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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 73, 2018 - Issue 6
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Original Articles

Control of separated fluid flow and heat transfer characteristics over a backward facing step

ORCID Icon &
Pages 366-384 | Received 04 Nov 2018, Accepted 22 Feb 2018, Published online: 26 Mar 2018
 

ABSTRACT

The control of laminar fluid flow and heat transfer characteristics over a backward facing step have been studied by varying location and orientation of a thin adiabatic fin mounted on the top wall. The detailed investigation of geometrical parameters of fin (length, location and orientation) for two different Reynolds numbers is performed numerically and the results are compared to the case without fin. It is found that fin location and orientation can be used to control the primary reattachment point and the peak of local Nusselt number effectively and it acts as a passive controller.

Nomenclature

AR=

aspect ratio,

Cf=

skin friction coefficient,

Cp=

specific heat at constant pressure

d=

location of fin from the step

ER=

expansion ratio,

h=

local heat transfer coefficient, W m−2 K−1

hu=

upstream channel height

H=

downstream channel height

lf=

fin height

Ld=

downstream channel length

Leff=

effective fin length, Lf cos α

Lu=

upstream channel length

Nu=

local nusselt number,

Nua=

average Nusselt number,

Num=

maximum value of Nu

Pr=

Prandlt number

Re=

Reynolds number based on bulk velocity and hydraulic diameter,

s=

step height, H − hs

Tc, Th=

cold and hot temperature (K)

u, v=

streamwise (x) and transverse (y) velocity

ub=

bulk or average velocity

W=

spanwise width in 3D

Xm=

location of maximum or peak Nu

Xr=

location of primary reattachment point

Nondimensional variables=
[D, Lf, S, X, Y] ==

[d, lf, s, x, y]/hu

P==

[U, V] ==

[u, v]/ub

Superscripts=
w=

without fin case

Greek symbols=
α=

fin inclination angle

η=

normal unit vector to the surface

ρ=

density of fluid (Kg m−3)

μ=

dynamic viscosity (m2 s)

κ=

fluid thermal conductivity, ()

ν=

kinematic viscosity (Pa s)

τ=

wall shear stress,

θ=

nondimensional temp.

Nomenclature

AR=

aspect ratio,

Cf=

skin friction coefficient,

Cp=

specific heat at constant pressure

d=

location of fin from the step

ER=

expansion ratio,

h=

local heat transfer coefficient, W m−2 K−1

hu=

upstream channel height

H=

downstream channel height

lf=

fin height

Ld=

downstream channel length

Leff=

effective fin length, Lf cos α

Lu=

upstream channel length

Nu=

local nusselt number,

Nua=

average Nusselt number,

Num=

maximum value of Nu

Pr=

Prandlt number

Re=

Reynolds number based on bulk velocity and hydraulic diameter,

s=

step height, H − hs

Tc, Th=

cold and hot temperature (K)

u, v=

streamwise (x) and transverse (y) velocity

ub=

bulk or average velocity

W=

spanwise width in 3D

Xm=

location of maximum or peak Nu

Xr=

location of primary reattachment point

Nondimensional variables=
[D, Lf, S, X, Y] ==

[d, lf, s, x, y]/hu

P==

[U, V] ==

[u, v]/ub

Superscripts=
w=

without fin case

Greek symbols=
α=

fin inclination angle

η=

normal unit vector to the surface

ρ=

density of fluid (Kg m−3)

μ=

dynamic viscosity (m2 s)

κ=

fluid thermal conductivity, ()

ν=

kinematic viscosity (Pa s)

τ=

wall shear stress,

θ=

nondimensional temp.

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