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ABSTRACT
This article examines the unsteady magnetohydrodynamic free convection flows of Al2O3 (alumina)-water and single-walled carbon nanotube (SWCNT)-water nanofluids within a symmetrical wavy trapezoidal enclosure with viscous and Joule dissipation effects. The governing equations and the corresponding initial and boundary conditions are nondimensionalized and the resulting initial boundary value problem is solved using the mixed finite-element method with polynomial pressure projection stabilization. Streamline and isotherm plots are used to represent the numerical results for the velocity and temperature, respectively. The effects of time t, Hartmann number Ha, wall amplitude a, and solid volume fraction ϕ on the fluid flow and heat transfer are studied.
Nomenclature
| cp | = | specific heat capacity, Jkg−1K−1 |
| Ec | = | Eckert number |
| Ha | = | Hartmann number |
| Nu | = | Nusselt number |
| p | = | pressure, kgm−1s−2 |
| Pr | = | Prandtl number |
| μ | = | viscosity, kgm−1s−1 |
| ρ | = | density, kgm−3 |
| σ | = | electrical conductivity, Ω−1m−1 |
| ϕ | = | solid volume fraction |
| ψ | = | stream function |
| Ra | = | Rayleigh number |
| t | = | time, s |
| T | = | temperature, K |
| u,v | = | velocity components, ms−1 |
| x,y | = | space coordinates, m |
| β | = | coefficient of thermal expansion, K−1 |
| κ | = | thermal conductivity, Wm−1K−1 |
| Subscripts | = | |
| f | = | fluid |
| nf | = | nanofluid |
| s | = | solid |
| av | = | average |
Nomenclature
| cp | = | specific heat capacity, Jkg−1K−1 |
| Ec | = | Eckert number |
| Ha | = | Hartmann number |
| Nu | = | Nusselt number |
| p | = | pressure, kgm−1s−2 |
| Pr | = | Prandtl number |
| μ | = | viscosity, kgm−1s−1 |
| ρ | = | density, kgm−3 |
| σ | = | electrical conductivity, Ω−1m−1 |
| ϕ | = | solid volume fraction |
| ψ | = | stream function |
| Ra | = | Rayleigh number |
| t | = | time, s |
| T | = | temperature, K |
| u,v | = | velocity components, ms−1 |
| x,y | = | space coordinates, m |
| β | = | coefficient of thermal expansion, K−1 |
| κ | = | thermal conductivity, Wm−1K−1 |
| Subscripts | = | |
| f | = | fluid |
| nf | = | nanofluid |
| s | = | solid |
| av | = | average |