H.W.: Q1: Consider steady two-dimensional heat transfer in a long solid body whose cross section is given in the figure. The temperatures at the selected nodes and the thermal conditions at the boundaries are as shown. The thermal conductivity of the body is k = 45 W/m - °C, and heat is generated in the body uniformly at a rate of g = 6 x 106 W/m3. Using the finite difference method with a mesh size of Ax = 4y = 5.0 cm, determine (a) the temperatures at nodes 1, 2, and 3 and (b) the rate of heat loss from the bottom surface through a 1-m-long section of the body. 200°C 5 cm 5 cm g=6x 10 W/m² 260 3 240 305 290 Insulation O Convection T₂= 20°C, h = 50 W/m². C 350°C 325

H.W.: Q1: Consider steady two-dimensional heat transfer in a long solid body whose cross section is given in the figure. The temperatures at the selected nodes and the thermal conditions at the boundaries are as shown. The thermal conductivity of the body is k = 45 W/m - °C, and heat is generated in the body uniformly at a rate of g = 6 x 106 W/m3. Using the finite difference method with a mesh size of Ax = 4y = 5.0 cm, determine (a) the temperatures at nodes 1, 2, and 3 and (b) the rate of heat loss from the bottom surface through a 1-m-long section of the body. 200°C 5 cm 5 cm g=6x 10 W/m² 260 3 240 305 290 Insulation O Convection T₂= 20°C, h = 50 W/m². C 350°C 325

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

solve by finite element method
A pipe with 8 cm internal diameter, 9 cm outer diameter, 2 meter long, thermal conductivity 30W/mK is insulated by glass wool material with which thermal conductivity 0,05W/mK, thickness 4 cm. Internal surface temperature of the pipe T1 is 80°C, surrounding temperature where pipe is located is 20°C, convection heat transfer constant on outer surface of insulation is 25W/m?K. Kpo 30W/mk T.= 20°C h. = 25W/MK 4cm K= 0,05W/mK a. Detemine the heat loss from the pipe to surrounding (W)? b. What is temperature of the surface between glass wooden and pipe (T2)? c. What is critical insulation radius for pipe? Is insulation on the pipe succesful? Explain
One of the strengths of numerical methods is their ability to handle complex boundary conditions. In the sketch, the boundary condition changes from specified heat flux ′′ qs (into the domain) to convection, at the location of the node (m, n). Write the steady-state, two- dimensional finite difference equation at this node.
Consider the square channel shown in the sketch operating under steady state condition. The inner surface of the channel is at a uniform temperature of 600 K and the outer surface is at a uniform temperature of 300 K. From a symmetrical elemental of the channel, a two-dimensional grid has been constructed as in the right figure below. The points are spaced by equal distance. Tout = 300 K k = 1 W/m-K T = 600 K (a) The heat transfer from inside to outside is only by conduction across the channel wall. Beginning with properly defined control volumes, derive the finite difference equations for locations 123. You can also use (n, m) to represent row and column. For example, location Dis (3, 3), location is (3,1), and location 3 is (3,5). (hint: I have already put a control volume around this locations with dashed boarder.) (b) Please use excel to construct the tables of temperatures and finite difference. Solve for the temperatures of each locations. Print out the tables in the spread…
I need the answer as soon as possible
Heat transfer
A long solid bar (k=30 W/m.K) of rectangular cross section is exposed to a constant heat flux on one surface and is subjected to convection on the opposite surface. The other two surfaces are maintained at constant temperatures as shown. Using a uniform mesh size Ax=Ay=1 cm, 6.1 express the finite difference equations for nodes 1, 2 and 3, and 6.2 solve for the nodal temperatures. 100 °C q=5,000 W/m² 300 °C ΔΧ 3 ду h = 150 W/m²K Too = 25 °C
Need help.
2. The slab shown is embedded in insulating materials on five sides, while the front face experiences convection off its face. Heat is generated inside the material by an exothermic reaction equal to 1.0 kW/m'. The thermal conductivity of the slab is 0.2 W/mk. a. Simplify the heat conduction equation and integrate the resulting ID steady form of to find the temperature distribution of the slab, T(x). b. Present the temperature of the front and back faces of the slab. n-20- 10 cm IT- 25°C) 100 cm 100 cm
10.The layout of a wall and the heat transfer parameters are shown in the figure below. Find the internal temperature of the wall, T₁. (o= 5.67 x 10-8 W/m²K4 ) (Ans: 569.5K) T1 k=1.1 W/m.K Icond L=0.12m T2=373K x=0.7 grad Iconv Tsur Air Tex = 300K h = = 290K : 18 W/m².K
1