Answered: Temperature profile in a wall (t = 0.1…

Temperature profile in a wall (t = 0.1 m, k = 75 W/m/C) is given by T=-15x + 70. Determine heat flux across the wall and temperature at the edges of wall.

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.

Chapter2: Steady Heat Conduction

Section: Chapter Questions

Problem 2.54P

See similar textbooks

Similar questions

1.10 A heat flux meter at the outer (cold) wall of a concrete building indicates that the heat loss through a wall of 10-cm thickness is . If a thermocouple at the inner surface of the wall indicates a temperature of 22°C while another at the outer surface shows 6°C, calculate the thermal conductivity of the concrete and compare your result with the value in Appendix 2, Table 11.
3.17 A 1.4-kg aluminum household iron has a 500-W heating element. The surface area is . The ambient temperature is 21°C, and the surface heat transfer coefficient is . How long after the iron is plugged in does its temperature reach 104°C?
2.30 An electrical heater capable of generating 10,000 W is to be designed. The heating element is to be a stainless steel wire having an electrical resistivity of ohm-centimeter. The operating temperature of the stainless steel is to be no more than 1260°C. The heat transfer coefficient at the outer surface is expected to be no less than in a medium whose maximum temperature is 93°C. A transformer capable of delivering current at 9 and 12 V is available. Determine a suitable size for the wire, the current required, and discuss what effect a reduction in the heat transfer coefficient would have. (Hint: Demonstrate first that the temperature drop between the center and the surface of the wire is independent of the wire diameter, and determine its value.)
Q1: Consider a large plane wall of thickness L = 0.4 m, thermal conductivity k=2.3 W/m °C, and surface area A= 20 m2. The left side of the wall at x= 0 is subjected of T1 = 80°C. while the right side losses heated by convection to the surrounding air at T-15 °C with a heat transfer coefficient of h=24 W/m2 C. Assuming constant thermal conductivity and no heat generation in the wall, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the wall, (b) obtain a relation for the variation of temperature in the wall by solving the differential equation, and (c) evaluate the rate of heat transfer through the wall Ans : (c) 6030 W
Q₁: Consider a large plane wall of thickness L = 0.4 m, thermal conductivity k-2.3 W/m °C, and surface area A= 20 m². The left side of the wall at x= 0 is subjected of T1 = 80°C. while the right side losses heated by convection to the surrounding air at T-15 °C with a heat transfer coefficient of h=24 W/m² °C. Assuming constant thermal conductivity and no heat generation in the wall, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the wall, (b) obtain a relation for the variation of temperature in the wall by solving the differential equation, and (c) evaluate the rate of heat transfer through the wall Ans: (c) 6030 W
Q: A large plane wall of thickness (L= 0.3 m), thermal conductivity (k = 40 W/m-°C), and surface area 0.4 m2. The left side of the wall is maintained at a constant temperature of 70°C while the right side loses heat to the surrounding air with heat flux q' expressed by: 1200k q = k+20L A- Find a relation to determine the variation of temperature in the wall. B- Determine the rate of heat transfer through the wall. C- Determine the temperature at the right side of the wall. wall T1= 70 °C L= 0.3m
Q1: Consider one-dimensional conduction in a plane composite wall (1m x Im) as shown in the figure below. The outer surfaces are exposed to a fluid at 25°C and a convection heat transfer coefficient of 1000 W/m2.K. The middle wall B experiences uniform heat generation dB, while there is no generation in walls A and C. The temperatures at the interfaces are T1=261°C and T2=211°C. Assuming negligible contact resistance at the interfaces: A) Determine the outside surface temperature of walls A and C? B) Compute the value of q;? T2 T h 25 241 A B -2LB Lc .03 Ta kA = 25 W/m-K kc = 50 W/m-K LA = 30 mm Lg = 30 mm Lc = 20 mm %3D
Problems within the wall is T(x) = a(L- ) +b where a = 10°C/m2 and b 30°C, what is the thermal con- ductivity of the wall? What is the value of the convec- tion heat transfer coefficient, h? 2.11 Consider steady-state conditions for one-dimensional conduction in a plane wall having a thermal conductiv- ity k 50 W/m K and a thickness L = 0.25 m, with no internal heat generation. 2. T2 T1 L Determine the heat flux and the unknown quantity for each case and sketch the temperature distribution, indi- cating the direction of the heat flux. 2 Case TC) dTldx (K/m) T2(°C) 1 50 -20 2 -30 - 10 3 70 160 4 40 -80 5 30 200
A copper tube (k-75 W/m*K) with inner radius r;-2 cm and outer radius r2-2.05 cm is used to transport a low-temperature refrigerant having an mean temperature T-350 K and convection coefficient h=50 W/m2*K. The tube is covered with insulation having inner radius r,-2.05 cm and outer radius r-4.6 cm. The conductivity of the insulation is k=0.05 W/m*K. The air on the outside of the insulation at T=400 K creates an verage convection coefficient of h,=16 W/m2*K. T a. Sketch the equivalent thermal circuit of the system and express all resistances in terms of relevant variables. Assume that T; and To are uniform along the length of the pipe. b. Use a thermal circuit to write an expression for the rate of heat transfer for a length of pipe L=4 meters in terms of the variables defined above.
A steel pipe with heat transfer coefficient of 42 W/mK contains flowing water. The outer diameter of the pipe is 90 mm and the wall thickness is 3mm. Calculate: i. The heat loss by convection and conduction per meter length of un-insulated pipe when the water temperature is 14°C, the outside air temperature is -10°C, the water side heat transfer coefficient is 30 KW/m^2K and the outside heat transfer coefficient is 20 KW/m^2K. ii. Calculate the corresponding heat loss when the pipe is lagged with insulation having an outer diameter of 200 mm, and thermal conductivity of K = 0.05 W/mK
You are designing a 3m x 3m floor with radiant heating. The floor has 12 parallel pex pipes (k = 40 W/mK) of L = 3m, OD = 25mm and ID = 20mm. Hot water (TInfintiy 1 = 90oC, h = 200 W/m2K) runs through the pipes continuously. The surface below the pipes is perfectly insulated. Above the pipes, there is a 3mm layer of bonding material (? = 12 W/mK) and a 9mm layer of tile (k = 2 W/mK). Above the tile, there is air (TInfinity 2 = 25oC, h = 20 W/m2K). Properties of Air: k = 0.025 W/mK, Pr = 0.72, v = 1.847 x 10−5, u = 16.84 x 10−6, p = 1.2 kg/m3, B = 1/Tf (ideal gas), Hint: Assume that the “layer” of pipe starts at the center point (e.g. for conduction purposes, the pipe is OD divided by 2 thick). For convection, consider the entire pipe surface. a) What is the total heat rate entering the room above the floor? b) What is the temperature of the top of the tile?
A heating cube with a size of 60 x 60 cm on the inside is made of refractory brick (k=1.04 watt/(m.°c) with a wall thickness of 12 cm. The inside of the kitchen is kept at 450°c, and the temperature on the outside is 50%c, calculate the heat loss through the wall.