Effects of Second-Order Velocity Slip and the Different Spherical Nanoparticles on Nanofluid Flow

• Main Authors: Jing Zhu, Ye Liu, Jiahui Cao
• Format: Article
• Language: English
• Published: MDPI AG 2021-12-01
• Series: Symmetry
• Subjects: nanofluid; second-order slip velocity; nanoparticles migration; homotopy analysis method
• Online Access: https://www.mdpi.com/2073-8994/13/1/64
• ISSN: 2073-8994

The paper theoretically investigates the heat transfer of nanofluids with different nanoparticles inside a parallel-plate channel. Second-order slip condition is adopted due to the microscopic roughness in the microchannels. After proper transformation, nonlinear partial differential systems are converted to ordinary differential equations with unknown constants, and then solved by homotopy analysis method. The residual plot is drawn to verify the convergence of the solution. The semi-analytical expressions between <inline-formula><math display="inline"><semantics><mrow><mi>N</mi><msub><mi>u</mi><mi>B</mi></msub></mrow></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><msub><mi>N</mi><mrow><mi>B</mi><mi>T</mi></mrow></msub></semantics></math></inline-formula> are acquired. The results show that both first-order slip parameter and second-order slip parameter have positive effects on <inline-formula><math display="inline"><semantics><mrow><mi>N</mi><msub><mi>u</mi><mi>B</mi></msub></mrow></semantics></math></inline-formula> of the MHD flow. The effect of second-order velocity slip on <inline-formula><math display="inline"><semantics><mrow><mi>N</mi><msub><mi>u</mi><mi>B</mi></msub></mrow></semantics></math></inline-formula> is obvious, and <inline-formula><math display="inline"><semantics><mrow><mi>N</mi><msub><mi>u</mi><mi>B</mi></msub></mrow></semantics></math></inline-formula> in the alumina–water nanofluid is higher than that in the titania–water nanofluid. The positive correlation between slip parameters and <inline-formula><math display="inline"><semantics><msub><mi>N</mi><mrow><mi>d</mi><mi>p</mi></mrow></msub></semantics></math></inline-formula> is significant for the titania–water nanofluid.