Impact of an effective Prandtl number model on the flow of nanofluids past an oblique stagnation point on a convective surface

Zafar Mahmood; Sayed M Eldin; Amal F Soliman; Taghreed A Assiri; Umar Khan; S R Mahmoud

doi:10.1016/j.heliyon.2023.e13224

Impact of an effective Prandtl number model on the flow of nanofluids past an oblique stagnation point on a convective surface

Heliyon. 2023 Jan 25;9(2):e13224. doi: 10.1016/j.heliyon.2023.e13224. eCollection 2023 Feb.

Authors

Zafar Mahmood¹, Sayed M Eldin², Amal F Soliman^{3

4}, Taghreed A Assiri⁵, Umar Khan¹, S R Mahmoud⁶

Affiliations

¹ Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan.
² Center of Research, Faculty of Engineering, Future University in Egypt New Cairo 11835, Egypt.
³ Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Addawasir, Saudi Arabia.
⁴ Department of Basic Science, Benha Faculty of Engineering, Benha University, Banha, Egypt.
⁵ Department of Mathematics, Faculty of Science, Umm Al-Qura University, Makkah, Saudi Arabia.
⁶ GRC Department, Applied College, King Abdulaziz University, Jeddah 21589, Saudi Arabia.

Abstract

The stretched surface's convective heat transfer capability can be improved by using nanoparticles. There is a significant role of the Prandtl number in determining the thermal and momentum stretching layer surfaces. It is proposed in this study that an effective Prandtl number model be used to explore the two-dimensional oblique stagnation point flow of $γ A l_{2} O_{3} - H_{2} O$ and $γ A l_{2} O_{3} - C_{2} H_{6} O_{2}$ nanofluids moving over a convective stretching surface. The fluid in question is subjected to a thorough investigation. It is necessary to apply non-linear ordinary differential equations in order to connect the controlling partial differential equations with the boundary conditions. To solve these equations, an efficient and reliable numerical technique is used. Shooting Method with Runge Kutta-IV in Mathematica software. Visual representations of normal and tangential velocity and temperature as well as streamlines as a function of many physical parameters are shown. The results show that as the volume fraction of nanoparticles increases, the fluid flow $f (y),$ $h (y)$ and velocity $f^{'} (y),$ $h^{'} (y)$ all increase, whereas the flow $f (y)$ and velocity $f^{'} (y)$ both increase against the stretching ratio parameter, while the flow $h (y)$ and velocity $h^{'} (y)$ both decrease. When the volume percentage of nanoparticles and the Biot number are both increased, the temperature rises. However, when the stretching ratio parameter is increased, the temperature falls. Physical attributes like the local skin friction coefficient and the heat flow may be characterized in many ways. A nanofluid comprised of $γ A l_{2} O_{3} - C_{2} H_{6} O_{2}$ outperformed a $γ A l_{2} O_{3} - H_{2} O$ nanofluid in terms of heat transfer rate. The source of zero skin friction may be observed to move to the left or right depending on the balance of obliqueness and straining motion at point $x_{s}$ . The computed numerical results of the current research correspond well with those accessible in the literature for the limiting scenario.

Keywords: Convective surface; Effective Prandtl number; Gamma alumina nanofluid; Numerical simulation; Oblique stagnation point.