Numerical Simulation of Solid and Porous Fins’ Impact on Heat Transfer Performance in a Differentially Heated Chamber

The development of different industrial fields, including mechanical and power engineering and electronics, demands the augmentation of heat transfer in engineering devices. Such enhancement can be achieved by adding extended heat transfer surfaces to the heated walls or heat-generating elements. This investigation is devoted to the numerical analysis of natural convective energy transport in a differentially heated chamber with isothermal vertical walls and a fin system mounted on the heated wall. The developed in-house computational code has been comprehensively validated. The Forchheimer–Brinkman extended Darcy model has been employed for the numerical simulation of transport phenomena in a porous material. The partial differential equations written, employing non-primitive variables, have been worked out by the finite difference technique. Analysis has been performed for solid and porous fins with various fin materials, amounts and heights. It has been revealed that porous fins provide a very good technique for the intensification of energy removal from heated surfaces.

A Nonstandard Finite Difference Method for a Generalized Black–Scholes Equation

An implicit finite difference scheme for the numerical solution of a generalized Black–Scholes equation is presented. The method is based on the nonstandard finite difference technique. The positivity property is discussed and it is shown that the proposed method is consistent, stable and also the order of the scheme respect to the space variable is two. As the Black–Scholes model relies on symmetry of distribution and ignores the skewness of the distribution of the asset, the proposed method will be more appropriate for solving such symmetric models. In order to illustrate the efficiency of the new method, we applied it on some test examples. The obtained results confirm the theoretical behavior regarding the order of convergence. Furthermore, the numerical results are in good agreement with the exact solution and are more accurate than other existing results in the literature.

Chemically Reactive MHD Eyring-Powell Nanofluid Flow past a Stretching Surface with Convergence Test

The motive of this work is to examine the transfer of heat as well as mass phenomena of Eyring-Powell fluid flow on a stretching type of porous medium. The impact of heat absorption and thermal radiation are also considered here to describe the characteristics of the fluid flow. Firstly, a mathematical model of this fluid flow is established which includes time dependent continuity, energy, momentum and concentration formula. Then the fundamental equations are formed to dimensionless format. After that an explicit type finite difference technique is imposed to solve the model by taking the help of FORTRAN. The stability as well as convergence analysis (SCA) is used to develop and check the precession of the overall system. Moreover, the fields of temperature, velocity, concentration, skin friction, Nusselt number and Sherwood number got affected significantly with the influences of various pertinent parameters which are presented in different color diagrams. However, the updated visualization of the fluid flows is also presented by both isotherms and streamlines for the impact of radiation parameter. Moreover, for Eyring-Powell fluid, an interesting observation has been made that the thermophoretic parameter is influencing the temperature field significantly rather than the Brownian parameter. Finally, for the validation of the ongoing investigation, a suitable comparison is also depicted with some published papers and a proper agreement is noticed.

An Approach to Identify Urban Waterlogging on a Deltaic Plain using ArcGIS on CHD based Flow Accumulation Models

The gradient for any point on the land surface can be calculated using the digital-elevation model. Some empirical correlations are available to determine the gradient of any points. A few studies were conducted for hilly forest areas to determine the aspect and gradient of various points using computational hydrodynamics (CHD) based techniques. On a plain surface, the accuracy of such techniques was rarely verified. The application of such techniques for a plain surface is also extremely challenging for its small slope. Therefore, the prime objective of the present study is to find out an advanced technique to more accurately determine the gradient of various points on a plain surface which may help in determining the key areas affected by run-off, subsequent flow accumulation, and waterlogging. Here, Kolkata city as a deltaic plain surface is chosen for this study. Upto 600 m × 600 grid sizes are used on the DEM map to calculate the run-off pattern using a D8 algorithm method and second-order, third-order, and fourth-order finite difference techniques of CHD. After finding out the gradient, the run-off pattern is determined from relatively higher to lower gradient points. Based on the run-off pattern, waterlogging points of a plain surface are precisely determined. The results obtained from all the different methods are compared with one other as well as with the actual waterlogging map of Kolkata. It is found that the D8 algorithm and fourth-order finite-difference-technique are the most accurate while determining the waterlogging areas of a plain surface. Next, true gradients of waterlogging points are calculated manually to compare the calculated gradient points using each method. This is also done to determine the relationship and error between the true and calculated gradient of waterlogged points using various statistical analysis methods. The relationship between true and calculated gradients is observed from weak to strong if the D8 algorithm is replaced by the newly introduced fourth-order finite difference technique. Better accuracy and stronger relationships can be achieved by using a smaller grid size.

Numerical Simulation of Magnetohydrodynamic Influences on Casson Model for Blood Flow through an Overlapping Stenosed Artery

Magnetohydrodynamic (MHD) effects of unsteady blood flow on Casson fluid through an artery with overlapping stenosis were investigated. The nonlinear governing equations accompanied by the appropriate boundary conditions were discretized and solved based on a finite difference technique, using the pressure correction method with MAC algorithm. Moreover, blood flow characteristics, such as the velocity profile, pressure drop, wall shear stress, and patterns of streamlines, are presented graphically and inspected thoroughly for understanding the blood flow phenomena in the stenosed artery.