Surfactants role in the enhancement of the heat transfer and stability of alumina oxide – distilled water nanofluid was introduced in this research, where there are limited studies that conjugate between the stability improvement and its effect on the heat transfer coefficients. Four weight concentrations for the experiment were used (0.1, 0.3, 0.6, and 0.9%) with 20 nm particle size under a constant wall temperature. The selection of appropriate surfactants weight was tested too by implementing three weight concentrations (0.5, 1, 1.5, and 2 %) related to each nanofluid concentration via measuring their effect on the zeta potential value. The heat transfer augmentation was tested through a double horizontal pipe under a constant wall temperature at entrance region with Reynolds number range (4000–11800). The results manifested the use of nanofluid worked on enhancement the heat transfer performance better than water, and the stable nanofluid elucidated better results.
By the iteration of the theta-formula and treating the neighbors explicitly such as the unconditionally positive finite difference (UPFD) methods, we construct a new 2-stage explicit algorithm to solve partial differential equations containing a diffusion term and two reaction terms. One of the reaction terms is linear, which may describe heat convection, the other one is proportional to the fourth power of the variable, which can represent radiation. We analytically prove, for the linear case, that the order of accuracy of the method is two, and that it is unconditionally stable. We verify the method by reproducing an analytical solution with high accuracy. Then large systems with random parameters and discontinuous initial conditions are used to demonstrate that the new method is competitive against several other solvers, even if the nonlinear term is extremely large. Finally, we show that the new method can be adapted to the advection–diffusion-reaction term as well.
Based on many previous experiments, the most efficient explicit and stable numerical method to solve heat conduction problems is the leapfrog-hopscotch scheme. In our last paper, we made a successful attempt to solve the nonlinear heat conduction–convection–radiation equation. Now, we implement the convection and radiation terms in several ways to find the optimal implementation. The algorithm versions are tested by comparing their results to 1D numerical and analytical solutions. Then, we perform numerical tests to compare their performance when simulating heat transfer of the two-dimensional surface and cross section of a realistic wall. The latter case contains an insulator layer and a thermal bridge. The stability and convergence properties of the optimal version are analytically proved as well.
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