Experimental Study of Mixed Convection from Horizontal ‎Isothermal Elliptic Cylinders at Different Aspect Ratios

ABSTRACT

Mixed convective heat transfer from horizontal isothermal elliptic cylinder is experimentally studied. Three elliptic test cylinders with same perimeter and length are studied giving axis ratio (AR) equal 1, 0.709 and 0.496. The corresponding Gr for the three test sections is 9.8 × 10⁵, 1.5 × 10⁶, and 2.1 × 10⁶, and Re varies from 111 to 1306. Consequently, the corresponding Ri is in range of 1 to 102. The angle of attack (ψ) is changed from 0° (assisting flow) to 180° (opposing flow) with an interval of 30°. New empirical correlation is obtained for the Nu_avg as a function of the AR, Ri, and ψ. The experimental results are presented in the form of the average Nusselt number around the elliptic cylinder. It has been concluded that as the axis ratio decreases the averageNusselt number increases, in addition, increasing the angle of attack from 0° to 180° decreases the averageNusselt number considerably. New empirical correlations are obtained for the average Nusselt number as a function of the Richardson number and the attack angle.

KEYWORDS:

• Experimental
• axis ratio
• mixed convection
• elliptic cylinder

Nomenclature

a	=	Major radius of test cylinder, m.
A	=	cross-sectional area of test cylinder, m2
Ad	=	Inner duct walls surface area, m2, Ad = 2 (W1+ H) Ld.
Adev	=	Epoxy (devcon) area, m2.
AR	=	axis ratio of the test cylinder (minor to major ratio), AR= b/a.
Aw	=	Outer surface area of test cylinder, m2.
b	=	Minor radius of test cylinder, m.
B	=	Blockage ratio, B =2b/ H.
Cp	=	Specific heat at constant pressure, kJ/kg K.
Cpl	=	Specific heat of the liquid condensate, kJ/kg K.
Cpv	=	Specific heat of the water vapor, kJ/kg K.
dequ	=	Equivalent diameter of Styrofoam insulation inner side, m,aaaaaaaaaaa
Dc,o	=	Outlet diameter of the Styrofoam insulation, m.
Dcti	=	Inlet diameter of the asbestos rope insulation of the condensate tube, m.
Dcto	=	Outlet diameter of the asbestos rope insulation of the condensate tube, m.
Dp	=	Inside diameter of the pipe carrying the orifice, m.
Eb,dev	=	Emissive power of the black body for epoxy (devcon), W/m2.
Eb,d	=	Emissive power of the black body for air duct wall, W/m2.
Eb,w	=	Emissive power of the black body for the test cylinder wall, W/m2.
Fdev-d	=	Radiation shape factor from epoxy (devcon) surface to duct walls surface.
Fw-d	=	Radiation shape factor from test cylinder wall to duct walls surface.
g	=	Gravitational acceleration, m/s2.
Gr	=	Grashof number,aaaaaaaaaaaaaaa
havg	=	Average heat transfer coefficient, W/m2 K
H	=	Duct height, m
hfg	=	Condensation latent heat corresponding to the steam pressure, kJ/kg.
kc	=	Thermal conductivity of Styrofoam insulation, W/m K.
kct	=	Thermal conductivity of the asbestos rope insulation of the condensate tube, W/m K.
kf	=	Thermal conductivity of fluid at film temperature, W/m K.
Ko	=	Flow coefficient.
Lc	=	Length of the Styrofoam insulation, m.
Lct	=	Length of the asbestos rope insulation wound around the condensate tube, m.
Ld	=	Duct Length, m.
Lx	=	Distance from the entrance edge to the test cylinder section, m.
${\dot{m}}_a$	=	Air mass flow rate, kg/s.
${\dot{m}}_c$	=	Water condensate mass flow rate and steam mass flow rate, kg/s.
Nuavg	=	Average Nusselt number.
P	=	Perimeter of the elliptic cylinder, m.
patm	=	Atmospheric air pressure, N/m2.
∆po	=	The pressure drop across the orifice plate, N/m2.
Pr	=	Prandtl number.
ps	=	Static pressure, N/m2.
P1	=	Upstream average pressure before orifice meter, N/m2.
Qc,ct	=	Conduction heat transfer from condensate tube to the asbestos rope insulation, W.
Qc,end	=	Conduction heat transfer form test cylinder ends to the asbestos rope insulation, W.
Qconv	=	Convective heat transfer to the air inside air duct, W.
Qrad	=	Radiation heat transfer to the inside walls surface of the air duct, W.
Qtot	=	Total heat transfer from the test cylinder surface, W.
Re	=	Reynolds number,aaaaaaaa
Ri	=	Richardson number, aaaaaaaaaaa
t	=	Condensate collected time, sec.
Tci1	=	Inside surface temperature of Styrofoam insulation at test cylinder inlet, K.
Tci2	=	Inside surface temperature of Styrofoam insulation at test cylinder outlet, K.
Tco1	=	Outside surface temperature of Styrofoam insulation at test cylinder inlet, K.
Tco2	=	Outside surface temperature of Styrofoam insulation at test cylinder outlet, K.
Tcon	=	Condensate temperature, K.
Tc.tub	=	Outside surface temperature of the asbestos rope insulation of the condensate tube, K.
Td	=	Duct inside average surface temperature, K.
Tf	=	Film temperature, K.
To	=	Absolute air temperature downstream of the orifice plate, K.
Tsat	=	Saturation steam temperature, K.
Tsi	=	Steam inlet temperature in the test cylinder, K.
Tw	=	Average outer test cylinder wall surface temperature, K.
T∞I	=	Air inlet temperature or free stream temperature at the test cylinder section, K.
T∞o	=	Air outlet temperature of downstream at the test cylinder section, K.
Ue	=	Velocity at air duct entrance, m/s.
U∞	=	Free stream velocity at the test cylinder section, m/s.
W1	=	Test cylinder length, m
Wc	=	Mass flow of the water condensate, kg.
Zo	=	Expansion factor, aaaaaaaaaaaa

Greek symbols

βf	=	Coefficient of volumetric thermal expansion at film temperature, K−1.
δx	=	Boundary layer thickness at the test cylinder section, m.
εd	=	Emissivity of the inside duct walls surface.
εdev	=	Emissivity of the epoxy (devcon).
μw	=	Emissivity of the test cylinder surface.
μf	=	Dynamic viscosity at film temperature, kg/m s.
μo	=	Dynamic viscosity of downstream air in orifice meter tube, kg/m s.
υf	=	Kinematic viscosity at film temperature, m2/s.
ρe	=	Air density at the duct entrance, kg/m3.
ρf	=	Air density at film temperature, kg/m3.
σ	=	Stefan-Boltzman constant = 5.669×10−8, W/m2 K4
ψ	=	Approach or attack angle between forced flow direction and upward vertical direction.