This article deals with steady-state laminar, electrically conducting immiscible fluids. The Newtonian fluid considered passes between two parallel vertical plates in a porous medium. The channel consists of two regions, one of them filled with engine-oil-based carbon nanotubes (CNTs) and the second region filled with water through a porous medium. The assumptions for the channel walls are electrically non-conducting and are at two different temperatures. Mathematical formulation is formed using rules for the conservation of mass, momentum and energy in both regions. Continuous conditions are used for velocity, temperature and also for shear pressure at the crossing area. The governing equations are first transformed in a non-dimensional form by using appropriate transformations, and then the subsequent differential equations are solved using a topological approach by means of the homotopy analysis method. It is found that the impact of the actual boundaries utilized in the issue is directed, and the outcomes are introduced graphically and discussed. It is noted that the engine-oil SWCNTs experience a significant increase in temperature profiles as compared to the engine-oil MWCNTs, while the movement of fluid slowdown in the nanofluid region due to the concentration of nanoparticles and the thickness of the thermal boundary layer increases by increasing the volume fraction of the carbon nanotubes.
The current paper describes the effect of insulation thickness in a vacuum resistance furnace. An existing furnace was optimized for insulation thickness using analytical and numerical studies. Furnace heating efficiency was improved up to 64% by controlling the heat flow at the insulation face. The numerical results were validated experimentally and vice versa. The numerical results predicted a decrease in heat flow of 70%, while the experimentally achieved value was 64%. The percentage difference in numerical and experimental results was calculated to be 1.5–5% maximum in temperature value. The effect of mesh finesse was evaluated for thermal analysis and it was concluded that a very little difference of 5 °C occurs when element size is reduced 5 times. The study using numerical methods will help in designing better and upgraded furnaces with greater energy savings. Also, the application of numerical methods is proposed as an effective design and performance prediction tool during manufacturing and operational activities of vacuum furnaces, respectively.
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