**Acknowledgements**

The authors gratefuly acknowledge High Impact Research Grant UM.C/HIR/MOHE/ENG/23 and the Faculty of Engineering, University of Malaya, Malaysia, for support in conducting this research work.

### **Nomenclature**

of the cavity had a complex-wavy geometry while upper and lower walls were both flat and insulated. Complex-wavy walls were modeled as the superposition of two sinusoidal func‐ tions. The results revealed that heat transfer performance may be optimized by tuning the wavy-surface geometry parameter in accordance with the Rayleigh number. Using optimal homotopy analysis method (OHAM), Nadeem et al. [92] examined 2-D stagnation point flow of a non-Newtonian Casson nanofluid over a convective-stretching surface. The governing non-linear partial differential equations were converted into non-linear ordinary differential equations and solved analytically using OHAM. The results showed that heat transfer rate is an increasing function of the stretching parameter, Prandtl and Biot numbers and it decreases with an increase in non-Newtonian parameter, Brownian motion, and thermophoresis.

The laminar axisymmetric flow of a nanofluid over a non-linearly stretching sheet was studied by Mustafa et al. [93], both numerically and analytically. The simultaneous effects of Brownian motion and thermophoretic diffusion of nanoparticles were taken into account. The numerical solution was computed by employing implicit finite difference scheme known as Keller-Box method. The results obtained from both solutions were in excellent agreement with each other. The results demonstrated that the effect of Brownian motion on fluid temperature and wall heat transfer rate is insignificant. Moreover, it was reported that increases in Schmidt number

A comprehensive review of popular methods in the simulation of the nanofluids was carried out. Different CFD approaches including single-phase, multiphase, and other methods were reviewed. For each model, the governing equations and recent literature were studied.

Conventional single-phase model was the most common method to study the convective heat transfer of nanofluids. This can be due to the fact that this model simplifies the simulation and in comparison to other models has the lowest computational cost. However, the results obtained from this model may have some deviation from the experimental data. For instance, it was reported in many studies that homogeneous model underestimates the heat transfer coefficient and Nusselt number, when compared to the dispersion and two-phase models. However, it was also revealed that using the temperature-dependent thermophysical proper‐ ties in homogeneous model can lead to more realistic results. On the other hand, dispersion model for both constant and temperature-dependent properties showed promising results, compared with experimental data. This model requires less computational time compared to two-phase model. In addition, the model takes into account thermal dispersion effect, which

Nanofluids are inherently multiphase fluids; therefore, employing two-phase model taking into account the slip velocity, Brownian motion, thermophoresis, and so forth, can lead to more appropriate results. Most of the publications confirmed that different two-phase models predict more accurate results than the homogeneous model. Also, higher values of the heat transfer coefficient were reported for two-phase models, compared to conventional single-

leads to more reliable results in comparison with the homogeneous model.

lead to a thinner nanoparticle volume fraction boundary layer.

**3. Conclusion**

210 Modeling and Simulation in Engineering Sciences



#### **Greek symbols**



#### **Super- and Subscripts**


#### **Author details**

Mohammad Reza Safaei1\*, AminHossein Jahanbin2 , Ali Kianifar3 , Samira Gharehkhani1 , Akeel Shebeeb Kherbeet4 , Marjan Goodarzi5 and Mahidzal Dahari6

\*Address all correspondence to: cfd\_safaei@um.edu.my; cfd\_safaei@yahoo.com

1 Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, Kuala Lumpur, Malaysia

2 Department of Industrial Engineering (DIN), University of Bologna, Bologna, Italy

3 Department of Mechanical Engineering, Engineering Faculty, Ferdowsi University of Mashhad, Mashhad, Iran

4 Department of Mechanical Engineering, KBU International College, Petaling Jaya, Selan‐ gor, Malaysia

5 Young Researchers and Elite Club, Mashhad Branch, Islamic Azad University, Mashhad, Iran

6 Department of Electrical Engineering, Faculty of Engineering, University of Malaya, Kuala Lumpur, Malaysia
