Fujii Tetsu

Laminar filmwise condensation of flowing vapour on a horizontal cylinder

Abstract Two-phase boundary layer equations of filmwise condensation on a horizontal cylinder are solved with an approximate method due to Jacobs. Numerical results for average coefficients of heat transfer are expressed as; for downward vapour flow, Nu=χ 1+ 0·276 χ 4 FrH 1 4 Re 1 2 especially forlarge vapour velocity, namely for gD U ∞ 2 H ⪡ χ 4 0·276 Nu=χ Re 1 2 where χ=0·9 1+ 1 RH 1 3 The heat transfer coefficients predicted by these expressions are in good agreement with experimental data, which are taken by the authors and Berman-Tumanov. Temperature distribution on the cylinder is usually affected by oncoming vapour velocity and surface heat flux, then the peripheral mean temperature must be adopted as the representative one.

Laminar natural-convective heat transfer from the outer surface of a vertical cylinder

Abstract Laminar natural convection along the outer surface of a vertical cylinder is compared with that along a vertical flat plate on heat transfer. For any Prandtl number and for arbitrary vertical temperature or heat flux distribution at the cylinder surface, local heat-transfer coefficients are represented non-dimensionally by the following approximate formulae. When surface temperature distributions are given, (Nu x ) c = (Nu x ) p + 0.435 x r w , x r w ≲ 0.7 (Nu) x ) p , and when surface heat flux distributions are given. (Nu x ) c = (Nu x ) p + 0.345 x r w , x r w ≲ 0.7 (Nu) x ) p , where (Nux)c and (Nux)p are the local Nusselt numbers for a cylinder and a flat plate respectively, x the vertical distance from the leading edge, and rw the radius of the cylinder.

Buoyant plume above a horizontal line heat source

Abstract The first problem dealt with in this paper is the solution of the equations concerning the steady laminar plume above a horizontal line heat source. While there are some controversies raised against what is proposed on this problem by Gebhart et al. [1], new numerical solutions which are more accurate are presented for Pr = 0.01, 0.03, 0.1, 0.3, 0.7, 1, 3, 5, 10, 30 and 100. Furthermore, the profiles of vertical velocity component and temperature are graphed so that there may be convenience of interpolation for an arbitrary Prandtl number. The relation between theory and experiment is taken up for consideration, by reviewing ail-inclusively the results of experiments made on the plumes in air, water and spindle oil as well as those hitherto reported on air and liquid silicone. While the natural motion of plume left undisturbed is extremely slow, it is considerably resembled to the fluttering of a flag. The photographs offered here represent typical motion of the plume in spindle oil. Generally speaking, experimental results are different from theories, but, so far as the temperature distribution in the plume is concerned, the similarity variable corresponding to the theory is applicable to it. The maximum temperatures in the plumes in air were about 15–20 per cent lower than the theoretical predictions in the whole range of Grashof number. Those in water and spindle oil were in good agreement with the theoretical predictions in the range of about Gr

Effect of vapour velocity on film condensation of R-113 on horizontal tubes in a crossflow

Abstract Film condensation of downward flowing R-113 vapour at near atmospheric pressure on single horizontal tubes was studied experimentally over wide ranges of vapour velocity and condensation temperature difference. The flow of condensate was visualized by injecting a dye tracer. Three flow regimes : smooth surface, two-dimensional waves and three-dimensional waves, were observed. In the last flow regime an abrupt thickening of the condensate film was seen at an angular position about 1.75 rad from the tube top. Turbulent mixing of condensate was observed in the thick film region. The present and earlier heat transfer results for R-113 and R-21 were compared with the laminar two-phase boundary-layer theory. The point at deviation from the theoretical prediction was found to be dependent on a dimensionless number which gave a transition criterion between smooth and wavy condensate surfaces. A correlation equation for the average heat transfer coefficient is proposed, where an equivalent Reynolds number is introduced for the high vapour velocity region.

A theoretical study of natural convection heat transfer from downward-facing horizontal surfaces with uniform heat flux

Abstract The paper treats of a theoretical study on steady laminar natural convection along a horizontal plate, which is heated with uniform heat flux and facing downwards. The boundary layer equations are solved by an approximate integral treatment, based on a concept of minimum boundary layer thickness which is derived from the consideration on the time evolution of unsteady flow field. While the solutions for an infinite strip and a circular plate are obtained analytically for any Prandtl numbers, the solution for a rectangular plate is obtained for the case of Pr → ∞ only. Approximate solutions by Galerkins method are also obtained for these three plates. The agreement found between the analytical and approximate solutions is fairly good, especially in the case of Pr → ∞. Local Nusselt number Nux is proportional to one-sixth power of modified Grashof number, whereas average Nusselt number Nu is proportional to one-fifth power of Grashof number. The value of Nu/Ra 1 5 increases with the increase of Prandtl number up to Pr = 100, becoming almost constant in the range of Pr > 100. Besides, it is the smallest for an infinite strip, and becomes larger toward a rectangular plate and a circular plate.

Influence of various surface roughness on the natural convection

Abstract Experimental results are presented with respect to the influence of various surface roughness on the natural convection of water and spindle oil along a vertical cylinder. Here are introduced the roughness of repeated-ribs of 0.5 mm height and 6.4, 12.8, 25.6 spacing-height ratio, that of dispersed-protrusions of 0.5 mm height, and that of dense-pyramids of 1.0 mm height. The local heat-transfer coefficients in the turbulent region, which are evaluated based on the base area of the cylinder, increase slightly in the case of water and decrease slightly in the case of oil. The magnitudes of the variations, however, are at most 10 per cent of the values in the case of the smooth surface. The upper limit of the laminar region is also not affected so much by the roughness. Some considerations on these results are presented in reference to the results of measurements made on temperature profiles in the boundary layer and rising velocities of vortex-pairs and turbulent lumps, beside those of observation done on the fluid motion in the boundary layer and those hitherto reported on the case of forced convection.

Natural convective heat transfer from a vertical isothermal surface to a non-Newtonian Sutterby fluid

This paper deals with the laminar natural convection of a non-Newtonian fluid along a vertical isothermal surface. The boundary-layer equations for a Sutterby fluid are solved numerically, and several characteristics of the non-similarity solution are represented graphically. An approximate expression of local Nusselt number Nux is proposed as Nux = 0·.50(Gr0xPr0)0·.25(1+m) , where m= 0−04 Pr00.23 A3·7 Pr0−0.34 Z00·63A0.66 Gr0x and Pr0 are Grashof number and Prandtl number based on zero viscosity respectively, and A and Z0 are non-Newtonian parameters. Local heat-transfer coefficients are obtained by experiments with aqueous solutions of polyethyleneoxide (PEO) and carboxymethylcellulose (CMC). The experimental results are in excellent agreement with the theoretical ones.

Laminar free convection flow rate in a vertical tube

This paper considers the flow rate of a laminar free convection inside a fully heated or a partly heated and partly cooled vertical tube placed in a large space. A theory based on a one-dimensional model which uses the Graetz solution for forced convection in a tube and which considers the pressure losses at the tube inlet and exit and in the hydrodynamic developing region is proposed for the range GrPr < 100. For the fully heated tube, the theory is compared with a two-dimensional numerical analysis and actual measurements using a quartz fiber anemometer. Their agreement is good when proper values of pressure loss coefficients are used in the theory. For the partly heated and partly cooled or partly adiabatic tube in thermally stratified and non-stratified ambients, the agreement between the theory and the experiment is also good. The effects of the tube-to-ambient temperature difference, the representative temperature of the stratified ambient, the tube length-to-diameter ratio and the temperature dependence of fluid properties upon the average mass velocity inside the tube are also clarified.

Natural convective heat-transfer from a vertical surface of uniform heat flux to a non-newtonian sutterby fluid

Abstract This paper deals with the laminar natural convection of a non-Newtonian fluid along a vertical surface with uniform heat flux. The boundary layer equations for a Sutterby fluid are solved numerically, and the typical results for the local Nusselt number Nux, are represented graphically. From the results an approximate expression of Nux, is proposed as Nu x = 0.62(Gr ∗ ox Pr o ) 0.2(1+m ∗ where m ∗ = 0.06Pr o −0.28 A 3.7 pr o -0.34 Z ∗ o 0.35A0.66 , Gr∗0x and Pr0 are Grashof and Prandtl numbers based on zero viscosity respectively, and A and Z ∗ 0 are non-Newtonian parameters. Local heat-transfer coefficients are obtained by experiments with aqueous solutions ofpolyethyleneoxide (PEO) and carboxymethylcellulose (CMC). The experimental results are in excellent agreement with the theoretical predictions.