5. =Average bulk air temperature
(Ts)x : local tube surface temperatures (Co)
: Average tube surface temperature (Co)
Greek symbols
=Coefficient for volumetric thermal expansion (K-1)
=Emissivity; inner surface and outer surface
μ=Fluid viscosity (kg/m.s)
=Kinematics viscosity (m2/s)
=Fluid density (kg/m3)
=Stefan-Boltzman constant (W/m2.K4)
=Inclination angle
I. INTRODUCTION
Natural convection induced by thermal buoyancy effects in a gravitational force field is
observed in many applications. These include electronic components design, air conditioning of
buildings, design of storage of hot fluids in solar power plants and food. Inclination of containers
filled with fluid, inside which convective heat or mass transfer occur, may have either desirable or
undesirable effects depending on the application. Effects of inclination on heat transfer have been
explored in practical applications involving solar energy heaters and double glazed windows. Martin
[1] made predictions of the lower limiting conditions of free convection in the vertical open circular
cross-section passage with uniform wall temperature. The overall heat transfer rate was independent
of tube length but proportional to radius, unless the length-radius ratio is about 1.8, in which case it
depends also on temperature conditions at the closed end..Shigeo and Adrian [2] studied
experimentally natural convection in a vertical pipe with different end temperature with (L/D=9).
The Rayleigh number was in the range 108Ra1010. It was concluded that the natural convection
mechanism departs considerably from the pattern known in the limit Ra 0. Specifically, the end-to-
end heat transfer was affected via two thin vertical jets, the upper (warm) jet proceeding along the
top of the cylinder toward the cold end and the lower (cold) jet advancing along the bottom in the
opposite direction. The Nusselt number for end-to-end heat transfer was shown to vary weakly with
the Rayleigh number. Shenoy [3] presented a theoretical analysis of the effect of buoyancy on the
heat transfer to non-newtonian power-law fluids for upward flow in vertical pipes under turbulent
conditions. The equation for quantitative evaluation of the natural convection effect on the forced
convection has been suggested to be applicable for upward as well as downward flow of the power-law
fluids by a change in the sign of the controlling term. Rahman and Sharif [4] conducted a
numerical investigation for free convective laminar flow of a fluid with or without internal heat
generation (Ra= 2 × 1010) in rectangular enclosures of different aspect ratios (from 0.25 to 4), at
39. μ:;
*
Pr=
……. (15)
Ram = Grm. Pr ……. (16)
All the air physical properties , μ, v and k were evaluated at the average mean film temperature
3
Holman [7].
5. EXPERIMENTAL UNCERTAINTY
Generally the accuracy of experimental results depends upon the accuracy of the individual
measuring instruments and the manufacturing accuracy of the circular tube. The accuracy of an
instrument is also limited by its minimum division (its sensitivity). In the present work, the
uncertainties in heat transfer coefficient (Nusselt number) and Rayleigh number were estimated
following Kline and McClintock differential approximation method reported by Holman [8]. For a
typical experiment, the total uncertainty in measuring the heater input power, temperature difference
(Ts-Tb), the heat transfer rate and the circular tube surface area were 0.38%, 0.48%, 2.6%, and1.3%
respectively. These were combined to give a maximum error of 2.12% in heat transfer coefficient
(Nusselt number) and maximum error of 2.51% in Rayleigh number.
6. RESULTS AND DISCUSSION
6.1 Temperature variation
The variation of tube surface temperature for different heat flux and for angle of inclination
= 0°(horizontal) , 30o, 60°, and 90°(vertical) are shown in Figs.(4)-(7) respectively . It is obvious
from these figures that the surface temperature increases as heat flux increases because of faster
increasing of the thermal boundary layer as heat flux increases. It can be seen from Fig.(4) that at +
0o, the tube surface temperature have no obvious change with the axial distance except at the end of
the tube due the conduction end losses. This behavior explained that there is no flow in the axial
direction so the bouncy effect is just in the radial direction .For = 30o, 60°, and 90°, the distribution
of the surface temperature (Ts) with tubes axial distance for different heat fluxes have the same
general shape as shown in Figs.(5)-(7). The surface temperature distribution exhibits the following
trend: the surface temperature gradually increases with the axial distance at the same rate of the
increasing for the tube until a certain limit to reach a maximum value at approximately(X*= 18)
beyond which it begins to decrease.