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Wall laminar nanofluid jet flow and heat transfer

Waqar Khan Usafzai (School of Mathematics and Physics, Nanjing Institute of Technology, Nanjing, China)
Rizwan Ul Haq (School of Natural Sciences, National University of Science and Technology (NUST), Islamabad, Pakistan)
Emad H. Aly (Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 9 December 2022




This work aims to investigates exact solutions of the classical Glauert’s laminar wall jet mass and heat transfer under wall suction, wall contraction or dilation, and two thermal transport boundary conditions; prescribed constant surface temperature and prescribed constant surface flux in nanofluidic environment.


The flow system arranged in terms of partial dif- ferential equations is non-dimensionalized with suitable dimensionless transformation variables, and this new set of equations is reduced into ordinary differential equations via a set of similarity transformations, where they are treated analytically for closed form solutions.


Exact solutions of nanofluid flow for velocity distributions, momentum flux, wall shear stress and heat transfer boundary layers for commonly studied nanoparticles; namely copper, alumina, silver, and titanium oxide are presented. The flow behavior of alumina and titanium oxide is identical, and a similar behavior is seen for copper and silver, making two pairs of identical traits. The mathematical expressions as well as visual analysis of wall shear drag and temperature gradient which are of practical interest are analyzed. It is shown that wall stretching or shrinking, wall transpiration and velocity slip together influences the jet flow mechanism and extends the original Glauert’s jet solutions. The exact solutions for the two temperature boundary layer conditions and temperature gradients are analyzed analytically. It is found that the effect of nanopar- ticles concentration on thermal boundary layer is intense, causing temperature uplift, whereas the wall transpiration causes a decrease in thermal layers.


The analysis carried out in nanofluid environment is genuinely new and unique, as our work generalizes the Glauert’s classical regular wall jet fluid problem.



The first author would like to acknowledge and express his gratitude for the financial support provided by Nanjing Institute of Technology, Nanjing, China under Grant number YKJ202126.


Khan Usafzai, W., Haq, R.U. and Aly, E.H. (2022), "Wall laminar nanofluid jet flow and heat transfer", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. ahead-of-print No. ahead-of-print.



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