Analysis of laminar mixed convection in shrouded arrays of heated rectangular blocks

Braaten, Mark E.; Patankar, S. V.

doi:10.1016/0017-9310(85)90144-9

Cited by 60 publications

(13 citation statements)

References 5 publications

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“…A recent paper by Zebib and Wo (1985) considers forced convection of a single electronic component in a horizonal geometry, neglecting free convection. Braaten and Patankar (1984) assessed the heat transfer enhancement by free convection for flow along the length of the blocks. In their analysis, the primary flow along the length of the components is assumed fully developed and buoyancy forces induce secondary flow, resulting in improvement in heat transfer.…”

Section: Introductionmentioning

confidence: 99%

Forced Convection Cooling Across Rectangular Blocks

Davalath

Bayazıtoğlu

1987

Journal of Heat Transfer

197

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Conjugate heat transfer for two-dimensional, developing flow over an array of rectangular blocks, representing finite heat sources on parallel plates, is considered. Incompressible flow over multiple blocks is modeled using the fully elliptic form of the Navier-Stokes equations. A control-volume-based finite difference procedure with appropriate averaging for the diffusion coefficients is used to solve the coupling between the solid and fluid regions. The heat transfer characteristics resulting from recirculating zones around the blocks are presented. The analysis is extended to study the optimum spacing between heat sources for a fixed heat input and a desired maximum temperature at the heat source.

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Section: Introductionmentioning

confidence: 99%

Forced Convection Cooling Across Rectangular Blocks

Davalath

Bayazıtoğlu

1987

Journal of Heat Transfer

197

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“…x-momentum, y-momentum, u-+-u-+-w-au 1 continuity, (9) In the above equations y is the dimensionless viscosity, y is the dimensionless thermal conductivity and 5 is the dimensionless heat capacity. The scaling leads to the appearance of the Prandtl number Pr = po C,,/k, and the Peclet number Pe = Pr Re in the energy equations.…”

Section: Model Equationsmentioning

confidence: 99%

“…Do while residual norm > tolerance P n = G r , , B, = P,/P, -1 u,=r,+B,qn P,= % I + Bn(4fl+ B n P n - 1 …”

Section: N=omentioning

confidence: 99%

A finite element solutionof three‐dimensional mixed convection gas flows in horizontal chnnels using preconditioned iterative metrix methods

Einset

Jensen

1992

Numerical Methods in Fluids

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SUMMARYAn algorithm is presented for the finite element solution of three-dimensional mixed convection gas flows in channels heated from below. The algorithm uses Newton's method and iterative matrix methods. Two iterative solution algorithms, conjugate gradient squared (CGS) and generalized minimal residual (GMRES), are used in conjunction with a preconditioning technique that is simple to implement. The preconditioner is a subset of the full Jacobian matrix centred around the main diagonal but retaining the most fundamental axial coupling of the residual equations. A domain-renumbering scheme that enhances the overall algorithm performance is proposed on the basis of an analysis of the preconditioner. Comparison with the frontal elimination method demonstrates that the iterative method will be faster when the front width exceeds approximately 500. Techniques for the direct assembly of the problem into a compressed sparse row storage format are demonstrated. Elimination of fixed boundary conditions is shown to decrease the size of the matrix problem by up to 30%. Finally, fluid flow solutions obtained with the numerical technique are presented. These solutions reveal complex three-dimensional mixed convection fluid flow phenomena at low Reynolds numbers, including the reversal of the direction of longitudinal rolls in the presence of a strong recirculation in the entrance region of the channel.

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“…The results showed that the inclination angle was an effective parameter on the rate of heat transfer. Another interesting research has been done by Braaten and Patankar et al [10] in a channel with an array of hot components. In this research the effects of Buoyancy force and Prandtl number on the Nusselt number have been investigated.…”

Section: Introductionmentioning

confidence: 98%