Analysis of Transient Heat Flow in a Long Narrow Tube with Convection and Radiation

In this study, transient heat flow in the tube with convection and radiation investigated using the newly developed analytic method, namely the homotopy analysis method (HAM) and particle swarm optimization (PSO) which is one of the modern methods of optimization to solve problems. This method is completely efficient and has good run time to solve problems. By The lumped parameter approach, neglecting and simplify some physical effect, system of equation changes into ordinary differential equation (ODE), and we show the power of HAM method to solve this non linear equation and at the second step, we have been solved the problem with PSO, and Finally The analytical results are compared with PSO and another numerical solution (NS) with 4th Runge‐Kutta. The comparison shows a good agreement between them. Also in this case we examine the effect of the various values of some physical dimensionless parameters.