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Influence of radiative heat transfer on the thermal characteristics of nanofluid flow over an inclined step in the presence of an axial magnetic field

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Abstract

This research analyzes the influences of radiation heat transfer and Brownian movement on the thermal characteristics of nanofluid flow over an inclined step in the presence of an axial magnetic field. The Rosseland approximation is applied to simulate the divergence of radiative heat flux in the energy equation. The Al2O3–H2O and CuO–H2O nanofluids are considered as the working fluid. The \({\text{KKL}}\) correlation is used for modeling the Brownian movement influence on the effective viscosity and thermal conductivity. The impacts of radiation parameter \(\left( {0 \le Rd \le 1} \right)\), nanoparticles concentration \(\left( {0 \le \phi \le 0.04} \right)\) and Lorentz force \(\left( {0 \le Ha \le 60} \right)\) on temperature fields, mean bulk temperature and convective, radiative and total Nusselt numbers are examined with full details. The results show that the impact of CuO nanoparticles on the average of total heat transfer rates is greater that the influence of Al2O3 nanoparticles on them. Besides, the highest values of total heat transfer rates occur in the absence of magnetic field and for the highest values of \(Rd\) and \(\phi\) parameters.

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Abbreviations

\(B_{0}\) :

Magnetic field strength

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

Specific heat (J kg−1 K−1)

\(h\) :

Channel height upstream of \({\text{BFS}}\), (m)

\(H\) :

Channel height downstream of \({\text{BFS}}\), (m)

\(Ha\) :

Hartmann number

\(\overrightarrow {{F_{\text{l}} }}\) :

Lorentz force

\(k\) :

Thermal conductivity, (W m−1 K−1)

\(L_{\text{D}}\) :

Channel length downstream of \({\text{BFS}}\), (m)

\(L_{\text{r}}\) :

Reattachment length, (m)

\(L_{\text{U}}\) :

Channel length upstream of \({\text{BFS}}\), (m)

\(Nu\) :

Nusselt number

\(p\) :

Pressure, (N m−2)

\(P\) :

Dimensionless pressure

\(Pr\) :

Prandtl number

\(\vec{q}\) :

Heat flux

\(Re\) :

Reynolds number

\(Rd\) :

Radiation parameter

\(T\) :

Temperature, (K)

\(\left( {u, v} \right)\) :

\(x\)- and \(y\)-components of velocity, (m s−1)

\(\left( {U, V} \right)\) :

Dimensionless \(X\)- and \(Y\)-component of velocity

\(\vec{V}\) :

Velocity vector

\(\phi\) :

Nanoparticles concentration

\(\mu\) :

Dynamic viscosity, (N s m−2)

\(\rho\) :

Density, (kg m−3)

\(\sigma\) :

Electrical conductivity

\(\varTheta\) :

Dimensionless temperature

\({\text{c}}\) :

Convective

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

Fluid

\({\text{in}}\) :

Inlet section

\({\text{nf}}\) :

Nanofluid

\({\text{r}}\) :

Radiative

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

Solid nanoparticles

\({\text{t}}\) :

Total

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Atashafrooz, M. Influence of radiative heat transfer on the thermal characteristics of nanofluid flow over an inclined step in the presence of an axial magnetic field. J Therm Anal Calorim 139, 3345–3360 (2020). https://doi.org/10.1007/s10973-019-08672-0

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