Consider a large plane wall of thickness L, thermal conductivity k, and surface area A. The left side of the wall is subjectedto a net heat flux of q while the temperature at that surface is measured to be T,. Assuming constant thermal conductivityand no heat generation in the wall.(a) Write the differential equation (in simplest form) and the boundary conditions for steady one-dimensional heatconduction through the pipe wall.(b) Obtain a relation for the variation of temperature in the plate by solving the differential equation.T

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Answered: Consider a large plane wal of thickness…

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

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Diagram of the problem, necessary formulas, clearance and numerical solution Two heat reservoirs with respective temperatures of 325 K and 275 K are brought into contact by an iron rod 200 cm long and 24 cm2 in cross section. Calculate the heat flux between the reservoirs when the system reaches its steady state. The thermal conductivity of iron at 25 ◦C is 79.5 W/m K.
Diagram of the problem, necessary formulas, clearance and numerical solution Two heat reservoirs with respective temperatures of 325 K and 275 K are brought into contact by an iron rod 200 cm long and 24 cm2 in cross section. Calculate the heat flux between the reservoirs when the system reaches its steady state. The thermal conductivity of iron at 25 ◦C is 79.5 W/m K.
Derive the one-dimensional heat conduction equation for a sphere.
Consider a single fin with circular cross-section as shown in the figure below. Geometrical parameters of the fin : • r = 4 mm • L = 10 cm Fin material properties: • Fin thermal conductivity: k = 200 W/mK Thermal boundary conditions: • Base temperature of the fin: Tbase = 80°C • Air temperature: Tair = 25°C • Convective heat transfer coefficient : h= 10 W/m²K Tbase L/4 T1 L/2 L/4 T2 a) Express the heat transfer problem through the fin as a thermal resistance network, derive equations for the unknown temperatures T, and T₂ representing the average temperatures for the control volumes shown in the figure above. b) Express the equations derived in a) in the form of AT = b where T: unknown temperature vector and A: coefficient matrix and solve for T₁ and T₂ c) Now, imagine a very thin wire is located at the center of the fin. The electrical current that goes through the wire generates heat uniformly along the length of the wire. The wire generates heat q = 2 W/m. Update the energy balance…
Diagram of the problem, necessary formulas, clearance and numerical solution Two heat reservoirs with respective temperatures of 325 K and 275 K are brought into contact by an iron rod 200 cm long and 24 cm2 in cross section. Calculate the heat flux between the reservoirs when the system reaches its steady state. The thermal conductivity of iron at 25 ◦C is 79.5 W/m K.
An insulated steam pipe is covered with two layers of insulation as seen figure below. Draw the thermal resistance network. Develop a formula to calculate the heat transfer rate per unit length of the pipe. How can you determine the temperature difference AT across the pipe wall and second insulation layer. T, = 250°C. Ins.2 Ins. 1 Pipe r3 -T, = 20°C
Consider a large plane wali of thickness L03 m thermal conductivity k25 /m K, end surfece aree A 12 m The left side of the well ot x=O is subjected to a net heat flux of go760 W/m while the temperature at that surfece is measured to be T 80°C Assuming constant thermal conductivity and no heat generation in the wall, ovaluate the temperature of the right surface of the wall at xEL The temperature of the right surfaoe of the wall at x Lis
The lining of box-type fumace is made up of a refractory layer and steel plate as shown in the figure. Steady state temperature at the surface of the refractory is 1273 K and that at the outer steel surface is 473 K. If the steady state heat flux through the refractory-steel plate composite is 1600 W/m², and heat flow is along x-direction only, the thermal contact resistance (m² K/W) between refractory and steel is_ steel Refractory 1273K Furnace 473K Ambient Given data: Thermal conductivity of refractory = 1.2 W/m-K Thickness of refractory lining = 80mm Thermal conductivity of steel = 32 W/mK Thickness of steel plate = 4mm
Two approaches used in development of the thermal resistance network in the x-direction for multi-dimensional problems are to assume any plane wall normal to the x-axis to be isothermal and to assume any plane parallel to the x-axis to be adiabatic. True or False True False
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