a b s t r a c tThe present study represents the heat transfer optimization of two-dimensional incompressible laminar flow of Al 2 O 3 -water nanofluids in a duct with uniform temperature corrugated walls. A two phase model is applied to investigate different governing parameters, namely: Reynolds number (100 Re 1000), nonofluids volume fraction (0% f 5%) and amplitude of the wavy wall (0 a 0.04 m). For optimization process, a recent spot-lighted method, called Artificial Bee Colony (ABC) algorithm, is applied, and the results are shown to be in a good accuracy in comparison with another well-known heuristic method, i.e. particle swarm optimization (PSO). The results indicate that the effect of utilizing nanoparticles and increasing Reynolds number is more intensified on growing the average Nusselt number than variations of the amplitude of the wavy wall. To prevent the worst possible heat transfer, the specific amplitude which leads to a minimum average Nusselt number is detected. The effect of using nanoparticles on thermal-hydraulic performance factor (j/f) is presented which considers both heat transfer and hydrodynamics aspects. The results showed that volume fraction has a direct and the wavy wall's amplitude has a converse effect on the thermal-hydraulic performance factor. Furthermore, an optimum value for Reynolds number is found to maximize the thermal-hydraulic performance factor.

In this article, heat transfer optimization of forced convection in a wavy channel with different phase shifts between the upper and lower wavy walls is represented. The flow is laminar in the range of (200 B Re B 800) and a uniform temperature of 350 K is considered in the wavy sections. The governing mass, momentum and energy equations are solved using the finite volume method. Different design parameters such as the channel height (h = 10, 15 and 20 mm), the amplitude of the wavy wall (A = 1.5, 2, 2.5 and 3 mm) and the phase shift of the upper wavy wall ð0 c 360 Þ are investigated. For optimization process, a recent method, named artificial bee colony (ABC) algorithm, is applied and compared with two other meta-heuristic algorithms, called particle swarm optimization (PSO) and differential evolution (DE). An ''in house'' code is developed which simultaneously uses the meta-heuristic algorithms and the computational fluid dynamics solver. The results indicate that ABC algorithm has higher accuracy and faster convergence rate than PSO and DE. The parameter considered for optimizing the average Nusselt number as the objective function was the phase shift. But, for optimizing the thermal performance factor, selected parameters were the wavy wall amplitude and the phase shift. The results showed that the maximum average Nusselt number is attained at c ¼ 250:2, A = 3 mm, h = 10 mm and Re = 800, in which the heat transfer rate has 96.6% enhancement rather than the parallel-plate channel. Also, it is found that c ¼ 283:3, A = 2.65 mm, h = 10 mm and Re = 800 are the optimized solutions to obtain the maximum thermal performance factor.