Determine the temperature distribution (nodal temperatures) of the structure shown in the figure using two equal-length, linear finite elements with the cross-sectional area of 1 m². The thermal conductivity is 10 W/m/°C. The left side is maintained at 300 °C. The right side is subjected to heat loss by convection with h = 1 W/m²/°C and T₁ = 30 °C. All other sides are insulated. T= 300 °C T₁ Insulated 20 m T₂ T3 T₁= 30 °C

Determine the temperature distribution (nodal temperatures) of the structure shown in the figure using two equal-length, linear finite elements with the cross-sectional area of 1 m². The thermal conductivity is 10 W/m/°C. The left side is maintained at 300 °C. The right side is subjected to heat loss by convection with h = 1 W/m²/°C and T₁ = 30 °C. All other sides are insulated. T= 300 °C T₁ Insulated 20 m T₂ T3 T₁= 30 °C

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.

Chapter1: Basic Modes Of Heat Transfer

Section: Chapter Questions

Problem 1.63P: 1.63 Liquid oxygen (LOX) for the space shuttle is stored at 90 K prior to launch in a spherical...

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.
2-88 A 1.5-mm-diameter stainless-steel rod [k = 19 W/m.°C] protrudes from a wall maintained at 45°C. The rod is 12 mm long, and the convection coefficient is 500 W/m² . °C. The environment temperature is 20°C. Calculate the temperature of the tip of the rod. Repeat the calculation for h = 200 and 1500 W/m² . °C.
The compartment below is used as a freezer of refrigerator compartment. Inner wall is at -15 C and outer wall is at 25 C. Insulator with a thermal conductivity of 0.035 W/(mK) is used to prevent the heat losses from the compartment. The shape is in square form with a side of 1.2 m and unit width into the page. Determine the thickness of the insulator if the compartment heat load is 700 W? * inner wall outer wall insulating material
The compartment below is used as a freezer of refrigerator compartment. Inner wall is at -15 C and outer wall is at 25 C. Insulator with a thermal conductivity of 0.035 W/(mK) is used to prevent the heat losses from the compartment. The shape is in square form with a side of 1.2 m and unit width into the page. Determine the thickness of the insulator if the compartment heat load is 700 W? * inner wall outer wall insulating material 5 cm O 9.6 mm 4.2 cm none
Consider a copper plate that has dimensions of 3 cm x 3 cm x 7 cm (length, width, and thickness, respectively). As shown in the following figure, the copper plate is exposed to a thermal energy source that puts out 126 J every second. The density of copper is 8,900 kg/m³. Assume there is no heat loss to the surrounding block. 126 J Copper Insulation Ⓡ What is the specific heat of copper (in J/(kg K))? J/(kg. K) What is the mass of the copper plate (in kg)? kg How much energy (in J) will be consumed during 11 seconds? J Determine the temperature rise (in K) in the plate after 11 seconds.
As shown in the sketh below, a steam pipe of 0.12-m inside diameter is insulated with a layer of calcium silicate. "2. Ta2} 1. Ta,1} Steam Insulation (a) If the insulation is 10 mm thick and its inner and outer surfaces are maintained at T, = 800 K and Ta = 490 K. respectively,. what is the rate of heat loss per unit length (q) of the pipe, in W/m? (b) Determine the rate of heat loss per unit length (d), in W/m, and outer surface temperature T,2, in K, for the steam pipe with the Inner surface temperature fixed at T = 800 K, inner radius = 0.06 m, and outer radius n = 0.18 m. The outer surface is exposed to an airflow (T 25°C) that maintains a convection coefficient of h = 25 W/m2-K and to large surroundings for which Tur = T, = 25°C. The surface emissivity of calcium silicate is approximately 0.8.
A Multi-layer wall of a building is shown in the following figure. The thermal conductivity of A, B, C, D, and E are: 30, 5, 1.67, 10.5, 6 W/m k, respectively. Assume one dimentional heat transfer. The area of A = D = E =4 m?, and B = C= 2 m². The thickness of each layer is 10 cm. The temperature of surface A is 25 °C, and the temperature of surface E is 38 °C. Calculate the heat transfer rate through the wall. B A D E C
#m 3 E D C F3 $ 4 R F Ac = 1m² V Too,1=1 K h₁ = 1 W/m²K (5) 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. Heat generation inside the wall is q=1W/m³. You may assume 1-D heat transfer, steady state condition, and neglect any thermal contact resistance. Find T(x). 44 % 5 Q Search F5 T G T₁ B x=0 * A 6 q=1 W/m³ k= 1W/mK L=1m F6 Y H F7 & 7 T₂ x= 1 m U N Top 2 = 1 K h₂=1 W/m²K PrtScn F8 8 Home M F9 ( 9 K End F10 0 L PgUp
1. Temperatures are measured at the left-hand face and at a point 4 cm from the left-hand face of the planar wall shown in the figure below. These temperatures are T₁ = 45.3 °C and T* = 21.2 °C. The heat flow through the planar wall is steady and one dimensional. What is the value of T2 at the right-hand surface of the wall? TI T* 4 cm 10 cm T2
Both ends of a 32 cm long rod are maintained a constant temperature of 100 °C. Dimensions and thermal parameters of the rod are as follows: Diameter D = 2 cm Convection coefficient h = 10 W/m2K Ambient temperature T¥ = 20 °C Thermal conductivity k = 10 W/mK What is the midpoint temperature of the rod?
Three (3) bricks, specifically A, B, and C were arranged horizontally in such a way that it can be illustrated as a sandwich panel. Consider the system to be in series and in the order of Brick A, Brick B and Brick C. The outside surface temperature of Brick A is 1,500℃ and 150 ℃ for the outside surface of Brick C. The thermal conductivities for Brick A, Brick B and Brick C, are 2 ?/? °? , 0.50 ?/? °? , 60 ?/? °?. The thickness of Brick A and Brick C are 50 cm and 22 cm. The rate of heat transfer per unit area is 1,000 ?/?2 . Determine the following: The thickness of Brick B in the unit of mm. Assume that all the conditions were retain except that the thickness of Brick B was increased to 800 mm, what is the new value for the rate of heat transfer per unit area in ???/ℎ? . ??2 please explain the principles to solve this
The composite wall of an oven consists of three materials, two of which are ofknown thermal conductivity, kA = 25 W/m ⋅ K and kC = 60 W/m ⋅ K, and knownthickness, LA = 0.40 m and LC = 0.20 m. The third material, B, which is sandwichedbetween materials A and C, is of known thickness, LB = 0.20 m, but unknownthermal conductivity kB. Under steady-state operating conditions, measurementsreveal an outer surface temperature of Ts,o = 20°C, an inner surface temperature ofTs,i = 600°C, and an oven air temperature of T∞ = 800°C. The inside convection coefficient h is known to be 25 W/m2 ⋅K. Neglecting convection transfer effect,what is the value of kB?