Semi-infinite Vertical Cylinder Research Articles

Entropy optimization in mixed convective boundary layer flow of CNTs Casson nanoliquid through a vertical cylinder moving with nonlinear velocity

This article inspects entropy generation and mixed convection boundary layer flow of carbon nanotubes (CNTs) Casson nanoliquid via semi-infinite vertical cylinder which moves with nonlinear velocity in Darcy-Forchheimer porous medium. Appropriate similarity variables have been employed to convert the original partial differential equations into ordinary differential equations that have been solved using overlapping grid spectral quasilinearisation method (SQLM). Comparison of accuracy, convergence and stability between the two methods is made. Rate of entropy generated, flow fields and engineering quantities are discussed for different embedding parameters. It is revealed that single-wall CNTs are more efficacious to improve heat transport features than multi-wall CNTs. The fluid flow and thermal dispersion processes improve with consideration of curved surface, CNTs, non-Newtonian fluid and injection of the fluid. The curvature surface and suction of the fluid contribute towards growth of skin friction factor and rate of thermal transference. Entropy generated expands by accounting for viscous nature of the fluid, strong nonlinearity, suction, non-Newtonian fluid, convective boundary condition and CNTs. The study finds applications in various processes, which are massively impacted by heat transport enhancement and high porosity. Boundary layer flow and heat transfer analysis through cylinders are relevant to various metallurgical and engineering solicitations.

Hybrid Nanofluid Flow and Heat Transfer Past a Vertical Cylinder in the Presence of MHD and Heat Generation

The basic objective of this work is to investigate the effects of Lorentz force and internal heat generation on the unsteady flow of a hybrid nanofluid and the heat transfer caused by a moving semi-infinite vertical cylinder. The governing partial differential equations are solved numerically using a robust implicit finite difference approach with proper boundary conditions. The current work is corroborated by existing literature on the subject of special situations of the problem. The effects of the magnetic parameter, the Grashof number, and the heat generation parameter on the Nusselt number, the skin friction coefficient, as well as the velocity and temperature fields, have been investigated and graphed. The results obtained can be applied to a variety of engineering devices, such as chemical reactors, heat exchangers, and solar collectors.

Multiple-linear regression to best-estimate of gravity parameters related to simple geometrical shaped structures

Abstract A new interpretative approach is proposed to best-estimate of gravity parameters related to simple geometrical shaped structures such as a semi-infinite vertical cylinder, an infinite horizontal cylinder, and a sphere like structures. The proposed technique is based on the multiple-linear regression oriented towards estimating the model parameters, e.g., the depth from the surface to the center of the buried structure (sphere or infinite horizontal cylinder) or the depth from the surface to the top of the buried object (semi-infinite vertical cylinder), the amplitude coefficient, and the horizontal location from residual gravity anomaly profile. The validity of the proposed approach is firstly demonstrated through testing different synthetic data set corrupted and contaminated by a white Gaussian random noise level. The theoretical synthetic obtained results obviously show that the estimated parameters values, derived by the proposed technique are close to the assumed true parameters values. This approach is applied on five real field residual gravity anomalies taken from Cuba, Sweden, Iran, USA, and Germany, where the efficacy of this new approach is consequently proven. A comparable and acceptable agreement is noticed between the results derived by this proposed approach and those obtained from the real field data information.

Marquardt inverse modeling of the residual gravity anomalies due to simple geometric structures: A case study of chromite deposit

Abstract In this paper, an inversion method based on the Marquardt’s algorithm is presented to invert the gravity anomaly of the simple geometric shapes. The inversion outputs are the depth and radius parameters. We investigate three different shapes, i.e. the sphere, infinite horizontal cylinder and semi-infinite vertical cylinder for modeling. The proposed method is used for analyzing the gravity anomalies from assumed models with different initial parameters in all cases as the synthetic data are without noise and also corrupted with noise to evaluate the ability of the procedure. We also employ this approach for modeling the gravity anomaly due to a chromite deposit mass, situated east of Sabzevar, Iran. The lowest error between the theoretical anomaly and computed anomaly from inverted parameters, determine the shape of the causative mass. The inversion using different initial models for the theoretical gravity and also for real gravity data yields approximately consistent solutions. According to the interpreted parameters, the best shape that can imagine for the gravity anomaly source is the vertical cylinder with a depth to top of 7.4 m and a radius of 11.7 m.

Transient Analysis of Third-Grade Viscoelastic Nanofluid Flow External to a Heated Cylinder with Buoyancy Effects

Nanotechnology is rapidly embracing numerous areas of manufacturing and process engineering. New types of nanomaterials are being exploited to improve, for example, coating integrity, anti-corrosion characteristics and other features of fabricated components. Motivated by these developments, in the current study a mathematical model is developed for unsteady free-convective laminar flow of third-grade viscoelastic fluid (doped with nanoparticles) from a semi-infinite vertical isothermal cylinder, as a model of thermal coating flow of a pipe geometry. Non-Newtonian behavior is simulated with the thermodynamically robust third-grade Reiner–Rivlin model which accurately represents polymer fluids. Nanoscale effects are analyzed with the Buongiorno two-component nanofluid model. The governing equations comprise a set of highly coupled, nonlinear, multi-degree partial differential equations featuring viscoelastic and nanofluid parameters. An implicit Crank–Nicolson numerical scheme is implemented to solve the emerging nonlinear problem with appropriate initial and boundary conditions. Detailed graphical plots for velocity, temperature and nanoparticle volume fraction are presented for a range of different parameters (i.e., third-grade fluid parameter, Brownian motion parameter, thermophoretic parameter, buoyancy ratio parameter, Lewis number). Additionally, distributions of the heat transfer coefficient, skin friction and Sherwood number at the cylinder surface are visualized. Furthermore, streamlines, isotherms and nanoparticle volume fraction contour plots are included for variation of the third-grade parameter. Contour plots for the third-grade nanofluid flow are found to deviate significantly from those corresponding to Newtonian nanofluids. Validation of the numerical solutions with earlier studies is also included.

Transient analysis of viscoelastic fluid past a semi-infinite vertical cylinder with respect to the Deborah and Hartmann numbers

This article investigates the visualizations of heatlines in a natural convection magnetohydrodynamic flow from a vertical cylinder via heat function concept. Fluid is electrically conducting in the existence of an applied magnetic field. The constitutive equations of time-dependent, coupled and highly nonlinear Jeffrey fluid model are evaluated mathematically by utilizing well-organized unconditionally stable finite-difference Crank–Nicolson method. Simulated results are given for several values of Deborah number and Hartmann number to present interesting aspects of the solution of the flow variables, friction factor and heat transfer rate. Results specify that required time to achieve time-independent state rapidly rises with the boosting values of Hartmann number. Boundary-layer flow visualization has been made using heatlines, isotherms and streamlines to perceive the understanding of heat and fluid flow. It is noticed that heat function value reduces for augmenting Hartmann number and also for all smaller physical parameter values and these heatlines become closer to the hot wall. It is also remarked that the hydromagnetic flow-field profiles concerning the Newtonian fluid show a different pattern from that of non-Newtonian Jeffrey fluid.

Bejan flow visualization of free convection in a Jeffrey fluid from a semi-infinite vertical cylinder

This article studies the pattern of heat lines in free convection non-Newtonian flow from a semi-infinite vertical cylinder via Bejan’s heat function concept. The viscoelastic Jeffrey fluid model is employed. The time-dependent, coupled, nonlinear conservation equations for momentum and energy (heat) are solved computationally with the unconditionally stable finite difference Crank–Nicolson method. Extensive graphical results are presented for the influence of Deborah number (viscoelastic parameter) and Prandtl number (with ranges 0–0.8 and 0.68–7.2, respectively) on thermal and flow characteristics including time histories of overall skin friction and heat transfer rate. Lower values of Deborah number indicate that the material acts in a more fluid-like manner, whereas the higher values of Deborah number correspond to the material showing characteristics more associated with a solid. The solutions indicate that the time taken for the flow-field variables to achieve the steady state is increased with higher values of Deborah number. Boundary flow visualization is presented using heat lines, isotherms and streamlines. It is observed that as Deborah number increases the intensity of heat lines increases and they tend to deviate from the hot cylindrical wall. Furthermore, the flow-field variables for the Newtonian fluid case exhibit a significantly different pattern from that of Jeffrey fluid.

Transient Natural Convection Heat Transfer to CO2 in the Supercritical Region

Present research paper investigates the transient laminar free convective supercritical carbon dioxide flow past a semi-infinite vertical cylinder using numerical methods. Two new thermodynamic models for the supercritical fluid (SCF) flow are considered. Based on these models, for supercritical carbon dioxide, two new equations for thermal expansion coefficient are obtained on the basis of Redlich–Kwong equation of state (RK-EOS) and Van der Waals equation of state (VW-EOS). Based on the calculated values of thermal expansion coefficient, it is shown that not only RK-EOS is closer to experimental values but also gives greater accuracy when compared to VW-EOS validating RK-EOS as suitable model for predicting natural convective properties of carbon dioxide under supercritical condition. The governing equations of SCF flow are solved numerically using Crank–Nicolson implicit finite difference scheme. Numerical simulations are performed for carbon dioxide in the region of its critical point. Results in subcritical, supercritical, and near-critical regions are shown graphically and discussed for different physical parameters. From the obtained numerical results, it is clear that the steady-state time increases for the increasing values of reduced temperature and reduced pressure for carbon dioxide in supercritical region.

THERMAL AND MASS DIFFUSIVE STUDIES ON A MOVING CYLINDER ENTRENCHED IN A POROUS MEDIUM

A numerical investigation is accomplished for an unsteady laminar free convective flow of a viscous incompressible fluid over an impulsively started semi-infinite vertical cylinder embedded in a porous medium. The level of temperature and concentration at the surface area of the cylinder are assumed to vary as functions of power law type, in the axial coordinate. The problem is governed by a system of coupled nonlinear boundary layer equations with appropriate variable surface boundary conditions and the numerical results are obtained using an implicit finite difference scheme of Crank-Nicholson type. The effects of physical parameters on velocity, temperature and concentration profiles and also on local and mean skin-friction coefficient, Nusselt number and Sherwood number are interpreted graphically. It is observed that the variable temperature and concentration exists in the boundary of cylinder relegates the rate of heat and mass transfer.

A numerical investigation of transient MHD free convective flow of a nanofluid over a moving semi-infinite vertical cylinder

PurposeThe purpose of this paper is to study numerically the influence of a magnetic field on the transient free convective boundary layer flow of a nanofluid over a moving semi-infinite vertical cylinder with heat transferDesign/methodology/approachThe problem is governed by the coupled non-linear partial differential equations with appropriate boundary conditions. The fluid is a water-based nanofluid containing nanoparticles of copper. The Brinkman model for dynamic viscosity and Maxwell–Garnett model for thermal conductivity are used. The governing boundary layer equations are written according to The Tiwari–Das nanofluid model. A robust, well-tested, implicit finite difference method of Crank–Nicolson type, which is unconditionally stable and convergent, is used to find the numerical solutions of the problem. The velocity and temperature profiles are studied for significant physical parameters such as the magnetic parameter, nanoparticles volume fraction and the thermal Grashof number Gr. The local skin-friction coefficient and the Nusselt number are also analysed and presented graphically.FindingsThe present computations have shown that an increase in the values of either magnetic parameter M or nanoparticle volume fraction decreases the local skin-friction coefficient, whereas the opposite effect is observed for thermal Grashof number Gr. The local Nusselt number increases with a rise in Gr and ϕ values. But an increase in M reduces the local Nusselt number.Originality/valueThis paper is relatively original and presents numerical investigation of transient two-dimensional laminar boundary layer free convective flow of a nanofluid over a moving semi-infinite vertical cylinder in the presence of an applied magnetic field. The present study is of immediate application to all those processes which are highly affected by heat enhancement concept and a magnetic field. Further the present study is relevant to nanofluid materials processing, chemical engineering coating operations exploiting nanomaterials and others.

Depth and shape solutions from residual gravity anomalies due to simple geometric structures using a statistical approach

AbstractWe have developed a simple and fast quantitative method for depth and shape determination from residual gravity anomalies due to simple geometrical bodies (semi-infinite vertical cylinder, horizontal cylinder, and sphere). The method is based on defining the anomaly value at two characteristic points and their corresponding distances on the anomaly profile. Using all possible combinations of the two characteristic points and their corresponding distances, a statistical procedure is developed for automated determination of the best shape and depth parameters of the buried structure from gravity data. A least-squares procedure is also formulated to estimate the amplitude coefficient which is related to the radius and density contrast of the buried structure. The method is applied to synthetic data with and without random errors and tested on two field examples from the USA and Germany. In all cases examined, the estimated depths and shapes are found to be in good agreement with actual values. The present method has the capability of minimizing the effect of random noise in data points to enhance the interpretation of results.

Steady State Analysis of Natural Convective Flow over a Moving Vertical Cylinder in the Presence of Porous Medium

A numerical study is carried out for a free convection flow past a continuously moving semi-infinite vertical cylinder in the presence of porous medium. The governing boundary layer equations are converted into a non-dimensional form and then they are solved by an efficient, accurate and unconditionally stable implicit finite difference scheme of Crank-Nicolson method. Stability and convergence of the finite difference scheme are established. The velocity, temperature and concentration profiles have been presented for various parameters such as Prandtl number, Schmidt number, thermal Grashof number, mass Grashof number and permeability of the porous medium. The local as well as average skin-friction, Nusselt number and Sherwood number are also shown graphically. It is observed that the increase in the permeability parameter leads to increase in velocity profile, local as well as average shear stress, Nusselt number and Sherwood number but leads to decrease in temperature and concentration profiles. The results of temperature and concentration profiles are compared with available result in literature and are found to be in good agreement.

Finite Difference Analysis of Unsteady MHD Free Convective Flow over Moving Semi-Infinite Vertical Cylinder with Chemical Reaction and Temperature Oscillation Effects

In the present study, the effects of chemical reaction on unsteady free convection flow of a viscous, electrically conducting, and incompressible fluid past a moving semi-infinite vertical cylinder with mass transfer and temperature oscillation is studied. The dimensionless governing partial differential equations are solved using an implicit finite-difference method of Crank–Nicolson type, which is stable and convergent. The transient velocity, transient temperature, and transient concentration profiles are studied for various parameters. The local as well as average skin-friction, Nusselt number, and Sherwood number are also analyzed and presented graphically. The results are compared with available computations in the literature, and are found to be in good agreement.

MHD Flow, Heat and Mass Transfer due to Axially Moving Cylinder in Presence of Thermal Diffusion, Radiation and Chemical Reactions in a Binary Fluid Mixture

the present paper we have studied the effects of magnetic field, thermal diffusion, thermal radiation and chemical reaction on velocity, temperature and concentration fields about an axially moving isothermal semi infinite solid vertical cylinder in two dimensional incompressible viscous binary fluid mixtures. The governing equations of continuity, momentum, energy and concentration are transformed into non similar boundary layer equations and are solved by using a regular perturbation method together with Matlab's built in solver bvp4c. Numerical solutions for axial velocity component, temperature and concentration of the rarer and lighter component of the binary fluid mixture are obtained on the basis of boundary layer approximation and presented graphically for axial curvature parameter, magnetic field parameter, thermal diffusion parameter, radiation parameter and chemical reaction parameter. It has been found that these parameters affect considerably the flow characteristics. The problem under consideration reduces to the flat plate case when the curvature parameter is absent. Keywordscylinder, magnetic field, thermal diffusion, radiation, chemical reaction, binary fluid mixture, MATLAB-bvp4c.

Accurate and Efficient Regularized Inversion Approach for the Interpretation of Isolated Gravity Anomalies

A very fast and efficient approach for gravity data inversion based on the regularized conjugate gradient method has been developed. This approach simultaneously inverts for the depth (z), and the amplitude coefficient (A) of a buried anomalous body from the gravity data measured along a profile. The developed algorithm fits the observed data by a class of some geometrically simple anomalous bodies, including the semi-infinite vertical cylinder, infinitely long horizontal cylinder, and sphere models using the logarithms of the model parameters [log(z) and log(|A|)] rather than the parameters themselves in its iterative minimization scheme. The presented numerical experiments have shown that the original (non-logarithmed) minimization scheme, which uses the parameters themselves (z and |A|) instead of their logarithms, encountered a variety of convergence problems. The aforementioned transformation of the objective functional subjected to minimization into the space of logarithms of z and |A| overcomes these convergence problems. The reliability and the applicability of the developed algorithm have been demonstrated on several synthetic data sets with and without noise. It is then successfully and carefully applied to seven real data examples with bodies buried in different complex geologic settings and at various depths inside the earth. The method is shown to be highly applicable for mineral exploration, and for both shallow and deep earth imaging, and is of particular value in cases where the observed gravity data is due to an isolated body embedded in the subsurface.

Soret and Dufour Effects on Transient Double Diffusive Free Convection of Couple-stress Fluid past a Vertical Cylinder

This study examines the influence of Soret and Dufour effects on double diffusive transient free convective boundary layer flow of a couple-stress fluid flowing over a semi-infinite vertical cylinder. A set of non-dimensional governing equations namely, the continuity, momentum, energy and concentration equations is derived and these equations are unsteady non-linear and coupled. As there is no analytical or direct numerical method available to solve these equations, they are solved by using the CFD techniques. An unconditionally stable Crank-Nicolson type of implicit finite difference scheme is employed to obtain the discretized forms of governing equations. These equations are solved using the Thomas and pentadiagonal algorithms. The numerical results are compared and found to be in good agreement with previously published results as special cases of the present investigation. Transient velocity, temperature and concentration profiles, average skin-friction, Nusselt number and Sherwood number are shown graphically for different values of Soret (So) and Dufour (Du) numbers. In all these profiles it is observed that, as the values of So decreases or the Du increases, the time required to reach the temporal maximum and the steady-state increases. It is also observed that the average values of skin-friction and heat transfer rate increases with the increasing values of So or decreasing values of Du. Whereas the reverse trend is observed for the average mass transfer rate.

Transient analysis of diffusive chemical reactive species for couple stress fluid flow over vertical cylinder

The unsteady natural convective couple stress fluid flow over a semi-infinite vertical cylinder is analyzed for the homogeneous first-order chemical reaction effect. The couple stress fluid flow model introduces the length dependent effect based on the material constant and dynamic viscosity. Also, it introduces the biharmonic operator in the Navier-Stokes equations, which is absent in the case of Newtonian fluids. The solution to the time-dependent non-linear and coupled governing equations is carried out with an unconditionally stable Crank-Nicolson type of numerical schemes. Numerical results for the transient flow variables, the average wall shear stress, the Nusselt number, and the Sherwood number are shown graphically for both generative and destructive reactions. The time to reach the temporal maximum increases as the reaction constant K increases. The average values of the wall shear stress and the heat transfer rate decrease as K increases, while increase with the increase in the Sherwood number.

New fast least-squares algorithm for estimating the best-fitting parameters due to simple geometric-structures from gravity anomalies

A new fast least-squares method is developed to estimate the shape factor (q-parameter) of a buried structure using normalized residual anomalies obtained from gravity data. The problem of shape factor estimation is transformed into a problem of finding a solution of a non-linear equation of the form f(q)=0 by defining the anomaly value at the origin and at different points on the profile (N-value). Procedures are also formulated to estimate the depth (z-parameter) and the amplitude coefficient (A-parameter) of the buried structure. The method is simple and rapid for estimating parameters that produced gravity anomalies. This technique is used for a class of geometrically simple anomalous bodies, including the semi-infinite vertical cylinder, the infinitely long horizontal cylinder, and the sphere. The technique is tested and verified on theoretical models with and without random errors. It is also successfully applied to real data sets from Senegal and India, and the inverted-parameters are in good agreement with the known actual values.

Numerical Investigation of Unsteady Free Convection on a Vertical Cylinder with Variable Heat and Mass Flux in the Presence of Chemically Reactive Species

A mathematical model is presented to study the effect of chemical reaction on unsteady natural convection boundary layer flow over a semi-infinite vertical cylinder. Taking into account the buoyancy force effects, for the situation in which the surface temperature and are subjected to the power-law surface heat and mass flux as and . The governing equations are solved by an implicit finite difference scheme of Crank-Nicolson method. Numerical results for the velocity, temperature and concentration profiles as well as for the skin-friction, Nusselt and Sherwood numbers are obtained and reported graphically for various parametric conditions to show interesting aspects of the solution.

A Fast Interpretation Method for Inverse Modeling of Residual Gravity Anomalies Caused by Simple Geometry

An inversion technique using a fast method is developed to estimate, successively, the depth, the shape factor, and the amplitude coefficient of a buried structure using residual gravity anomalies. By defining the anomaly value at the origin and the anomaly value at different points on the profile, the problem of depth estimation is transformed into a problem of solving a nonlinear equation of the form . Knowing the depth, the shape factor can be estimated and finally the amplitude coefficient can be estimated. This technique is applicable for a class of geometrically simple anomalous bodies, including the semiinfinite vertical cylinder, the infinitely long horizontal cylinder, and the sphere. The efficiency of this technique is demonstrated with gravity anomaly due to a theoretical model, in each case with and without random errors. Finally, the applicability is illustrated using the residual gravity anomaly of Mobrun ore body, situated near Noranda, QC, Canada. The interpreted depth and the other model parameters are in good agreement with the known actual values.