Numerical simulations of a two-dimensional laminar forced convection flow adjacent to inclined backward-facing step in a rectangular duct are presented to examine effects of baffle on flow, heat transfer and entropy generation distributions. The main aim of using baffles is to enhance the value of convection coefficient on the bottom wall. But the useful energy can be destroyed due to intrinsic irreversibilities in the flow by the baffle. In the present work, the amount of energy loss is estimated by the computation of entropy generation. The values of velocity and temperature which are the inputs of the entropy generation equation are obtained by the numerical solution of momentum and energy equations with blocked-off method using computational fluid dynamic technique. Discretized forms of the governing equations in the (x, y) plane are obtained by the control volume method and solved using the SIMPLE algorithm. Numerical expressions, in terms of Nusselt number, entropy generation number, Bejan number and coefficient of friction are derived in dimensionless form. Results show that although a baffle mounted onto the upper wall increases the magnitude of Nusselts number on the bottom wall, but a considerable increase in the amount of entropy generation number takes place because of this technique. For validation, the numerical results for the Nusselt number and entropy generation number are compared with theoretical findings by other investigators and reasonable agreement is found.

An outer-connected dominating set for an arbitrary graph G is a setD ⊆ V such thatD is a dominating set and the induced subgraph G[V \D] be connected. In this paper, we focus on the outerconnected domination number of the product of graphs. We investigate the existence of outer-connected dominating set in lexicographic product and Corona of two arbitrary graphs, and we present upper bounds for outer-connected domination number in lexicographic and Cartesian product of graphs. Also, we establish an equivalent form of the Vizing's conjecture for outer-connected domination number in lexicographic and Cartesian product asγc(G • K)γc(H • K) ≤γc(G H) • K. Furthermore, we study the outer-connected domination number of the direct product of finitely many complete graphs.

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In this research study, a new combination search algorithm, based on indexing its constituent processes, is proposed to solve global optimisation problems. As optimisation problems become more complex, especially real‐world problems, the use of higher‐performance algorithms has become essential. One of the techniques that lead to design of an algorithm with stronger strategies in exploration and exploitation, as well as a better balance between these two strategies, is the appropriate combination of parent algorithm processes. The proposed algorithm was developed using a new innovation with the help of the supply‐demand‐based optimisation and the Harris hawks optimisation algorithms processes as parent algorithms. In this algorithm, the local and global search sections of its parent algorithms, are separated, and then based on a new indexing method in each iteration, according to the current population indexing, a global search and a local search are selected from the processes of its parent algorithms, and then the current population is updated with two selected sections. The performance and effectiveness of the proposed algorithm in solving well‐known standard benchmark problems and in solving real‐world engineering problems have been tested and validated by statistical tools. The results of the research study show that the proposed algorithm can provide very effective results compared to other competing algorithms as well as its parent algorithms in many tests. The results show that the proper combination of optimisation algorithm processes can be used as a technique to design more powerful algorithms to solve global optimisation problems, especially complex real‐world problems.