Purpose The purpose of this paper is to analyze the heat and momentum transfer for steady two-dimensional incompressible nanofluid flow through a wavy channel with linearly varying amplitude in the entrance region. Design/methodology/approach The mass, momentum and energy conservation equations for laminar flow of Cu-water nanofluids are computationally solved using the finite element method. A parametric study is carried out by varying the dimensionless length of the channel section with varying amplitude (EL), Reynolds number (Re) and nanoparticle volume fraction (Φ) in the ranges 0 ≤ EL ≤ 25.5, 105 ≤ Re ≤ 900 and 0 ≤ Φ ≤ 0.04. Findings A higher heat transfer rate is seen in the wavy channel compared to a plane channel beyond a critical value of Re (Recrit) whose value varies with EL; moreover, the overall heat transfer decreases with EL. The heat transfer rate increases with phi for all EL values investigated. The combined effects of the increase in the overall heat transfer and the associated pressure drop in the wavy channel compared to the parallel plate channel are presented as performance factor (PF) against EL. For the highest value of EL (= 25.5), PF monotonically decreases with Re. For smaller values of EL (= 5.5 and 11.5) and also for EL = 0, PF decreases with Re in the lower and the higher Re regimes, while it increases in the intermediate Re regime. In all cases, PF is higher for φ = 0.04 than for the base fluid. The sensitivity of the average Nusselt number to nanoparticle volume fraction follows a non-monotonic trend with the change in Re, φ and EL. Practical implications This study finds relevance in several applications such as solar collectors, heat exchangers and heat sinks. Originality/value To the best of the authors’ knowledge, the analysis of forced convection flow of nanofluid through a wavy channel with linearly varying amplitude is reported for the first time in the literature.

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