A Study on Numerical Methodologies in Solving Fluid Flow and Heat Transfer Problems

Abstract Numerical methods are described as techniques by which several mathematical problems are formulated, because they may be easily solved with arithmetic operations. These methodologies have a great impact on the current development of finite element theory and other areas. We have given a short study of numerical methodologies applied in fluid flow and heat and mass transfer problems in mechanical engineering which includes finite difference method, Finite element method, Boundary value problems (general), Lattice Boltzmann’s methods, Crank-Nicolsan scheme methods, boundary integral method, Runge-Kutta method, Taylor series method and so on. We have discussed some phenomena taking place in fluids such as surface tension, coning, water scattering, Stokes law, gravity-capillary, and unsteady free-surface flows, swirling, and so on. We have also analyzed boundary value problems on boundary problems, eigenvalue problems and found a numerical way to solve these problems. We have presented different numerical methods applied to different fundamental modeling approaches in heat transfer and the performance of the mechanisms (modes) vary concerning the methods applied. The paper is dedicated to demonstrating how the methods are beneficial in solving real-life heat transfer problems in engineering applications. Results of the parameters like thermal conductivity, energy flux, entropy, temperature, etc. have been compared with the existing methods