Q3: A steam pipe of outside temperature of (T = 500 °C) and outside radius of(R. 100 mm) is insulated with three layers of thermal insulation materials of equal thicknessof (t 100 mm), as shown in Fig. Q.3. The thermal insulation is exposed to an ambienttemperature of (T = 20 °C). If the thermal conductivity of the thermal insulation layers are(K₁ = 0.4 W/m. K), (K₂ = 0.25 W/m. K) and (K3 = 0.1 W/m. K) and the convection heattransfer coefficient is (h = 40 W/m2.K). Find the temperature distribution along the three layersof thermal insulation materials using the FVM with a uniform grid of (Ar = 50 mm). The one-dimensional steady state energy equation for this problem is given as follows:1 dr dr(rk:dT= 0h-40 W/m².KT-20°C7,500 CFig. Q.3K₁ =0.4 W/m.KK₁ = 0.25 W/m.KK₁ 0.1 W/m.K

Here's a step-by-step solution for finding the temperature distribution along the three layers of…

Answered: Q3: A steam pipe of outside temperature…

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 2.24P

See similar textbooks

Similar questions

1.3 A furnace wall is to be constructed of brick having standard dimensions of Two kinds of material are available. One has a maximum usable temperature of 1040°C and a thermal conductivity of 1.7 W/(m K), and the other has a maximum temperature limit of 870°C and a thermal conductivity of 0.85 W/(m K). The bricks have the same cost and are laid in any manner, but we wish to design the most economical wall for a furnace with a temperature of 1040°C on the hot side and 200°C on the cold side. If the maximum amount of heat transfer permissible is 950 , determine the most economical arrangement using the available bricks.
As a designer working for a major electric appliance manufacturer, you are required to estimate the amount of fiberglass insulation packing (k = 0.035 W/m K) that is needed for a kitchen oven shown in the figure below. The fiberglass layer is to be sandwiched between a 2-mm-thick aluminum cladding plate on the outside and a 5-mm-thick stainless steel plate on the inside that forms the core of the oven. The insulation thickness is such that the outside cladding temperature does not exceed 40C when the temperature at the inside surface of the oven is 300C. Also, the air temperature in the kitchen varies from 15Cto33C, and the average heat transfer coefficient between the outer surface of the oven and air is estimated to be 12.0W/m2K. Determine the thickness of the fiberglass insulation that is required for these conditions. What would be the outer surface temperature when the inside surface of the oven is at 475C?
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.
1.2 The weight of the insulation in a spacecraft may be more important than the space required. Show analytically that the lightest insulation for a plane wall with a specified thermal resistance is the insulation that has the smallest product of density times thermal conductivity.
1.37 Mild steel nails were driven through a solid wood wall consisting of two layers, each 2.5-cm thick, for reinforcement. If the total cross-sectional area of the nails is 0.5% of the wall area, determine the unit thermal conductance of the composite wall and the percent of the total heat flow that passes through the nails when the temperature difference across the wall is 25°C. Neglect contact resistance between the wood layers.
Homework O H.W. 1: The walls of a refrigerator are typically constructed by sandwiching a layer of insulation between sheet metal panels. Consider a wall made from fiberglass insulation of thermal conductivity k; = 0.046 W/m.K and thickness L, = 50 mm and steel panels, each of thermal conductivity k, = 60 W/m.K and thickness L, = 3 mm. If the wall separates refrigerated air at T = 4 C from ambient air at T,. = 25 C, what is the heat gain per unit surface area? Coefficients associated with natural convection at the inner and outer surfaces may be approximated as h, = h, = 5 W/m?.K. %3D %3D L; = 0.050 m K K Lo = 0.003 m Refrigerated air Ambient air Too.i = 4°C hi = 5 W/m2-K To,o = 25°C ho = 5 W/m2-K %3D Panel (2) kp = 60 W/m-K Insulation k; = 0.046 W/m-K 22 Warith Alanbiyaa (Dr. ALI M) Heat Transfer Page 11 of
Q2. Steam pumped through a long- insulated pipe at a temperature of T= 500 K and provides a convection coefficient of h, = 100 W/m?K at the inner surface of the pipe. The inner and outer radius of the pipe and insulation material are r1 = 10, r2 = 12 and r3 = 17 cm, respectively. The thermal conductivity of the pipe is 100 W/mK. The insulation material is glass fiber and its outer surface is exposed to ambient air at 300 K. If the ambient air provides a convection coefficient of ho = 20 Internal flow Ambient air W/m?K, determine the followings: a. What are the thermal resistance coefficients for convections and conductions b. What is the heat transfer rate per unit length of the pipe c. If the pipe is 30 m long, what will be total heat transfer rate from the pipe. t00 noints)
3. A cylindrical pipe of negligible thickness holding a hot fluid at 140°C and having an outer diameter of 0.4 m is insulated with three layers of each 50 mm thick insulation of k₁ = 0.02: k2 = 0.06 and k3 = 0.16 W/m-K (starting from inside). The outside surface temperature is 30°C. Solve for the value of T2 (°C). • show conversions, units, and box in your final answers
Quiz #2 (Homework) Problem: A plane wall 6.0 cm thick generates heat internally at the rate of 0.3 MW/m³3. One side of the wall is insulated, and the other side is exposed to an environment at 93°C. The convection heat-transfer coefficient between the wall and the environment is 570 W/m² °C. The thermal conductivity of the wall is 21 W/m.°C. (a) Find the temperature distribution in the wall. (b) Sketch the temperature distribution in the wall and fluid environment adjacent to the wall. (c) What is the maximum temperature in the wall? (d) Calculate the heat transfer rate at wall surface. (e) Is the heat transfer rate equal at each point in the wall? Given : Solution:
4x F2 # 3 E 4, F3 54 $ R F4 Ac = 1m² ▬ H DII x= 1 m (4) Consider a wall (as shown above) of thickness L-1 m and thermal conductivity k-1 W/m-K. The left (x=0) and the right (x=1 m) surfaces of the wall are subject to convection with a convectional heat transfer coefficient h= 1 W/m²K and an ambient temperature T. 1 K. There is no heat generation inside the wall. You may assume 1-D heat transfer, steady state condition, and neglect any thermal contact resistance. Find T(x). % To,1 = 1 K h₁ = 1 W/m²K 5 Q Search F5 T T₁ A 6 x=0 F6 à = 0 W/m³ k= 1W/mK L=1m Y 994 F7 & 7 T₂ U Ton2 = 1 K h₂ = 1 W/m²K1 PrtScn F8 Page of 7 ) 0 PgUp F11 P
Q1/ A thick wall consists two layers of Gypsum, insulation and brick as shown in figure below. The ambient temperature is 20 °C and heat transfer coefficient is 5 W/m2. K in the left side. The surface temperature of right side is 45 °C. find the heat losses per meter length. What will happen if the insulation's thickness * .increases by 25% Gypsum k = 0.04W/m. K T = 45 °C h=5 W/m'. K T. = 20 °C 5 cm Insulation k = 0.04W/m. K Brick k = 0.69 W/m. K
Q1. Consider a plane wall (thermal conductivity, k = 0.8 W/mK, and thickness, fb1 = 100 mm) of a house as shown in Fig. Q1(a). The outer surface of the wall is exposed to solar radiation and has an absorptivity of a = 0.5 for solar energy, or=600 W/m². The temperature of the interior of the house is maintained at T1 = 25 °C, while the ambient air temperature outside remains at T2 = 5 °C. The sky, the ground and the surfaces of the surrounding structures at this location can be modelled as a surface at an effective temperature of Tsky = 255 K for radiation exchange on the outer surface. The radiation exchange inside the house is negligible. The convection heat transfer coefficients on the inner and the outer surfaces of the wall are h₁ = 5 W/m²-K and /1₂ = 20 W/m².K, respectively. The emissivity of the outer surface is = 0.9. T1 = 25 °C Ţ₁ Too1 = 25 °C T₁ k 100 mm Fig. Q1(a) Assuming the heat transfer through the wall to be steady and one-dimensional: (a) Solve the steady 1D heat…

SEE MORE QUESTIONS

Recommended textbooks for you

Principles of Heat Transfer (Activate Learning wi…

Mechanical Engineering

ISBN:

9781305387102

Author:

Kreith, Frank; Manglik, Raj M.

Publisher:

Cengage Learning