Streamfunction-velocity computation of natural convection around heated bodies placed in a square enclosure

Dutta, Sailen; Kumar, Pankaj; Kalita, Jiten C.

doi:10.1016/j.ijheatmasstransfer.2020.119550

Cited by 9 publications

(3 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The numerical approach used here follows the recent work of the authors, 62 where steady‐state natural convection around embedded heated bodies in a square enclosure was investigated using the streamfunction–velocity formulation on compact nonuniform Cartesian grids (Figure 2). Equation (1) is discretized using the scheme of Kumar and Kalita, 63 which is given as

A ψ_{i + 1, j + 1} + B ψ_{i, j + 1} + C ψ_{i - 1, j + 1} + D ψ_{i + 1, j} + E ψ_{i, j} + F ψ_{i - 1, j} + G ψ_{i + 1, j - 1} + H ψ_{i, j - 1} + I ψ_{i - 1, j - 1} = f_{i, j} .

The expressions for

A, B, C, D, E, F, G, H, I

, and

f_{i j}

are detailed in Kumar and Kalita 63 .…”

Section: Numerical Schemementioning

confidence: 99%

“…While the code has been validated recently, 62 in this section, we consider two more cases. First, we consider the flow over BFS only and compare our results with well‐established numerical and experimental results in the literature.…”

Section: Code Validationmentioning

confidence: 99%

“…Recently, the authors investigated steady‐state natural convection around embedded heated bodies in a square enclosure, 62 by reconstructing a finite difference (FD) scheme 63 for the

ψ

‐

v

form of the N–S equations and combining it with an HOC scheme 50 for the temperature equation. This new approach was shown to be robust and versatile, and was able to capture flow configurations previously unreported.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

ψ‐v Computation of steady‐state conjugate heat transfer in backward‐facing step flow

2021

Self Cite

View full text Add to dashboard Cite

In this paper, we study steady‐state conjugate heat transfer over a backward‐facing step flow using a combination of a compact finite difference scheme for the ψ ‐ v form of the Navier–Stokes equations and a higher‐order compact scheme for the temperature equations on nonuniform grids. We investigate the effect of Reynolds number ( 200 ≤ R e ≤ 800 ), conductivity ratio ( 1 ≤ k ≤ 1000 ), Prandtl number ( 0.1 ≤ P r ≤ 15 ), and slab thickness ( h ≤ b ≤ 6 h ) on the heat transfer characteristics. Isotherms remain clustered near the reattachment point in the fluid, while the temperature in the solid decreases vertically, with the minima at the reattachment point. Heat transfer rate (HTR) increases with Re, the maximum at the reattachment point. The HTR increases with k till k = 100 after, which it becomes invariant as k → ∞ . Isotherms at the inlet become more disorderly with increasing Pr, and progressively clustered near the interface, indicating an increase in HTR, while the temperature in the solid region decreases with Pr. Increasing b decreases the HTR. In addition to obtaining an excellent match with results previously reported in the literature, we offer more comprehensive and previously unreported insights on flow physics.

show abstract

A ψ_{i + 1, j + 1} + B ψ_{i, j + 1} + C ψ_{i - 1, j + 1} + D ψ_{i + 1, j} + E ψ_{i, j} + F ψ_{i - 1, j} + G ψ_{i + 1, j - 1} + H ψ_{i, j - 1} + I ψ_{i - 1, j - 1} = f_{i, j} .

The expressions for

A, B, C, D, E, F, G, H, I

, and

f_{i j}

are detailed in Kumar and Kalita 63 .…”

Section: Numerical Schemementioning

confidence: 99%

Section: Code Validationmentioning

confidence: 99%

“…Recently, the authors investigated steady‐state natural convection around embedded heated bodies in a square enclosure, 62 by reconstructing a finite difference (FD) scheme 63 for the