The aim of this research is an analytical investigation of heat and mass transfer for the MHD nanofluid flow passed between non-parallel stretchable/shrinkable walls. In order to model nanofluid flow, effects of Thermophoresis, Brownian diffusion, and Joule heating are considered. The governing mass, momentum, and energy equations are solved analytically by applying Duan-Rach method, which caused to get a solution for the undetermined coefficients from conjectured profiles of variables without using numerical methods. Comparison between the current results with the numerical results of other references shows good agreement. The effects of the Reynolds number, opening angle parameter, and the Hartman number on the temperature, velocity, and concentration profiles have been investigated in the case of both convergent and divergent plates, either stretched or shrunk. Also, the effects of the Thermophoretic and Brownian parameters on the Nusselt number are obtained. This study indicates that increasing the Hartman number decreases the concentration profile and increasing in the temperature profile for divergent channels. In this case, as the opening angle parameter rises, the thickness of the thermal boundary layer increases. Also, for convergent and divergent channels, the increase in the thermophoretic parameter causes increases the Nusselt number. By applying an identical magnetic field to two divergent stretching and shrinking channels, the concentration profile in the stretching channel is more than the shrinking one. For convergent channels, this treatment of concentration profile is completely vice versa.

The heat pipe is an efficient heat transfer device and can transfer large amounts of heat with a small temperature difference between the hot and cold sources quickly. In the present study, a two-dimensional numerical simulation method was used to analyze the thermal performance of heat pipes with double-ended cooling with the middle evaporator and to investigate the effect of operating conditions, wick and retaining chamber characteristics on it. The governing equations were discretized by ANSYS Fluent software and then solved using suitable boundary conditions. The wall temperature profile of the heat pipe was obtained. Then, to validate the results and to investigate the effect of using two condensers on the thermal resistance of the heat pipes, an experimental apparatus was used. Numerical results were compared with the valid numerical and experimental results that had very good and acceptable accordance. The results showed that the heat pipes with double-ended cooling with a middle evaporator had a lower thermal resistance than conventional heat pipes. The amount of thermal resistance increased with increasing the thickness and porosity of the wick. However, increasing the evaporators and condensers length, as well as increasing the thickness and internal diameter of the retaining chamber, reduced the thermal resistance. The results also showed that the heat pipes, which the materials with higher thermal conductivity were used in their wick and retaining chamber's manufacturing, had a lower thermal resistance. Finally, it was found that the increase of thermal power had no significant effect on the thermal resistance.