TY - JOUR

T1 - Mixed convection from a localized heat source in a cavity with conducting walls

T2 - A numerical study

AU - Papanicolaou, E.

AU - Jaluria, Y.

N1 - Funding Information:
The authors acknowledge the partial support for this work from NSF, under grant CBT-88-03049,a nd from the Depamnent of Mechanical and Aerospace Engineering, Rutgers University.

PY - 1993/6

Y1 - 1993/6

N2 - Mixed convection is studied numerically in the case of an isolated, constant source of heal input within a rectangular enclosure. An external flow enters the enclosure through an opening in the left vertical wall and exits from another opening in the right vertical wall. This configuration leads to a conjugate heat transfer problem and simulates the air cooling of electronic components. Various parameters arise in this problem, particularly the Reynolds number, the buoyancy parameter Gr/Re2the ratio of the thermal conductivity of the wall material to that of the fluid taken as air, and several geometric parameters. The time-dependent continuity and Navier-Stokes equations are transformed into a system of equations with the stream function and the vorticity as the dependent variables. The energy equation is solved over the entire domain, using the corresponding properties for the solid and fluid regions. The control volume approach is employed in order to discretize the governing equations for their numerical solution. A time marching procedure is followed, until steady state is reached. Results are presented for different values of the buoyancy parameter in the laminar regime, and the critical value of Gr/Re2i.e., the highest value that leads to a convergent steady solution, is determined. Oscillatory results characterized by a single frequency were observed as this value was exceeded, up to a point where the oscillations showed irregular patterns, indicating that the flow was approaching the turbulent regime. Of particular interest here is the heat transfer, from the heat source to the fluid and from all the inner walls (solid-fluid interfaces) to the fluid, expressed in terms of the corresponding Nusselt numbers.

AB - Mixed convection is studied numerically in the case of an isolated, constant source of heal input within a rectangular enclosure. An external flow enters the enclosure through an opening in the left vertical wall and exits from another opening in the right vertical wall. This configuration leads to a conjugate heat transfer problem and simulates the air cooling of electronic components. Various parameters arise in this problem, particularly the Reynolds number, the buoyancy parameter Gr/Re2the ratio of the thermal conductivity of the wall material to that of the fluid taken as air, and several geometric parameters. The time-dependent continuity and Navier-Stokes equations are transformed into a system of equations with the stream function and the vorticity as the dependent variables. The energy equation is solved over the entire domain, using the corresponding properties for the solid and fluid regions. The control volume approach is employed in order to discretize the governing equations for their numerical solution. A time marching procedure is followed, until steady state is reached. Results are presented for different values of the buoyancy parameter in the laminar regime, and the critical value of Gr/Re2i.e., the highest value that leads to a convergent steady solution, is determined. Oscillatory results characterized by a single frequency were observed as this value was exceeded, up to a point where the oscillations showed irregular patterns, indicating that the flow was approaching the turbulent regime. Of particular interest here is the heat transfer, from the heat source to the fluid and from all the inner walls (solid-fluid interfaces) to the fluid, expressed in terms of the corresponding Nusselt numbers.

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U2 - 10.1080/10407789308913683

DO - 10.1080/10407789308913683

M3 - Article

AN - SCOPUS:0027610166

VL - 23

SP - 463

EP - 484

JO - Numerical Heat Transfer; Part A: Applications

JF - Numerical Heat Transfer; Part A: Applications

SN - 1040-7782

IS - 4

ER -