A numerical study on thin film flow and heat transfer enhancement for copper nanoparticles dispersed in ethylene glycol
Umer Hayat, Ramzan Ali, Shakil Shaiq, Azeem Shahzad
Abstract
Abstract The current study examines thin film flow and heat transfer phenomena with some additional effects such as magnetohydrodynamic, viscous dissipation, and slip condition over unsteady radially stretching surfaces for various shapes of copper <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mo>(</m:mo> <m:mi mathvariant="normal">Cu</m:mi> <m:mo>)</m:mo> </m:math> \left({\rm{Cu}}) nanoparticles dispersed in ethylene glycol <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mo>(</m:mo> <m:mi mathvariant="normal">EG</m:mi> <m:mo>)</m:mo> </m:math> \left({\rm{EG}}) . The effective thermal conductivity of a nanofluid made of Cu nanometer-sized particles distributed in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi mathvariant="normal">EG</m:mi> </m:math> {\rm{EG}} is significantly higher than that of pure EG. Partial differential equations are transformed into ordinary differential equations using the proper transformations. An effective convergent technique ( i.e. , BVP4C) is used to compute the solutions of nonlinear systems. MATLAB software is used to perform the calculations. The effect of numerous emerging physical characteristics on temperature and velocity, such as unsteadiness parameter <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mspace width=" 1em"/> <m:mo>(</m:mo> <m:mi>S</m:mi> <m:mo>)</m:mo> </m:math> \hspace{ 1em}\left(S) , slip parameter <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mo>(</m:mo> <m:mi>K</m:mi> <m:mo>)</m:mo> </m:math> \left(K) , Hartmann number <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mo>(</m:mo> <m:mi>M</m:mi> <m:mo>)</m:mo> </m:math> \left(M) , solid volume fraction <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mrow> <m:mi>ϕ</m:mi> </m:mrow> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> (\phi ) , and Eckert number <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mo>(</m:mo> <m:mi mathvariant="normal">EC</m:mi> <m:mo>)</m:mo> </m:math> \left({\rm{EC}}) is investigated and illustrated graphically. The physical quantities, such as the skin friction coefficient and the Nusselt number, are calculated, described, and displayed in tabular form. It is observed that blade-shaped Cu nanoparticles had the lowest surface drag, highest heat transfer rate, and minimum film thickness compared to the brick and cylinder-shaped nanoparticles. According to our detailed investigation blade-shaped <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi mathvariant="normal">Cu</m:mi> </m:math> {\rm{Cu}} nanoparticle is the most suited solution for manufacturing unsteady radially stretching modules.