study, we investigate the heat transfer performance and entropy generation rate in a mixed convective flow of a hydromagnetic Aluminum oxide-water Powell-Eyring nanofluid flow through a vertical channel. The nanofluid dynamic viscosity adopted is based on experimental data. The combined effects of the magnetic field, nonlinear thermal radiation, viscous dissipation, suction/injection and convective cooling on the heat transfer and entropy generation were considered. The dimensionless equations describing the flow and energy balance were solved using an efficient iterative spectral local linearization method. The computational analysis of the rate of entropy generation in the channel for various flow parameters is presented. The result shows that increasing the nanoparticle volume fraction and thermal radiation parameter enhanced the temperature profiles, entropy generation and the Bejan number. The results from this study may help engineers in the optimization of thermal systems.

Modelling the spatiotemporal dynamics of chemovirotherapy cancer treatment.

Chemovirotherapy is a combination therapy with chemotherapy and oncolytic viruses. It is gaining more interest and attracting more attention in the clinical setting due to its effective therapy and potential synergistic interactions against cancer. In this paper, we develop and analyse a mathematical model in the form of parabolic non-linear partial differential equations to investigate the spatiotemporal dynamics of tumour cells under chemovirotherapy treatment. The proposed model consists of uninfected and infected tumour cells, a free virus, and a chemotherapeutic drug. The analysis of the model is carried out for both the temporal and spatiotemporal cases. Travelling wave solutions to the spatiotemporal model are used to determine the minimum wave speed of tumour invasion. A sensitivity analysis is performed on the model parameters to establish the key parameters that promote cancer remission during chemovirotherapy treatment. Model analysis of the temporal model suggests that virus burst size and virus infection rate determine the success of the virotherapy treatment, whereas travelling wave solutions to the spatiotemporal model show that tumour diffusivity and growth rate are critical during chemovirotherapy. Simulation results reveal that chemovirotherapy is more effective and a good alternative to either chemotherapy or virotherapy, which is in agreement with the recent experimental studies.

Spatio-Temporal Variation and Futuristic Emission Scenario of Ambient Nitrogen Dioxide over an Urban Area of Eastern India Using GIS and Coupled AERMOD-WRF Model.

The present study focuses on the spatio-temporal variation of nitrogen dioxide (NO2) during June 2013 to May 2015 and its futuristic emission scenario over an urban area (Durgapur) of eastern India. The concentration of ambient NO2 shows seasonal as well as site specific characteristics. The site with high vehicular density (Muchipara) shows highest NO2 concentration followed by industrial site (DVC- DTPS Colony) and the residential site (B Zone), respectively. The seasonal variation of ambient NO2 over the study area is portrayed by means of Geographical Information System based Digital Elevation Model. Out of the total urban area under consideration (114.982 km2), the concentration of NO2 exceeded the National Ambient Air Quality Standard (NAAQS) permissible limit over an area of 5.000 km2, 0.786 km2 and 0.653 km2 in post monsoon, winter and pre monsoon, respectively. Wind rose diagrams, correlation and regression analyses show that meteorology plays a crucial role in dilution and dispersion of NO2 near the earth's surface. Principal component analysis identifies vehicular source as the major source of NO2 in all the seasons over the urban region. Coupled AMS/EPA Regulatory Model (AERMOD)-Weather Research and Forecasting (WRF) model is used for predicting the concentration of NO2. Comparison of the observed and simulated data shows that the model overestimates the concentration of NO2 in all the seasons (except winter). The results show that coupled AERMOD-WRF model can overcome the unavailability of hourly surface as well as upper air meteorological data required for predicting the pollutant concentration, but improvement of emission inventory along with better understanding of the sinks and sources of ambient NO2 is essential for capturing the more realistic scenario.

On a bivariate spectral relaxation method for unsteady magneto-hydrodynamic flow in porous media.

The paper presents a significant improvement to the implementation of the spectral relaxation method (SRM) for solving nonlinear partial differential equations that arise in the modelling of fluid flow problems. Previously the SRM utilized the spectral method to discretize derivatives in space and finite differences to discretize in time. In this work we seek to improve the performance of the SRM by applying the spectral method to discretize derivatives in both space and time variables. The new approach combines the relaxation scheme of the SRM, bivariate Lagrange interpolation as well as the Chebyshev spectral collocation method. The technique is tested on a system of four nonlinear partial differential equations that model unsteady three-dimensional magneto-hydrodynamic flow and mass transfer in a porous medium. Computed solutions are compared with previously published results obtained using the SRM, the spectral quasilinearization method and the Keller-box method. There is clear evidence that the new approach produces results that as good as, if not better than published results determined using the other methods. The main advantage of the new approach is that it offers better accuracy on coarser grids which significantly improves the computational speed of the method. The technique also leads to faster convergence to the required solution.

The Effects of Thermal Radiation on an Unsteady MHD Axisymmetric Stagnation-Point Flow over a Shrinking Sheet in Presence of Temperature Dependent Thermal Conductivity with Navier Slip.

In this paper, the magnetohydrodynamic (MHD) axisymmetric stagnation-point flow of an unsteady and electrically conducting incompressible viscous fluid in with temperature dependent thermal conductivity, thermal radiation and Navier slip is investigated. The flow is due to a shrinking surface that is shrunk axisymmetrically in its own plane with a linear velocity. The magnetic field is imposed normally to the sheet. The model equations that describe this fluid flow are solved by using the spectral relaxation method. Here, heat transfer processes are discussed for two different types of wall heating; (a) a prescribed surface temperature and (b) a prescribed surface heat flux. We discuss and evaluate how the various parameters affect the fluid flow, heat transfer and the temperature field with the aid of different graphical presentations and tabulated results.

The Effect of Thermophoresis on Unsteady Oldroyd-B Nanofluid Flow over Stretching Surface.

There are currently only a few theoretical studies on convective heat transfer in polymer nanocomposites. In this paper, the unsteady incompressible flow of a polymer nanocomposite represented by an Oldroyd-B nanofluid along a stretching sheet is investigated. Recent studies have assumed that the nanoparticle fraction can be actively controlled on the boundary, similar to the temperature. However, in practice, such control presents significant challenges and in this study the nanoparticle flux at the boundary surface is assumed to be zero. We have used a relatively novel numerical scheme; the spectral relaxation method to solve the momentum, heat and mass transport equations. The accuracy of the solutions has been determined by benchmarking the results against the quasilinearisation method. We have conducted a parametric study to determine the influence of the fluid parameters on the heat and mass transfer coefficients.

Analysis of virotherapy in solid tumor invasion.

Cancer treatment is an inexact science despite traditional cancer therapies. The traditional cancer treatments have high levels of toxicity and relatively low efficacy. Current research and clinical trials have indicated that virotherapy, a procedure which uses replication-competent viruses to kill cancer cells, has less toxicity and a high efficacy. However, the interaction dynamics of the tumor host, the virus, and the immune response is poorly understood due to its complexity. We present a mathematical analysis of models that study tumor-immune-virus interactions in the form of differential equations with spatial effects. A stability analysis is presented and we obtained analytical traveling wave solutions. Numerical simulations were obtained using fourth order Runge-Kutta and Crank-Nicholson methods. We show that the use of viruses as a cancer treatment can reduce the tumor cell concentration to a very low cancer dormant steady state or possibly deplete all tumor cells in body tissue. The traveling waves indicated an exponential increase and decrease in the cytotoxic-T-lymphocytes (CTLs) density and tumor load in the long term respectively.

Effect of immunotherapy on the response of TICLs to solid tumour invasion.

There is clinical evidence that some people have lived with a benign tumour for their entire life time. This is explained by cancer dormancy which is attributed to the interaction of tumour infiltrating cytotoxic lymphocytes (TICLs) with tumour cells. We present two mathematical models to study the mechanism of interaction of TICLs with tumour cells, with and without clinical intervention. Stability analysis and numerical simulations of the models reveal the existence of a stable tumour dormant state.

Dispersion characteristics of blood during nanoparticle assisted drug delivery process through a permeable microvessel.

Nanoparticle assisted drug delivery holds considerable promise as a means of next generation of medicine that allows for the intravascular delivery of drugs and contrast agents. We analyze the dispersion characteristics of blood during a nanoparticle-assisted drug delivery process through a permeable microvessel. The contribution of molecular and convective diffusion is based on Taylor's theory of shear dispersion. The aggregation of red blood cells in blood flowing through small tubes (less than 40 µm) leads to the two-phase flow with a core of rouleaux surrounded by a cell-depleted peripheral layer. The core region models as a non-Newtonian Casson fluid and the peripheral region acts as a Newtonian fluid. We investigate the influence of the nanoparticle volume fraction, the permeability of the blood vessel, pressure distribution, yield stress and the radius of the nanoparticle on the effective dispersion. We show that the effective diffusion of the nanoparticles reduces with an increase in nanoparticle volume fraction. The permeability of the blood vessels increases the effective dispersion at the inlet. The present study contributes to the fundamental understanding on how the particulate nature of blood influences nanoparticle delivery, and is of particular significance in nanomedicine design for targeted drug delivery applications.