Non-dimensional Quantities Research Articles

Triple stratification impacts on an inclined hydromagnetic bioconvective flow of micropolar nanofluid with exponential space-based heat generation

The present work aims to analyze the effects of magnetohydrodynamics, heat and mass transfer, and gyrotactic microorganism behavior on the bioconvective micropolar nanofluid flow subject to triple stratifications and Cattaneo–Christov double diffusion over a stretched surface. The dimensional system of differential equations has been simplified to dimensionless with suitable non-dimensional quantities and suitable similarity transformations. An efficient numerical technique bvp4c through MATLAB has been implemented to devise the solution of the non-dimensionalized system of governing equations. The significant outcomes of the current analysis are that the amplification of magnetic parameter intensifies the flow velocity and shows the reverse effect for the fluid temperature. The enhancement of micropolar parameter upgrades microrotation, while it exhibits opposite effect for the fluid temperature and nanoparticle concentration. Microorganism concentration peters out with a rise in Peclet number. Gyrotactic microorganism thermal stratification augmentation leads to the diminution of velocity and thermal boundary layer thickness. When gyrotactic microorganism concentration difference parameter rises from 0.1 to 0.8, skin friction whittles down by 12.5%, and wall motile microorganism number ameliorates by 50%.

Forecasting seasonal sargassum events across the tropical Atlantic: Overview and challenges

Proliferation of sargassum across the tropical Atlantic since 2011 has motivated a range of forecasting methods. Statistical methods based on basin-scale satellite data are used to address seasonal timescales. Other methods involve explicit Lagrangian calculations of trajectories for particles that are representative of drifting sargassum over days-months. This computed sargassum drift is attributed to the combined action of surface currents, winds and waves, individually or in various combinations. Such calculations are undertaken with both observed surface drift and simulated currents, each involving strengths and weaknesses. Observed drift implicitly includes the action on sargassum of winds and waves, assumed equivalent between drifters and sargassum mats. Simulated currents provide large gridded datasets that facilitate computation of ensembles, enabling some quantification of the uncertainty inherent in an eddy-rich ocean, further subject to interannual variability. A more limited number of forecasts account for in situ growth or loss of sargassum biomass, subject to considerable uncertainty. Forecasts provide either non-dimensional indices or quantities of sargassum, accumulated in specified areas or counted across specified transects over a given time interval. Proliferation of different forecast methodologies may reduce uncertainty, if predictions for given seasons are consistent in broad terms, but there is scope to coordinate different approaches with common geographical foci and predicted variables, to facilitate direct inter-comparisons. In an example of forecasting westward sargassum flux into the Caribbean during the first half of 2022, challenges and opportunities are highlighted. In conclusion, prospects for closer alignment of complementary forecasting methods, and implications for sargassum management, are identified.

Analysis of energy and momentum transport for Casson nanofluid in a microchannel with radiation and chemical reaction effects

ABSTRACT The study of Casson nanofluid plays a prominent role in biomedicine, magnetic resonance imaging and thermal enhancement of energy system due to the eminence of its thermophysical properties. By considering various practical applications, in this article the steady, laminar, electromagnetohydrodynamic flow of Casson nanofluid across parallel plates with the effect of Hall current, chemical reaction, modified Darcy's law and Joule heating have been taken into consideration. Gold and Silver nanoparticles of sphere shape are considered in blood taken as conventional base fluid with volume fraction of 1%. However, for comparison, other shapes of nanoparticles are also considered. The system of dimensional governing equations of nanofluid are converted to dimensionless set of equations using pertinent non-dimensional quantities. The analytical solutions are presented for the system of equations. The obtained exact solution for nanofluid velocity, nanofluid temperature, nanofluid concentration, Sherwood number, Nusselt number and shear stress are displayed graphically to see the effectiveness of sundry parameters. It is found that the velocity and temperature decreases, while concentration of Ag-blood and Au-blood rises with increased values of nanoparticle volume fraction. Performance of nanoparticle of sphere shape is lowest and lamina shape is highest in terms of heat and mass transfer. The present study may be useful in further studies of tumour therapy, biomedical imaging and cancer therapy.

Unsteady thermally radiative Prandtl fluid flow past a magnetized inclined porous stretching device with double-diffusion, viscous dissipation, and Joule heating

The extensive applications and complex nature of non-Newtonian fluids inspire researchers to explore them so it serves more precisely humankind. In this scenario, the Prandtl fluid over the inclined porous surface has been explored and formulated the mathematical model considering the magnetic, thermal radiation, and double diffusion effect. Also, the viscous dissipation and joule heating effect are taken into account to explore more features of the flow situation. The mathematical model of flow is renovated with the effective implementation of similarity invariants. The numerical investigation is carried out using the Runge–Kutta method and the results obtained are interpreted graphically. The effects of physical parameters such as Dufour and Soret number, radiation parameter, magnetic parameter, etc., on non-dimensional quantities, are graphically illustrated with MATLAB. The thermal boundary layer gets elevation for rising values of Eckert number, magnetic parameter, unsteadiness parameter, Dufour number, and thermal radiation.

Nonlinear bending analysis of FG-CNTRC plate resting on elastic foundation by natural element method

A nonlinear numerical analysis is addressed for a functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plate on elastic foundation. The large deflection bending problem is formulated according to the von Kármán nonlinear theory and the (1,1,0)* hierarchical model. And, it is numerically solved by 2-D (two-dimensional) natural element method (NEM) which is characterized by a high accuracy even for coarse grid. The derived nonlinear matrix equations are iteratively calculated by combining the load increment scheme and the Newton-Raphson iteration method. The present method was verified through the benchmark test, where the present method shows excellent agreement with the reference solutions. The nonlinear behavior of FG-CNTRC plate on elastic foundation is evaluated in terms of the non-dimensional deflection and bending moment. These non-dimensional quantities are examined with respect to the foundation stiffness, the volume fraction and gradient pattern of CNT, the aspect and width-thickness ratios of plate and the boundary condition. From the parametric experiments, it is found that both non-dimensional quantities are significantly influenced by such parameters.

Impact of Variable Fluid Properties and Double Diffusive Cattaneo–Christov Model on Dissipative Non-Newtonian Fluid Flow Due to a Stretching Sheet

The present work focuses on the attributes of flow, heat, and mass transfer together with double diffusive Cattaneo–Christov mechanism with regards to their applications. The aim of this study is to investigate the non-Newtonian Powell–Eyring fluid flow, taking into account the twofold impact of the heat generation mechanism and the viscous dissipation due to an extensible sheet. The chemical reaction between the fluid particles and the fluid variable properties is assumed in this study. The motive behind this study is the continuous and great interest in the utilization of non-Newtonian liquids in organic and technical disciplines. This model is administered and governed by the momentum equation, energy equation, and concentration, all of which are in the form of partial differential equations. With the help of the shooting technique, the numerical solution is obtained. Graphs show the characteristics of flow, heat, and mass transfer mechanisms for various governing parameters. Additionally, significant physical non-dimensional quantities have been presented in a tabular form. The outcomes detect that increasing the Deborah number, which is connected with the mass transfer field and the chemical reaction parameter, decreases the concentration distribution.

Flame attachment and downstream heating effect of inclined line fires

Experiments were conducted to quantify downstream heating from inclined fires generated by a 25 cm wide, 5 cm deep gaseous line burner. A variety of orientation angles (θ) and fire heat-release rates (HRR) were employed simulating, at reduced scale, the dynamics of two-dimensional (2-D) inclined flame spread as found in wildland or building fires. The total heat flux q˙f″(x) to a nearly-adiabatic surface ahead of the burner was measured by a water-cooled total heat flux gage at different downstream locations (x). It was found that, with an increase in fire HRR or θ, q˙f″(x) increases. The same is true for both the flame projection length on the inclined surface (Lf,p) and the flame attachment length (La). The location of flame attachment divides a flame into an attachment region (0≤x≤La) and a liftoff region (La<x≤Lf,p). A scaling analysis was performed to correlate the modified non-dimensional heat flux q˙f*(x) and the normalized downstream distance x/La in these two regions as a piecewise power-law function. Lf,p is scaled by a non-dimensional HRR, Q˙θ*=Q˙/(ρ∞cpT∞(gcosθ)1/2D3/2L), together with the angle between a flame and an inclined surface (α). La is well represented by two derived non-dimensional quantities, L/Lf,0 and Lf,p/Lf,0 (Lf,0 is free flame height), based on the analysis of the balance between the buoyancy force of a flame (upward) and the inertial force due to air entrainment (horizontal). The quantitative comparison with previous flame spread tests over inclined PMMA samples demonstrates the effectiveness of the proposed correlations in predicting downstream heating of 2-D flame spread over inclined terrains.

Temperature-dependent variable viscosity and thermal conductivity effects on non-Newtonian fluids flow in a porous medium

Purpose The purpose of this paper is to consider the simultaneous flow of Casson Williamson non Newtonian fluids in a vertical porous medium under the influence of variable thermos-physical parameters. Design/methodology/approach The model equations are a set of partial differential equations (PDEs). These PDEs were transformed into a non-dimensionless form using suitable non-dimensional quantities. The transformed equations were solved numerically using an iterative method called spectral relaxation techniques. The spectral relaxation technique is an iterative method that uses the Gauss-Seidel approach in discretizing and linearizing the set of equations. Findings It was found out in the study that a considerable number of variable viscosity parameter leads to decrease in the velocity and temperature profiles. Increase in the variable thermal conductivity parameter degenerates the velocity as well as temperature profiles. Hence, the variable thermo-physical parameters greatly influence the non-Newtonian fluids flow. Originality/value This study considered the simultaneous flow of Casson-Williamson non-Newtonian fluids by considering the fluid thermal properties to vary within the fluid layers. To the best of the author’s knowledge, such study has not been considered in literature.

On the Theoretical Prediction of Microalgae Growth for Parallel Flow

The established microalgae growth models are semi-empirical or considerable fitting coefficients exist currently. Therefore, the ability of the model prediction is reduced by the numerous fitting coefficients. Furthermore, the predicted results of the established models are dependent on the size of the photobioreactor (PBR), light intensity, flow and concentration field. The growth mechanism of microalgae has not clearly understood in PBR cultivation. It is difficult to predict the microalgae growth by theoretical methods, owing to the aforementioned factors. We developed an exploratory bridging microalgae growth model to predict the microalgae growth rate in PBRs by using the nondimensional method which is effectively in fluid dynamics and heat transfer. The analytical solution of the growth rate was obtained for the parallel flow. The nondimensional growth rate expressed as function of Reynolds number and Schmidt number, which can be used for arbitrary parallel flow due to the solution was expressed as nondimensional quantities. The theoretically predicted growth rate is compared with the experimentally measured microalgae growth rate on the order of magnitude. The nondimensional method successfully applied to the microalgae growth problem for the first time. The general nondimensional solution can unify the numerous experimental data for different laboratory conditions, and give a direction for the disorder of the microalgae growth problem. The nondimensional solution may be useful to explain the growth mechanism of microalgae and design large-scale PBRs for microalgae biofuel production. The significance of the work is to give a theoretical foundation and methodology of biological theory of microalgae growth.

Heat Transfer of Casson Fluid over a Vertical Plate with Arbitrary Shear Stress and Exponential Heating

The basic objective of this work is to study the heat transfer of Casson fluid of non-Newtonian nature. The fluid is considered over a vertical plate such that the plate exhibits arbitrary wall shear stress at the boundary. Heat transfers due to exponential plate heating and natural convection are due to buoyancy force. Magnetohydrodynamic (MHD) analysis in the occurrence of a uniform magnetic field is also considered. The medium over the plate is porous and hence Darcy’s law is applied. The governing equations are established for the velocity and temperature fields by the usual Boussinesq approximation. The problem is first written in dimensionless form using some useful non-dimensional quantities and then solved. The exact analysis is performed and hence solutions via integral transform are established. The analysis of various pertinent parameters on temperature distribution and velocity field are reported graphically. It is found that pours medium permeability parameter retards the fluid motion whereas, velocity decreases with increasing magnetic parameter. Velocity and temperature decrease with increasing Prandtl number whereas the Grashof number enhances the fluid motion. Further, it is concluded from this study that the results obtained here are more general and in a limiting sense several other solutions can be recovered. The Newtonian fluid results can be easily established by taking the Casson parameter infinitely large i.e., when .

EFFECT OF HEAT AND MASS TRANSFER AND THERMAL RADIATION ON A STEADY MHD CONVECTIVE FLOW WITH VISCOUS DISSIPATION AND SUCTION/INJECTION

Our motive is to examine the impact of thermal radiation and suction or injection with viscous dissipation on an MHD boundary layer flow past a vertical porous stretched sheet immersed in a porous medium. The set of the flow equations is converted into a set of non-linear ordinary differential equations by using similarity transformation. We use Runge Kutta method and shooting technique in MATLAB Package to solve the set of equations. The impact of non-dimensional physical parameters on flow profiles is analysed and depicted in graphs. We observe the influence of non-dimensional physical quantities on the Nusselt number, the Sherwood number, and skin friction and presented in tables. A comparison of the obtained numerical results with existing results in a limiting sense is also presented. We enhance radiation to observe the deceleration of fluid velocity and temperature profile for both suction and injection. While enhancing porosity parameter accelerates velocity whereas decelerates temperature profile. As the heat source parameter increases, the temperature of the fluid decreases for both suction and injection, it has been found. With the increasing values of the radiation parameter, the skin friction and heat transfer rate decreases. Increasing magnetic parameter decelerates the skin friction, Nusselt number, and Sherwood number.

RETRACTED: Theoretical study of MHD electro-osmotically flow of third-grade fluid in micro channel

• MHD electro-osmotic flow of non-Newtonian fluid. • Perturbation and Pseudo-Spectral collocation methods. • Velocity of the fluid retards subject to strong magnetic fields. • Velocity and temperature diminishing via electro-kinetic parameter Γ 2 . The electro-osmatic flow of non-newtonian fluid in a micro-channel is investigated in this article. The governing equations are derived with the help of a stress tensor then later transformed into dimensionless form with non-dimensional quantities. The perturbation method is used to obtain the approximate analytical solution of the given problem. The viscosity of the fluid is taken as a variable in terms of temperature. The validity of the perturbation solution is provided. The Pseudo-spectral collocation method is used to calculate the error in the perturbation solution of velocity and temperature. The magnitude of error in velocity and temperature is 10 −4 and 10 −2 , respectively. The impact of emerging parameters on velocity and heat profiles is also presented. The computational results reveal that the velocity profile diminishing via non-Newtonian parameter Γ 1 , electro-kinetic parameter Γ 2 , magnetic field parameter M and viscosity parameter D while an opposite behavior is noted in the velocity versus pressure gradient parameter Γ 3 , viscosity parameter E and wall's temperature θ w , respectively. Further, the temperature profile increases against the enhancement of Brinkman number, Joule heating parameter, pressure gradient parameter, wall's temperature, viscosity parameter D while reverse behavior is observed via electro-kinetic and magnetic field parameters. This study will help to understand the basic idea of MHD electro osmotic flow of non-Newtonian fluid bounded within a microchannel under the influence of variable viscosity. Further, this research can be useful to design the different types of biomedical lab-on-a-chip and thermal microfluidic devices. The developed devices can be helpful in DNA analysis and biomedical diagnosis etc.

Heat Transportation of Ferrofluid in a Micro Annulus

This article investigated the effect of magnetic field on heat-absorbent ferrofluid in a vertical loop consisting of a pair of concentric cylinders with surface sliding and temperature jumping. For this puprose, the control equation was converted into the dimensional form using non-dimensional quantities and parameters. The system of equations was solved analytically using an integration technique. Subsequently, the solution was obtained in the form of first and second type of Bessel functions. The results are presented graphically and show that velocity increases with the increase in the nanoparticle size. Resultantly, the rate of heat transfer of the fluid in the inner cylinder reduces.

Mathematical modeling and simulation of MHD electro-osmotic flow of Jeffrey fluid in convergent geometry

The multiphase flow of Jeffery fluid under the impact of Magnetohydrodynamic is examined in this analysis. The nanoparticles of Hafnium metal are mixed up in the base fluid along with the impact of the electroosmotic phenomenon having a great significance in the present decade. Two different models, namely particulate and fluid phases, are considered for a convergent geometry with numerous usages in practical life, especially in modern technologies like microfluidic devices, chemical analysis, soil analysis, and other industries. The set of partial differential equations are converted into ordinary differential equations by using the non-dimensional quantities and obtained the exact solution of the resulting boundary value problem. The impact of physical parameters involving in the study is highlighted through graphs. To observe the flow pattern, the streamlines are also constructed. The Hartman number and Jeffrey fluid parameter slow down the velocity of fluid and particle phases. The Helmholtz-Smoluchowski parameter reduces the streamlines while the flow pattern remains unchanged via U HS . Moreover, the results are also compared with the previously published literature and noted excellent agreement with each other. The developed mathematical will be helpful in the diverse geometries used widely in medical and engineering walks to incorporate the fluid in complicated places like species separation, biomedical lab-on-a-chip devices, DNA sequences and stimulated drugs in diverse veins colliers, etc.

Theoretical model for diffusion-reaction based drug delivery from a multilayer spherical capsule

Controlled drug delivery from a multilayer spherical capsule is used for several therapeutic applications. Developing a theoretical understanding of mass transfer in the multilayer capsule is critical for understanding and optimizing targeted drug delivery. This paper presents an analytical solution for the mass transport problem in a general multilayer sphere involving diffusion as well as drug immobilization in various layers due to binding reactions. An eigenvalue-based solution for this multilayer diffusion-reaction problem is derived in terms of various non-dimensional quantities including Sherwood and Damköhler numbers. It is shown that unlike diffusion-reaction problems in heat transfer, the present problem does not admit imaginary eigenvalues. The effect of binding reactions represented by the Damköhler numbers and outer surface boundary condition represented by the Sherwood number on drug delivery profile is analyzed. It is shown that a low Sherwood number not only increases drug delivery time, but also reduces the total mass of drug delivered. The mass of drug delivered is also shown to reduce with increasing Damköhler number. The impact of shell thickness is analyzed. The effect of a thin outer coating is accounted for by lumping the mass transfer resistance in series with convective boundary resistance, and a non-dimensional number involving the thickness and diffusion coefficient of the coating is shown to govern its impact on drug delivery characteristics. The analytical model presented here improves the understanding of mass transfer in a multilayer spherical capsule in presence of binding reactions, and may help design appropriate experiments for down-selecting candidate materials and geometries for drug delivery applications of interest.

Heat transfer and fluid flow analysis of non‐Newtonian fluid in a microchannel with electromagnetohydrodynamics and thermal radiation

AbstractThe study of electromagnetohydrodynamics (EMHD) of non‐Newtonian fluid plays a significant role for optical design, thermal management of electronic components, and various operations of microfluidic devices. The use of parallel geometry is seen in the circulatory system, extrusion process, and respiratory system. By considering various practical applications, in the current study, the Poiseuille flow of an incompressible Casson liquid between the plates is investigated. The effects of MHD, Joule heating, thermal radiation, modified Darcy's law, and chemical reaction have been taken into account. The dimensional governing equations have been converted into dimensionless equations with pertinent nondimensional quantities. The resulting system of nondimensional system of equations has been analytically solved with nondimensional slip boundary conditions. The graphical results have been displayed with various fluid flow parameters. From the current study, it is concluded that the influence of Darcy number and Casson fluid parameter enhances the velocity profile, but the concentration declines with the enhancement of Casson fluid parameter. The radiation parameter and Prandtl number suppress the temperature profile.

Heat transfer analysis of longitudinal fins of trapezoidal and dovetail profile on an inclined surface

The trapezoidal and dovetail profiled longitudinal fin structures exposed to a convective-radiative environment and mounted on an inclined surface have been considered for the analysis. The fin structures have been assumed to be porous and fully wet in nature. The Darcy model has been implemented to simulate the fluid-solid interactions. Further, the convective and radiative heat transfer coefficients have been taken to be temperature-dependent. The resulting equation has been reduced by introducing the non-dimensional quantities and then solved by employing the Runge-Kutta Fehlberg 4th–5th order method along with the shooting technique. The effect of tip tapering, angle of inclination, fully wet nature, porosity, internal heat generation, and other pertinent parameters on the fin thermal profile and fin heat transfer rate has been presented graphically and discussed. It has been inferred that the dovetail fin profile achieves the highest heat transfer rate followed by rectangular and trapezoidal fin profiles provided the internal heat generation is minimal. The present work is significant for fin design purposes and also acts as a verification tool for future research.

The magnetic field about a three-dimensional block neodymium magnet

Neodymium magnets were independently discovered in 1984 by General Motors and Sumitomo. Today, they are the strongest type of permanent magnets commercially available. They are the most widely used industrial magnets with many applications, including in hard disk drives, cordless tools and magnetic fasteners. We use a vector potential approach, rather than the more usual magnetic potential approach, to derive the three-dimensional (3D) magnetic field for a neodymium magnet, assuming an idealized block geometry and uniform magnetization. For each field or observation point, the 3D solution involves 24 nondimensional quantities, arising from the eight vertex positions of the magnet and the three components of the magnetic field. The only unknown in the model is the value of magnetization, with all other model quantities defined in terms of field position and magnet location. The longitudinal magnetic field component in the direction of magnetization is bounded everywhere, but discontinuous across the magnet faces parallel to the magnetization direction. The transverse magnetic fields are logarithmically unbounded on approaching a vertex of the magnet. doi:10.1017/S1446181120000097

Semi-analytical framework for stress–conductivity correlations in periodic granular assemblies under compaction

The contact network, defined by a fabric tensor, influences phenomena such as force or heat transfer in a granular assembly. The correlation between fabric, stress, and conductivity has, however, been least explored. Furthermore, a link between these quantities may help to build a benchmark method to assist experiments substantially. The present work bridges the gap between the macroscopic quantities, such as stress and conductivity tensor, using its microscopic connection and the fabric tensor. The study presents a few interesting functional forms and non-dimensional macroscopic quantities that couple conductivity, stress, and fabric. The main feature of these functional forms is that they are independent of friction. These functional forms will provide a good estimate of fabric and conductivity which can be used real-time during the experimental investigations as well.

Vibrations of Inhomogeneous Viscothermoelastic Nonlocal Hollow Sphere under the effect of Three-Phase-Lag Model

Herein, the free vibrations of inhomogeneous nonlocal viscothermoelastic sphere with three-phase-lag model of generalized thermoelasticity have been addressed. The governing equations and constitutive relations with three-phase-lag model have been solved by using non-dimensional quantities. The simple power law has been presumed to take the material in radial direction. The series solution has been established to derive the solution analytically. The relations of frequency equations for the continuation of viable modes are developed in dense form. The analytical results have been authenticated by the reduction of nonlocal and three–phase–lag parameters. To investigate the quality of vibrations, frequency equations are determined by applying the numerical iteration method. MATLAB software tools have been used for numerical computations and simulations to present the results graphically subject to natural frequencies, frequency shift, and thermoelastic damping. The numerical results clearly show that the variation of vibrations is slightly larger in case of nonlocal elastic sphere in contrast to elastic sphere.