A brass rod (k = 133 W/m-K) with a diameter of 5 mm and a length...
A brass rod (k = 133 W/m-K) with a diameter of 5 mm and a length of 100 mm is used to enhance heat transfer from a surface which is maintained at 200 C. The cylindrical surface of the rod is exposed to a convection environment with h = 30 W/m2-K and an ambient temperature of 20 C.
a) Calculate the heat convected away from the rod.
b) Calculate the temperature 50 mm from the wall.
c) Plot the temperature of the rod from the base to the tip.
d) Assume you are now allowed to vary the rod length and you wish to minimize the weight of the rod while maximizing the heat transfer from the rod. What rod length would you use?
Homework Answers
A long cylindrical rod of diameter 220 mm with thermal conductivity 0.5 W/m-K expe riences uniform...
A long cylindrical rod of diameter 220 mm with thermal conductivity 0.5 W/m-K expe riences uniform volumetric heat generation of 25,000 W/m3. The rod is encapsulated by a circular sleeve having 7 W/m K. The outer surface of the sleeve is exposed to cross flow of air at 25°C with a convection coefficient of 25 W/m2-K. Find the temperature at the interface between the rod and sleeve, and on the outer surface. an outer diameter of 410 mm and thermal...
G4 Problem Statement: Circular fins of uniform cross section, with diameter of 14 mm and length 7...
G4 Problem Statement: Circular fins of uniform cross section, with diameter of 14 mm and length 70 mm are attached to the wall with surface temperature o C. The fin is made of material with thermal conductivity of 210 W/mk, and exposed to an ambient air condition of 24 °C and the convection heat transfer coefficient of 190 W/m2k. f 300 1- Plot the temperature variation for the following boundary conditions a- Infinitely long fin b- Adiabatic fin tip c-...
A rod of 10-mm diameter and 250-mm length has one end maintained at 100°C
A rod of 10-mm diameter and 250-mm length has one end maintained at 100°C. The surface of the rod experiences free convection with the ambient air at 25°C and a convection coefficient that depends on the difference between the temperature of the surface and the ambient air. Specifically, the coefficient is prescribed by a correlation of the form, hfc = 2.89[0.6 +0.624(T - T∞)1/6]2, where the units are hfc (W/m².K) and T (K). The surface of the rod has an...
A very long rod of 5-mm diameter and uniform thermal conductivity k = 25 W/m-K is subjected to a heat treatment process
A very long rod of 5-mm diameter and uniform thermal conductivity k = 25 W/m-K is subjected to a heat treatment process. The center, 30-mm-long portion of the rod within the induction heating coil experiences uniform volumetric heat generation of 7.5 x 106 W/m3. The unheated portions of the rod, which protrude from the heating coil on either side, experience convection with the ambient air at T∞ = 20 °C and h = 10 W/m2K. Assume that there is no convection...
Consider a rectangular fin (k = 180 W/m-K) of length L =10 mm, thickness i =1...
Consider a rectangular fin (k = 180 W/m-K) of length L =10 mm, thickness i =1 mm, and width w» t. The base temperature of the finis Ty = 150°C, and the finis exposed to a fluid of temperature T, =25°C. Assuming a uniform convection coefficient of h = 110 W/m2.K over the entire fin surface, determine the fin heat transfer rate per unit width 4; efficiency ng: effectiveness es, thermal resistance per unit width and the tip temperature T...
A rod of diameter D = 25 mm and thermal conductivity of 60 W/m K protrudes from a furnace with a wall temperature of 200°C.
A rod of diameter D = 25 mm and thermal conductivity of 60 W/m K protrudes from a furnace with a wall temperature of 200°C. The rod is welded to the furnace wall and is used as a hangar for instrumentation cables. To avoid damaging the cables, the surface temperature of last 100 mm of the rod must be kept below 100°C. The ambient air temperature is 25°C and the convection coefficient is 15 W/m2K. (a) Write the finite-difference equation for...
1. A fin with a diameter of 5 mm, a length of 100 mm, and a...
1. A fin with a diameter of 5 mm, a length of 100 mm, and a thermal conductivity of 133 w/m"C is attached to a base plate, which is at 200 oC. The fin is surrounded by a fluid at 20 ° C, and has a convection heat transfer coefficient of 30 W/(m2. c). 1.1 compute the temperature of the rod at 20 mm, 60 mm, and 100 mm points from the base 1.2 compute the total heat transfer rate...
1. A fin with a diameter of 5 mm, a length of 100 mm, and a...
1. A fin with a diameter of 5 mm, a length of 100 mm, and a thermal conductivity of 133 w/m.oC is attached to a base plate, which is at 200 oC. The fin is surrounded by a fluid at 200 C, and has a convection heat transfer coefficient of 30 W/(m·℃). 1.1 compute the temperature of the rod at 20 mm, 60 mm, and 100 mm points from the base 1.2 compute the total heat transfer rate from the...
a rectangular fin (k= 235w/m*K) is attached to a wall and has a length of 5...
a rectangular fin (k= 235w/m*K) is attached to a wall and has a length of 5 cm, a width of 10 cm, and a thickness of 5 mm. the surface temperature of the wall is 350 degrees Celcius and the ambient air is 25 degrees celcius. what is the efficiency, the heat transfer rate, and the fin effectiveness? assume an adiabatic fin tip condition and a convection heat transfer coefficient of 154 W/m^2 * K
A brass rod, 1 cm in diameter and 15 cm long, with a tip subject to...
A brass rod, 1 cm in diameter and 15 cm long, with a tip subject to a breeze with a convection coefficient of 68 W/m2 K in a room where the ambient air temperature is 23°C. The base is 79°C and the tip is designed to maintain a constant temperature of 29°C. The manufacturer finds that the thermal conductivity, in units of W/m*K, to be k(T) 43*In(T)- 128, where T is in units of Kelvin. Plot the temperature profile for...
A long cylindrical rod of diameter 220 mm with thermal conductivity 0.5 W/m-K expe riences uniform volumetric heat generation of 25,000 W/m3. The rod is encapsulated by a circular sleeve having 7 W/m K. The outer surface of the sleeve is exposed to cross flow of air at 25°C with a convection coefficient of 25 W/m2-K. Find the temperature at the interface between the rod and sleeve, and on the outer surface. an outer diameter of 410 mm and thermal...
G4 Problem Statement: Circular fins of uniform cross section, with diameter of 14 mm and length 70 mm are attached to the wall with surface temperature o C. The fin is made of material with thermal conductivity of 210 W/mk, and exposed to an ambient air condition of 24 °C and the convection heat transfer coefficient of 190 W/m2k. f 300 1- Plot the temperature variation for the following boundary conditions a- Infinitely long fin b- Adiabatic fin tip c-...
Consider a rectangular fin (k = 180 W/m-K) of length L =10 mm, thickness i =1 mm, and width w» t. The base temperature of the finis Ty = 150°C, and the finis exposed to a fluid of temperature T, =25°C. Assuming a uniform convection coefficient of h = 110 W/m2.K over the entire fin surface, determine the fin heat transfer rate per unit width 4; efficiency ng: effectiveness es, thermal resistance per unit width and the tip temperature T...
1. A fin with a diameter of 5 mm, a length of 100 mm, and a thermal conductivity of 133 w/m"C is attached to a base plate, which is at 200 oC. The fin is surrounded by a fluid at 20 ° C, and has a convection heat transfer coefficient of 30 W/(m2. c). 1.1 compute the temperature of the rod at 20 mm, 60 mm, and 100 mm points from the base 1.2 compute the total heat transfer rate...
1. A fin with a diameter of 5 mm, a length of 100 mm, and a thermal conductivity of 133 w/m.oC is attached to a base plate, which is at 200 oC. The fin is surrounded by a fluid at 200 C, and has a convection heat transfer coefficient of 30 W/(m·℃). 1.1 compute the temperature of the rod at 20 mm, 60 mm, and 100 mm points from the base 1.2 compute the total heat transfer rate from the...
A brass rod, 1 cm in diameter and 15 cm long, with a tip subject to a breeze with a convection coefficient of 68 W/m2 K in a room where the ambient air temperature is 23°C. The base is 79°C and the tip is designed to maintain a constant temperature of 29°C. The manufacturer finds that the thermal conductivity, in units of W/m*K, to be k(T) 43*In(T)- 128, where T is in units of Kelvin. Plot the temperature profile for...
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