Analytical investigation of squeezing unsteady nanofluid flow between parallel plates by LSM and CM

An analytical investigation is applied for unsteady flow of a nanofluid squeezing between two parallel plates. Collocation Method (CM), Least Square Method (LSM) and fourth-order Runge-Kutta numerical method (NM) are used to solve the present problem. The results were compared with those obtained from Collocation Method (CM), Least Square Method and the established Numerical Method (Fourth order Runge-Kutta) scheme. It demonstrated LSM and CM presented accurate results. Water (H2O) was the base fluid that contained different kinds of nanoparticles that is, Copper, Silver, Alumina and Titanium Oxide. The effective thermal conductivity and viscosity of the nanofluid are calculated using the Maxwell–Garnetts (MG) and Brinkman models, respectively. The analytical investigation is carried out for various governing parameters such as the squeeze number, nanoparticle volume fraction and Eckert number. As a main outcome from the present study, it is observed that the results of LSM are more accurate than CM and they are in excellent agreement with numerical ones, so LSM can be used for finding analytical solutions of coupled equations in nanofluid problems easily. The results demonstrate when two plates are moving together, the Nusselt number increases b of nanoparticle volume fraction and Eckert number while it decreases with growth of the squeeze number.