just now i sent this questions.
this is the answer given. however the answer i afraid
that he used formula that is not for constant surface temperature
and noncircular formula.
this is the formula foe the noncircular tube. because
the question ask about triangle.
my problem is, i cannot answer question 1(b) that ask
the heat transfer coefficient, h. please help me. thank you.
this pic is a note on constant surface temperature.
ref: HEAT AND MASS TRANSFER: FUNDAMENTALS &
APPLICATIONS, FIFTH EDITION. yunus A. Cengel.
1. Nitrogen at 1 atm and 100 °C enters into an equilateral triangular cross section duct of each side 5 cm long with an average velocity of 5 m/s. The duct wall is maintained at a constant surface temperature of 600 °C and the outlet mean temperature is 300 °C. a) What is the bulk mean temperature Tim and Reynolds number Re? b) What is the convection heat transfer coefficient h? c) Estimate the length L of the duct and the pumping power required. 2. Juice in cans 150 mm long and 60 mm in diameter is initially at 27°C and is to be cooled by placement in a refrigerator compartment at 4°C. In the interest of maximizing the cooling rate, should the cans be laid horizontally or vertically in the compartment? tue 14:01 pm …0.8KB/sweco CD + Answer 1 of 1 + —)- – ) 971522 09. 52 SAS . OS. 5S-CIRI-3 OC 03 271503 tue 14:01 pm … 1.2KB’s w e CD + Answer 1 of 1 + – — c) : 0-013 * Tower -509517451) OSYAS 5.9. m Laminar Flow in Noncircular Tubes The friction factor f and the Nusselt number relations are given in Table 8-1 for fully developed laminar flow in tubes of various cross sections. The Reynolds and Nusselt numbers for flow in these tubes are based on the hydraulic diameter D = 4Alp, where A is the cross-sectional area of the tube and p is its perimeter. Once the Nusselt number is available, the con- vection heat transfer coefficient is determined from h = KNu/D, TABLE 8-1 Nusselt number and friction factor for fully developed laminar flow in tubes of various cross sections (D = 4A/P, Re = Vau D.lv, and Nu = hD /K) Nusselt Number Friction Factor alb or gº Tube Geometry To= Const. 3.66 ds = Const. 4.36 Circle 64.00/Re Rectangle 2.98 3.39 3.96 4.44 5.14 5.60 7.54 3.61 4.12 4.79 5.33 6.05 6.49 8.24 56.92/Re 62.20/Re 68.36/Re 72.92/Re 78.80/Re 82.32/Re 96.00/Re Ellipse 4.36 4.56 3.66 3.74 3.79 3.72 3.65 4.88 5.09 64.00/Re 67.28/Re 72.96/Re 76.60/Re 78.16/Re 5.18 Isosceles Triangle 1.61 10° 30° 60° 90° 2.26 2.47 2.34 2.00 2.45 2.91 3.11 2.98 2.68 50.80/Re 52.28/Re 53.32/Re 52.60/Re 50.96/Re 120° WULIL 15 U JIL DU VEL UI e I . Constant Surface Temperature (T = constant) From Newton’s law of cooling, the rate of heat transfer to or from a fluid flowing in a tube can be expressed as O = 4,7 = AT,- (W) where h is the average convection heat transfer coefficient, A, is the heat transfer surface area (it is equal to DL for a circular pipe of length L) and AT is some appropriate average temperature difference between the fluid and the surface. Below we discuss two suitable ways of expressing AT In the constant surface temperature (T. = constant) case, A7 can be expressed approximately by the arithmetic mean temperature difference AT as AT + AT (T.-T) + (T. -T.) T T + T. AT.,-47…- -T, – To where 7= (T) + T.X2 is the bulk mean fluid temperature, which is the arithmetic average of the mean fluid temperatures at the inlet and the exit of the tube. IT. -1,-1, 2 CHAPTER 8 Note that the urithmetic meant temperature difference AT… is simply the average of the temperature differences between the surface and the fluid at the inlet and the exit of the tube. Inherent in this definition is the assumption that the mean fluid temperature varies linearly along the tube, which is hardly ever the case when T, = constant. This simple approximation often gives accept- able results, but not always. Therefore, we need a better way to evaluate AT Consider the heating of fluid in a tube of constant cross section whose inner surface is maintained at a constant temperature of T. We know that the mean temperature of the fluid T., increases in the flow direction as a result of heat transfer. The energy balance on a differential control volume shown in Fig. 8-12 gives T AT (T. pecaches 7 asymptotically me, T.-T – TMA, (8-27) That is, the increase in the energy of the fluid (represented by an increase in its mean temperature by dT) is equal to the heat transferred to the fluid from the tube surface by convection. Noting that the differential surface area is dA, = pdx, where p is the perimeter of the tube, and that dr. = -dT.-T.) since T is constant, the relation above can be rearranged as AT, – pa T- TE Integrating from x = 0 (tube inlet where T = T) to .x = L (tube exit where T = 7.) gives T.- TA In T.-T. (8-29) FIGURE 8-14 The variation of the mexin fluid temperature along the tube for the case of constant temperature. 7. = orc 1-20 NTU = 7°C where A, = pL is the surface area of the tube and his the constant average convection heat transfer coefficient. Taking the exponential of both sides and solving for T. gives the following relation which is very useful for the deter- mination of the mean flacid lemperature at the the exit: T-T-17,-) exp-14,/ic) (8-30 This relation can also be used to determine the mean fluid temperature T(X) at anyx by replacing A, = pl by pr. Note that the temperature difference between the fluid and the surface decays exponentially in the flow direction, and the rate of decay depends on the magnitude of the exponent hArc. as shown in Fig. 8-14. This dimen- sionless parameter is called the number of transfer nits, denoted by NTU, and is a measure of the effectiveness of the heat transfer systems. For NTU > 5. the exit temperature of the fluid becomes almost equal to the surface tempera- ture, T, T.(Fig. 8-15). Noting that the fluid temperature can approach the surface temperature but cannot Cr it, an NTU of about 5 indicates that the limit is reached for heat transfer, and the heat transfer does not increase no matter how much we extend the length of the tube. A small value of NTU. on the other hand, indicates more opportunities for heat transfer, and the heat transfer continues to increase is the tube length is increased. A large NTU and thus a large heat transfer surface area which means a large tube) may be desirable from a heat transfer point of view, but it may be unacceptable from an economic point of view. The selection of heat transfer equipment usually reflects a compromise between heat transfer performance and cost. 239 995 100 100) FIGURE 8-15 An NTU greater than 5 indicates that the fluid flowing in a tube will reach the surface temperature at the exit regardless of the inlet temperature,