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ABSTRACT
Unsteady laminar heat transfer enhancement in asymmetrically heated vertical baffled channel under buoyancy effect is investigated numerically. The baffles are installed on the two walls in an offset manner with constant spacing. The governing equations are solved by the finite volume formulation using openFoam© open-source code. Air (Pr = 0.71) is used as working fluid. The effects of Reynolds number (100–1400) and Grashof number (2.5 × 104 to 2 × 105) in addition to the baffle height (0.1–0.5) on heat transfer and friction factor are studied. The results are given in the form of dimensionless isotherm contours and streamlines in addition to the Nusselt number and friction factor. The results obtained revealed that the flow bifurcates to self-sustained oscillatory flow at moderate Reynolds number (below 600 for a blockage ratio of 0.25). The unsteady self-sustained flow leads to heat transfer enhancement up to 2.8 times for baffle height hb = 0.25 and up to 3.7 when compared to the smooth channel. Unfortunately, this heat transfer is accompanied by an important increase in pumping power.
Nomenclature
| cp | = | specific heat of air (J kg−1 K−1) |
| d | = | baffle distance (m) |
| D | = | dimensionless baffle distance (D = d/H = 1) |
| f | = | friction factor ( |
| fs | = | friction factor in smooth channel |
| g | = | gravitational acceleration (m s−2) |
| Gr | = | Grashof number [Gr = gβ(Tw − T0)H3/ν2] |
| h | = | baffle height (m) |
| H | = | channel width (m) |
| hb | = | dimensionless baffle height or blockage ratio (hb = h/H) |
| K | = | thermal conductivity (W m−1 K−1) |
| Lh | = | dimensionless heated part length (Lh = lh/H) |
| Lin | = | dimensionless inlet length (Lin = lin/H) |
| Lout | = | dimensionless outlet length (Lout = lout/H) |
| Nu | = | mean Nusselt number |
| = | time-averaged mean Nusselt number | |
| NuX | = | local Nusselt number |
| = | time-averaged local Nusselt number | |
| p | = | pressure (Pa) |
| Pe | = | Péclet number (Pe = RePr) |
| Pm | = | dimensionless pressure ( |
| Pr | = | Prandtl number (Pr = ν/α) |
| Re | = | Reynolds number (Re = u0H/ν) |
| Ri | = | Richardson number (Ri = Gr/Re2) |
| t | = | time (s) |
| T | = | temperature (K) |
| u, v | = | velocity components in x- and y-directions (ms−1) |
| U, V | = | dimensionless velocity components (U = u/u0, V = v/u0) |
| x, y | = | dimensional Cartesian coordinates (m) |
| X, Y | = | dimensionless Cartesian coordinates (X = x/H, Y = y/H) |
| ΔP | = | pressure drop (Pa) |
| Greek letter | = | |
| α | = | thermal diffusivity of air (m2 s−1) |
| β | = | thermal expansion coefficient of air (K−1) |
| Δ | = | time step |
| η | = | Index efficiency |
| θ | = | dimensionless temperature (θ = (T − T0)/ (Tw − T0)] |
| μ | = | dynamic viscosity of air (kg s−1 m−1) |
| ν | = | kinematic viscosity of air (m2 s−2) |
| ρ | = | density of air (kg m−3) |
| τ | = | dimensionless time (τ = tu0/H) |
| Subscripts | = | |
| 0 | = | at inlet conditions |
| m | = | bulk |
| s | = | smooth channel |
| w | = | wall |
Nomenclature
| cp | = | specific heat of air (J kg−1 K−1) |
| d | = | baffle distance (m) |
| D | = | dimensionless baffle distance (D = d/H = 1) |
| f | = | friction factor ( |
| fs | = | friction factor in smooth channel |
| g | = | gravitational acceleration (m s−2) |
| Gr | = | Grashof number [Gr = gβ(Tw − T0)H3/ν2] |
| h | = | baffle height (m) |
| H | = | channel width (m) |
| hb | = | dimensionless baffle height or blockage ratio (hb = h/H) |
| K | = | thermal conductivity (W m−1 K−1) |
| Lh | = | dimensionless heated part length (Lh = lh/H) |
| Lin | = | dimensionless inlet length (Lin = lin/H) |
| Lout | = | dimensionless outlet length (Lout = lout/H) |
| Nu | = | mean Nusselt number |
| = | time-averaged mean Nusselt number | |
| NuX | = | local Nusselt number |
| = | time-averaged local Nusselt number | |
| p | = | pressure (Pa) |
| Pe | = | Péclet number (Pe = RePr) |
| Pm | = | dimensionless pressure ( |
| Pr | = | Prandtl number (Pr = ν/α) |
| Re | = | Reynolds number (Re = u0H/ν) |
| Ri | = | Richardson number (Ri = Gr/Re2) |
| t | = | time (s) |
| T | = | temperature (K) |
| u, v | = | velocity components in x- and y-directions (ms−1) |
| U, V | = | dimensionless velocity components (U = u/u0, V = v/u0) |
| x, y | = | dimensional Cartesian coordinates (m) |
| X, Y | = | dimensionless Cartesian coordinates (X = x/H, Y = y/H) |
| ΔP | = | pressure drop (Pa) |
| Greek letter | = | |
| α | = | thermal diffusivity of air (m2 s−1) |
| β | = | thermal expansion coefficient of air (K−1) |
| Δ | = | time step |
| η | = | Index efficiency |
| θ | = | dimensionless temperature (θ = (T − T0)/ (Tw − T0)] |
| μ | = | dynamic viscosity of air (kg s−1 m−1) |
| ν | = | kinematic viscosity of air (m2 s−2) |
| ρ | = | density of air (kg m−3) |
| τ | = | dimensionless time (τ = tu0/H) |
| Subscripts | = | |
| 0 | = | at inlet conditions |
| m | = | bulk |
| s | = | smooth channel |
| w | = | wall |