-1. Natural Convection from an Oven Wall. The oven wall in Example 15.5-1 is insu- lated so that the surface temperature is 366.5 K instead of 505.4 K. Calculate the natural convection heat-transfer coefficient and the heat-transfer rate per m of width. Use both Eq. (15.5-4) and the simplified equation. (Note: Radiation is being neglected in this calculation.) Use both SI and English units. Table 15.5-1. Constants for Use with Eq. (15.5-4) for Natural Convection Boundary-layer velocity profile for natural convection heat transfer froma heated vertical plate 4047 Physical Geometry NGrNpr а т Vertical planes and cylinders [vertical height L <1 m (3 ft)] Ть <104 1.36 104 10 1 0.59 х > 10 0.13 Horizontal cylinders [diameter D used for L and D<0.20 m (0.66 ft)] y rential momentum-balance equation is written for the x andy directions for the e (dx dy 1). The driving force is the buoyancy force in the gravitational field the density difference of the fluid. The momentum balance becomes 0.49 10-5-10-3 0.71 10-3-1 1.09 1 10 1.09 (T-2 21) - (d - )8 ay2 x v (15.5-1) дх ду 10- 10 0.53 e density at the bulk temperature Tp and r the density at T. The density differ- xpressed in terms of the volumetric coefficient of expansion B and substituted (15.5-1): >109 0.13 Horizontal plates Upper surface of heated plates lower surface of heated plates Lower surface of heated plates upper surface of cooled plates 105- 2 x 107 2 x 107 -3 x 1010 0.54 or 0.14 or В 3 p(Т - Т,) (15.5-2) 10- 101 0.58 or B = 1/T. The energy-balance equation can be expressed as follows: Э'т Әт Эт (15.5-3) k + v. y рс, ay2 ду дх temperature T = (T, + Th)/2. In general, for a vertical cylinder with length equations g is 32.174 x (3600)2 ft/h2. The Grashof number can be interpreted physically resents the ratio of the buoyancy forces to the viscous forces in free convect role similar to that of the Reynolds number in forced convection. can be used as for a vertical plate. In English units, B is 1/(T;°F + 4 ions of these equations have been obtained by using integral methods of analy- n Section 11.1B. Results have been obtained for a vertical plate, which is the c bprct as a dimensionless nu and serves to introduce the dimensionless Grashof number discussed below. ther physical geometries the relations are too complex and empirical correla- n obtained. These are discussed in the following sections. al Convection from Various Geometries vection from vertical planes and cylinders. For an isothermal vertical surface eight L less than 1 m expressed by the following general equation: EXAMPLE 15.5-1. Natural Convection from the Vertical Wall of a A heated vertical wall 1.0 ft (0.305 m) high of an oven for baking food surface at 450°F (505.4 K) is in contact with air at 100°F (311 K). Calc heat-transfer coefficient and the heat transfer/ft (0.305 m) width of w that heat transfer for radiation will not be considered. Use English and (P3), the average natural convection heat-transfer coef- (Ľp'gBAT C, a(NGNp hL (15.5-4) N Nu Pr a 2 k k Solution: The film temperature is are constants from Table 15.5-1, NGr the Grashof number, p the density in -ISCOsity in kg/m s, AT the positive temperature difference between the wall or vice versa in K, k the thermal conductivity in W/m K, c, the heat capacity the volumetric coefficient of expansion of the fluid in 1/K [for gases B is g is 9.80665 m/s2. All the physical properties Ty +T T, 450+100 = 275° F- 505.4 +311408.2 f 2 2 2 The physical properties of air at 275°F are k 0.0198 btu/h ft °F,0.0343 p 0.0541 lbm/ft', 0.867 kg/m; Npr= 0.690; L = (0.0232 cp) x (2.4191) 0. ft h 2.32 x 10 Pa s; B = 1/408.2 2.45 x 103 K1; B 1/(460 are evaluated at the film rt Processes: Momentum, Heat, and Mass O3-1-n- 1-1m1n

-1. Natural Convection from an Oven Wall. The oven wall in Example 15.5-1 is insu- lated so that the surface temperature is 366.5 K instead of 505.4 K. Calculate the natural convection heat-transfer coefficient and the heat-transfer rate per m of width. Use both Eq. (15.5-4) and the simplified equation. (Note: Radiation is being neglected in this calculation.) Use both SI and English units. Table 15.5-1. Constants for Use with Eq. (15.5-4) for Natural Convection Boundary-layer velocity profile for natural convection heat transfer froma heated vertical plate 4047 Physical Geometry NGrNpr а т Vertical planes and cylinders [vertical height L <1 m (3 ft)] Ть <104 1.36 104 10 1 0.59 х > 10 0.13 Horizontal cylinders [diameter D used for L and D<0.20 m (0.66 ft)] y rential momentum-balance equation is written for the x andy directions for the e (dx dy 1). The driving force is the buoyancy force in the gravitational field the density difference of the fluid. The momentum balance becomes 0.49 10-5-10-3 0.71 10-3-1 1.09 1 10 1.09 (T-2 21) - (d - )8 ay2 x v (15.5-1) дх ду 10- 10 0.53 e density at the bulk temperature Tp and r the density at T. The density differ- xpressed in terms of the volumetric coefficient of expansion B and substituted (15.5-1): >109 0.13 Horizontal plates Upper surface of heated plates lower surface of heated plates Lower surface of heated plates upper surface of cooled plates 105- 2 x 107 2 x 107 -3 x 1010 0.54 or 0.14 or В 3 p(Т - Т,) (15.5-2) 10- 101 0.58 or B = 1/T. The energy-balance equation can be expressed as follows: Э'т Әт Эт (15.5-3) k + v. y рс, ay2 ду дх temperature T = (T, + Th)/2. In general, for a vertical cylinder with length equations g is 32.174 x (3600)2 ft/h2. The Grashof number can be interpreted physically resents the ratio of the buoyancy forces to the viscous forces in free convect role similar to that of the Reynolds number in forced convection. can be used as for a vertical plate. In English units, B is 1/(T;°F + 4 ions of these equations have been obtained by using integral methods of analy- n Section 11.1B. Results have been obtained for a vertical plate, which is the c bprct as a dimensionless nu and serves to introduce the dimensionless Grashof number discussed below. ther physical geometries the relations are too complex and empirical correla- n obtained. These are discussed in the following sections. al Convection from Various Geometries vection from vertical planes and cylinders. For an isothermal vertical surface eight L less than 1 m expressed by the following general equation: EXAMPLE 15.5-1. Natural Convection from the Vertical Wall of a A heated vertical wall 1.0 ft (0.305 m) high of an oven for baking food surface at 450°F (505.4 K) is in contact with air at 100°F (311 K). Calc heat-transfer coefficient and the heat transfer/ft (0.305 m) width of w that heat transfer for radiation will not be considered. Use English and (P3), the average natural convection heat-transfer coef- (Ľp'gBAT C, a(NGNp hL (15.5-4) N Nu Pr a 2 k k Solution: The film temperature is are constants from Table 15.5-1, NGr the Grashof number, p the density in -ISCOsity in kg/m s, AT the positive temperature difference between the wall or vice versa in K, k the thermal conductivity in W/m K, c, the heat capacity the volumetric coefficient of expansion of the fluid in 1/K [for gases B is g is 9.80665 m/s2. All the physical properties Ty +T T, 450+100 = 275° F- 505.4 +311408.2 f 2 2 2 The physical properties of air at 275°F are k 0.0198 btu/h ft °F,0.0343 p 0.0541 lbm/ft', 0.867 kg/m; Npr= 0.690; L = (0.0232 cp) x (2.4191) 0. ft h 2.32 x 10 Pa s; B = 1/408.2 2.45 x 103 K1; B 1/(460 are evaluated at the film rt Processes: Momentum, Heat, and Mass O3-1-n- 1-1m1n

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter11: Heat Transfer By Radiation

Section: Chapter Questions

Problem 11.50P

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Question

-1. Natural Convection from an Oven Wall. The oven wall in Example 15.5-1 is insu-
lated so that the surface temperature is 366.5 K instead of 505.4 K. Calculate the
natural convection heat-transfer coefficient and the heat-transfer rate per m of
width. Use both Eq. (15.5-4) and the simplified equation. (Note: Radiation is being
neglected in this calculation.) Use both SI and English units.

Transcribed Image Text:Table 15.5-1. Constants for Use with Eq. (15.5-4) for Natural Convection Boundary-layer velocity profile for natural convection heat transfer froma heated vertical plate 4047 Physical Geometry NGrNpr а т Vertical planes and cylinders [vertical height L <1 m (3 ft)] Ть <104 1.36 104 10 1 0.59 х > 10 0.13 Horizontal cylinders [diameter D used for L and D<0.20 m (0.66 ft)] y rential momentum-balance equation is written for the x andy directions for the e (dx dy 1). The driving force is the buoyancy force in the gravitational field the density difference of the fluid. The momentum balance becomes 0.49 10-5-10-3 0.71 10-3-1 1.09 1 10 1.09 (T-2 21) - (d - )8 ay2 x v (15.5-1) дх ду 10- 10 0.53 e density at the bulk temperature Tp and r the density at T. The density differ- xpressed in terms of the volumetric coefficient of expansion B and substituted (15.5-1): >109 0.13 Horizontal plates Upper surface of heated plates lower surface of heated plates Lower surface of heated plates upper surface of cooled plates 105- 2 x 107 2 x 107 -3 x 1010 0.54 or 0.14 or В 3 p(Т - Т,) (15.5-2) 10- 101 0.58 or B = 1/T. The energy-balance equation can be expressed as follows: Э'т Әт Эт (15.5-3) k + v. y рс, ay2 ду дх temperature T = (T, + Th)/2. In general, for a vertical cylinder with length equations g is 32.174 x (3600)2 ft/h2. The Grashof number can be interpreted physically resents the ratio of the buoyancy forces to the viscous forces in free convect role similar to that of the Reynolds number in forced convection. can be used as for a vertical plate. In English units, B is 1/(T;°F + 4 ions of these equations have been obtained by using integral methods of analy- n Section 11.1B. Results have been obtained for a vertical plate, which is the c bprct as a dimensionless nu and serves to introduce the dimensionless Grashof number discussed below. ther physical geometries the relations are too complex and empirical correla- n obtained. These are discussed in the following sections. al Convection from Various Geometries vection from vertical planes and cylinders. For an isothermal vertical surface eight L less than 1 m expressed by the following general equation: EXAMPLE 15.5-1. Natural Convection from the Vertical Wall of a A heated vertical wall 1.0 ft (0.305 m) high of an oven for baking food surface at 450°F (505.4 K) is in contact with air at 100°F (311 K). Calc heat-transfer coefficient and the heat transfer/ft (0.305 m) width of w that heat transfer for radiation will not be considered. Use English and (P3), the average natural convection heat-transfer coef- (Ľp'gBAT C, a(NGNp hL (15.5-4) N Nu Pr a 2 k k Solution: The film temperature is are constants from Table 15.5-1, NGr the Grashof number, p the density in -ISCOsity in kg/m s, AT the positive temperature difference between the wall or vice versa in K, k the thermal conductivity in W/m K, c, the heat capacity the volumetric coefficient of expansion of the fluid in 1/K [for gases B is g is 9.80665 m/s2. All the physical properties Ty +T T, 450+100 = 275° F- 505.4 +311408.2 f 2 2 2 The physical properties of air at 275°F are k 0.0198 btu/h ft °F,0.0343 p 0.0541 lbm/ft', 0.867 kg/m; Npr= 0.690; L = (0.0232 cp) x (2.4191) 0. ft h 2.32 x 10 Pa s; B = 1/408.2 2.45 x 103 K1; B 1/(460 are evaluated at the film rt Processes: Momentum, Heat, and Mass O3-1-n- 1-1m1n

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