Abstract
This paper reports the results of a numerical and experimental investigation of mixed convection from a heat-generating element in a vented cavity with/without a baffle arrangement. Numerical investigations are carried out to determine the best position of the baffle on the walls of a rectangular chamber. The effect of varying the baffle heights and the position on the enhancement of heat transfer from the heater is investigated. Experiments were carried out for a heater located centrally in a parallelepiped that has an air inlet and an outlet port. The vertical baffle is fixed on the bottom wall of the chamber. After a detailed parametric study, correlations have been developed for the average Nusselt number and the maximum dimensionless temperature occurring in the heat generating element. Comparison of the numerical and experimental results for the geometry considered showed good agreement.
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Abbreviations
- A :
-
area in m2
- C p :
-
specific heat at constant pressure (J/kgK)
- C v :
-
specific at constant volume (J/kgK)
- corr:
-
correlation
- E :
-
total energy (J)
- exptl:
-
experimental
- Gr :
-
Grashof number, \( \frac{{g\beta \Updelta TL^{3} }}{{\nu^{2} }} \)
- g :
-
gravitational acceleration (9.81 m/s2)
- G k :
-
production of turbulent kinetic energy (kg/m s3)
- G b :
-
buoyant production of turbulent kinetic energy (kg/m s3)
- h :
-
heat transfer coefficient (W/m2 K)
- K :
-
turbulence intensity (m2/s2)
- k :
-
thermal conductivity (W/mK); turbulent kinetic energy per unit mass (J/kg)
- L :
-
height of the heater (m)
- Nu :
-
Nusselt number, \( \frac{hL}{k} \)
- P :
-
pressure (Pa)
- Pr :
-
Prandtl number, \( \frac{{\mu C_{\text{p}} }}{k} \)
- q v :
-
volumetric heat generation (W/m3)
- Q :
-
total heat input (W)
- R :
-
universal gas constant (8.31447 × 103 J/kg mol K)
- Ra :
-
Rayleigh number, Gr Pr
- Re :
-
Reynolds number, \( \frac{{u_{\infty } L}}{\nu } \)
- Ri :
-
Richardson number, \( \frac{Gr}{{{Re}^{2} }} \)
- R ε :
-
a term in the RNG turbulence model
- S :
-
dimensionless location of the heater (X/W)
- S k :
-
user defined source term in the RNG turbulence model
- S ε :
-
user defined source term in the RNG turbulence model
- T avg :
-
average temperature of the heater (K)
- T ∞ :
-
ambient temperature (K)
- T w :
-
wall temperature (K)
- ΔT ref :
-
reference temperature difference, \( \frac{{q_{v} L^{2} }}{{k_{s} }}\;({\text{K)}} \)
- u :
-
horizontal component of the velocity (m/s)
- u ∞ :
-
inlet velocity (m/s)
- u τ :
-
frictional velocity \( \sqrt {\tau_{\text{w}} /\rho } ,\;({{\text{m}} \mathord{\left/ {\vphantom {{\text{m}} {\text{s}}}} \right. \kern-\nulldelimiterspace} {\text{s}}}) \)
- v :
-
vertical component of the velocity (m/s)
- X :
-
location of the heater in the horizontal direction from left wall (m)
- x :
-
horizontal distance (m)
- y :
-
vertical distance (m)
- y + :
-
dimensionless distance from the wall \( u_{\tau } y/\nu \)
- W :
-
width of the chamber (100 mm)
- α :
-
thermal diffusivity (m2/s)
- β :
-
coefficient of thermal expansion (1/T, 1/K)
- δ ij :
-
Kronecker delta
- ε :
-
emissivity of the surface or dissipation rate of turbulent kinetic energy as the case may be (m2/s3)
- μ :
-
dynamic viscosity (N s/m2)
- ν :
-
kinematic viscosity (m2/s)
- ρ :
-
density of air (kg/m3)
- σ :
-
Stefan Boltzmann constant (5.67 × 10−8 W/m2 K4)
- τ :
-
shear stress (N/m2)
- τ w :
-
wall shear stress (N/m2)
- Φ:
-
dimensionless temperature, \( \frac{{T_{\text{avg}} - T_{\infty } }}{{\Updelta T_{\text{ref}} }} \)
- avg:
-
average
- ∞:
-
inlet and ambient
- f:
-
fluid
- s:
-
solid
- v:
-
volumetric
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Radhakrishnan, T.V., Joseph, G., Balaji, C. et al. Effect of baffle on convective heat transfer from a heat generating element in a ventilated cavity. Heat Mass Transfer 45, 1069–1082 (2009). https://doi.org/10.1007/s00231-008-0474-5
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DOI: https://doi.org/10.1007/s00231-008-0474-5