Evaluation of candidate strategies for the estimation of local heat transfer coefficient from wall jets

ABSTRACT

This paper reports results of experimental investigations on planar and three-dimensional wall jets over a flat surface. The local heat transfer coefficient is estimated at transient conditions with a semi-infinite approximation and at steady state conditions with a uniform wall heat flux boundary. Liquid crystal thermography and infrared thermography are used to map the surface temperatures. Experiments are performed for 2000 $\le$ Re $\le$ 8000 and 0 $\le$ x/L $\le$ 80. Results show that transient infrared thermography with semi-infinite approximation is a better candidate for the estimation of the heat transfer coefficient from wall jets.

KEYWORDS:

• Wall jet heat transfer
• semi infinite approximation
• infrared thermography
• uniform wall heat flux condition

Nomenclature

A,B	=	calibration constants of the hot-wire anemometer in Equation (1)
D	=	diameter of the jet,m
E	=	voltage across the hot-wire, V
h	=	local convective heat transfer coefficient, W/(m2 K)
k	=	thermal conductivity, W/(mK)
l	=	thickness of the plate, m
L	=	characteristic dimension, w or D
Nu	=	local Nusselt number, h L/k${ }_a$
Re	=	Reynolds number based on jet exit velocity, U${ }_0$ L/$\nu$
S	=	length of the slot, m
t	=	time, s
T(x,z,t)	=	temperature of the wall at any given time, ${ }^{\circ }$C
T	=	temperature, °C
u	=	streamwise mean velocity, m/s
$U_{max}$	=	local maximum velocity, m/s
U0	=	(volume flow rate)/(area of jet), m/s
w	=	width of the slot, $m$
x	=	distance along the streamwise direction, m
x/L	=	non dimensional streamwise distance
y	=	distance normal to the wall, m
$y_{max}$	=	distance normal to the wall where $\times$ U${ }_{max}$ occurs, m
$y_{0.5}$	=	distance normal to the wall where 0.5 $\times$ U${ }_{max}$ occurs, m
z	=	distance along the spanwise direction, m
z/S	=	non dimensional span wise distance

Greek letters

$\alpha$	=	thermal diffusivity, m2/s
$\eta$	=	effectiveness Equation (12)
$\mu$	=	dynamic viscosity, kg/ms
$\nu$	=	kinematic viscosity, m2/s
$\rho$	=	density, kg/m3
$\tau$	=	time, s

Subscripts

a	=	air
amb	=	ambient
i	=	initial
j	=	jet
rms	=	root mean square
s	=	semi-infinite solid body
sur	=	surface

Acronyms and other notations

1D	=	one-dimensional
2D	=	two-dimensional
3D	=	three-dimensional
UWHF	=	uniform wall heat flux
TI	=	turbulence intensity, $\frac{u_{rms}}{U_{max}}\times 100$

Acknowledgments

Financial assistance for this work provided by Gas Turbine Research Establishment (GTRE), Defense Research and Development Organization (DRDO), Government of India is gratefully acknowledged.