An approximation of the analytical solution of some nonlinear heat transfer equations: a survey by using Homotopy analysis method

Abstract In this letter, the approximate solution of nonlinear heat diffusion and heat transfer and also the energy balance for a differential fin element are developed via Homotopy Analysis Method HAM. This method is a strong and easy-to-use analytic tool for investigating nonlinear problems, which does not need small parameters. Homotopy analysis method contains the auxiliary parameter h , which provides us with a simple way to adjust and control the convergence region of solution series. By suitable choice of the auxiliary parameter h , we can obtain reasonable solutions for large modulus. In this study, we compare obtained results through HAM results, with those of homotopy perturbation method and the exact solutions. The first differential equation to be solved is a straight fin with a temperature-dependent thermal conductivity and the second one is the modeling equation of a cooling Lumped system with variable specific heat

Experimental investigation of water droplets' behavior in dielectric medium: the effect of an applied D.C. electric field

In this article, the behavior of water droplets which are suspended in silicon oil is qualitatively investigated and some phenomena such as liquid's burst are reported. The movement of droplet in perpendicular line is considered while many studies have considered small droplets fluctuating between two horizontal electrodes. Additionally any deformation caused by increasing voltage was observed from start to finish until short contact occurred. As can be seen two oppositely charged drops contacting each other do not necessarily result in coalescence. Repelling can be expected occasionally. By increasing the voltage, the droplets, which spread through the domain due to frequent breakups, tend to gather in a certain line

Natural convection in a nanofluids-filled portioned cavity: The Lattice-Boltzmann method

Numerical simulation of natural convection in a nanofluids-filled partitioned square cavity is presented. Two independent solvers, an in-house LBE-BGK code and the commercially available software CFD-ACE, are used to achieve this goal. While the partitioning plates are generating heat at a uniform temperature, the vertical walls are isothermally cooled allowing for the removal of the internally generated heat with the horizontal walls being adiabatic. While the particle volume fraction is kept constant at 5%, the effective Rayleigh number, the length, and the orientation of the partition have been parametrically varied from 10(3)-10(7), 0.25H-0.75H, and horizontal to vertical, respectively