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SADI approach programming on GPU: convective heat transfer of nanofluids flow inside a wavy channel

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Abstract

In this study, the numerical simulation of convective heat transfer of nanofluids (Al2O3/water and CuO/water) inside a sinusoidal wavy channel is performed using the Graphics Processing Units (GPU). The governing equations including stream-function, vorticity transport, and energy are discretized using the fourth-order Spline Alternating-Direction Implicit (SADI) approach in combination with the curvilinear coordinates mapping. The final tridiagonal-matrices are solved by Parallel-Thomas-Algorithm (PTA) on GPU. A homogenous one-phase model is also applied to consider the effective characteristics of the nanofluids flow. In the first part of the results section, the effects of nanoparticle volume fraction, Reynolds number, and amplitude of the wavy wall on average Nusselt number and the skin friction coefficient of the channel are investigated. In the second part of the results section, the ability of GPU to accelerate the computation (or runtimes) is compared to the classic Thomas algorithm that runs on a Central Processing Unit (CPU). The results demonstrate that the speedup of PTA against CPU runtime for the finest grid is around 18.32×.

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Abbreviations

\(\bar{a}\) :

Amplitude of wavy surface (m)

\(c_{\text{p}}\) :

Specific heat (J kg−1 K−1)

\(c_{\text{f}}\) :

Skin-friction coefficient

d :

Diameter (m)

h :

Heat transfer coefficient (W m−2 K−1)

k :

Thermal conductivity (W m−1 K−1)

\(\bar{H}\) :

Half width of channel (m)

Nu:

Nusselt number

Pr:

Prandtl number

Re:

Reynolds number

\(\bar{S}\) :

Surface geometry function

t :

Time (s)

\(\bar{T}\) :

Temperature (K)

\(\bar{u},\bar{v}\) :

Velocities components (m s−1)

\(\bar{U}_{\text{m}}\) :

Average velocity (m s−1)

\(\bar{x},\bar{y}\) :

Cartesian coordinates (m)

\(\beta\) :

Volumetric thermal expansion coefficient (K−1)

\(\theta\) :

Dimensionless temperature

\(\mu\) :

Dynamic viscosity (Ns m−2)

\(\xi ,\eta\) :

Body-fitted coordinates

\(\rho\) :

Density (kg m−3)

\(\tau\) :

Dimensionless time

\(\varphi\) :

Volume fraction of particles (%)

\(\bar{\psi }\) :

Stream function (m2 s−1)

\(\psi\) :

Dimensionless stream function

\(\omega\) :

Dimensionless vorticity

\(\bar{\omega }\) :

Vorticity (s−1)

−:

Dimensional quantity

′:

Derivative with respect to x

\({\text{x}}\) :

Local value

\({\text{f}}\) :

End point of wavy wall

\({\text{m}}\) :

Mean value

\({\text{s}}\) :

Starting point of corrugated wall

\({\text{w}}\) :

Surface conditions

\({\text{f}}\) :

Base fluid

nf:

Nanofluid

p:

Particles

in:

Inlet

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Acknowledgements

The authors would like to acknowledge the Shahrood University of Technology, which supported this study.

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Authors and Affiliations

  1. Department of Mechanical and Mechatronics Engineering, Shahrood University of Technology, P. Box: 3619995161, Shahrood, Iran

    S. M. H. Taghavi & P. Akbarzadeh

  2. School of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran

    H. Mahmoodi Darian

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  1. S. M. H. Taghavi
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  3. H. Mahmoodi Darian
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Correspondence to P. Akbarzadeh.

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Taghavi, S.M.H., Akbarzadeh, P. & Mahmoodi Darian, H. SADI approach programming on GPU: convective heat transfer of nanofluids flow inside a wavy channel. J Therm Anal Calorim 146, 31–46 (2021). https://doi.org/10.1007/s10973-020-09924-0

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