Problem # 2 Heat Generation in a Solid A long homogeneous resistance wire of radius ro = 5 mm is being used to heat the air in a room by the passage of electric current. Heat is generated in the wire uniformly at a rate of g = 5 × 107 W/m³ as a result of resistance heating. If the temperature of the outer surface of the wire remains at 180°C, determine the temperature at r = 2 mm after steady operation conditions are reached. Take the thermal conductivity of the wire to be k = 8 W/m · °C. Answer: 212.8°C %3D 180°C Resistance wire

Problem # 2 Heat Generation in a Solid A long homogeneous resistance wire of radius ro = 5 mm is being used to heat the air in a room by the passage of electric current. Heat is generated in the wire uniformly at a rate of g = 5 × 107 W/m³ as a result of resistance heating. If the temperature of the outer surface of the wire remains at 180°C, determine the temperature at r = 2 mm after steady operation conditions are reached. Take the thermal conductivity of the wire to be k = 8 W/m · °C. Answer: 212.8°C %3D 180°C Resistance wire

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

Related questions

Q: A cylindrical electrical heating element is used to heat up a baking oven. The heating element bears…

Q: In the continuous regime, there is a constant heat generation of 3×107 W/m³ in a one-dimensional…

A: Given data: The heat generation in the wall is q˙=3×107 Wm3 The thickness of the wall is t=20 mm The…

Q: You are asked to estimate the maximum human body temperature if the metabolic heat produced in your…

A: The temperature distribution is The thermal conductivity is The radius of cylinder is .The…

Q: figure below, five faces are insulated. The sixth thermally with the ambient, with a convective heat…

A: Given data h=10W/m2K Ta =30 oC qgen=100 W/m3

Q: Problems within the wall is T(x) = a(L- ) +b where a = 10°C/m2 and b 30°C, what is the thermal con-…

A: Given data as per questionAssumptionsSteady state condition.One dimensional conductionNo internal…

Q: Heat Transfer Mechanisms 5- In a certain experiment, cylindrical samples of diameter 4 cm and length…

Q: A spherical object that is made of a material with specific heat=383 J/kg.K, and density = 8954…

Q: Calculate the heat transfer per unit area of a concrete which has a thickness of 300 mm, the…

Q: heat from a small motorcycle engine. If the average engine surface temperature is 112 C, Exercise…

A: Since we are allowed to answer one question at a time. We’ll answer the first question since the…

Q: An internal engine of a rocket (180°C furnace) generates heat flow of 23.2564 kW through a first…

A: ◆ This is the case of heat transfer through the cylindrical layer. ◆ The temperature profile for…

Q: As shown in the figure, a 100 W/m² heat flux is applied to one side of the slab having thickness of…

A: q" = 100 W/m2L = 10 cm = 0.1 mk = 1 W/m.Kh = 10 W/K.m2To find temperature at L = 8 cm = 0.08 m

Q: A slab of thickness L with one side (x=0) insulated and the other side (x=L) is maintained at a…

A: Write the expression temperature variation. ∂2T∂x2+q˙gk=0∂T∂x+Pxk=C1T+Px22k=C1x+C2

Q: Consider a conduction in a plane composite wall as shown. The outer hotter air temperature at 60 C…

Q: n internal engine of a rocket (180°C furnace) generates heat flow of 23.2564 kW through a first…

A: Given:Ti=180°CQ=23.2564 KWd1=3 mt1=0.0065 mk1=0.6 W/m.Kt2=0.05 mk2=0.16 W/mLTo=12°C

Q: Write clearly and explain.

A: Understand that the uniform heat generated is one-dimensional, steady-state conduction. Write the…

Q: How long should it take to boil an egg? Model the egg as a sphere with radius of 2.3 cm that has…

Q: 3- A large plane wall has a thickness L=50 cm and thermal conductivity k=25 W/m.K. On the left…

Q: A composite wall is formed by sandwiching a 0.1 m thickness material between two steel slabs. The…

Q: 3. A cylindrical pipe of negligible thickness holding a hot fluid at 140°C and having an outer…

A: GivenT1=140oCd=0.4mt=70mm=0.070mk1=0.02 W/mKk2=0.06 W/mKk3=0.16 W/mKTo=30oC

Q: thickness L= 20 mm with a thermal conductivity k=45 W/m·K has a uniform volumetric heat generation…

Q: Consider a homogeneous spherical piece of radioactive material of radius r0 = 5 cm that is…

A: Write the given data with suitable variables. ro=5 cmq˙=3.8×107 W/m3T∞=27 °C=27 °C+273 K=300 Kh=110…

Q: Q: Consider the section of multilayers wall as shown in the figure, assuming one dimensional heat…

Q: 1. For a steam pipe with a given diameter of 10 cm covered by two (2) layers of insulation. The…

A: (a) Write the data given in the problem. T2=27°C r1=10 cm2 =5 cm r2=5 cm+4 cm =9 cm r3=9…

Q: 2) Determine (a) the location of the centroid and (b) the second moment of mass about x- and y- axes…

Q: a large plane vall of m. wall sui is insulated, while the surface at x =L is maintained at a…

Q: Find the temperature of a rod 0 < x < thermally insulated along the surface, if heat sources of…

Q: heating cube with a size of 60 x 60 cm on the inside is made of refractory brick (k=1.04 watt/(m.°c)…

A: Given Data K=1.04 W/mK X=12 cm

Question

Problem # 2 Heat Generation in a Solid
A long homogeneous resistance wire of radius ro = 5 mm is being used to heat
the air in a room by the passage of electric current. Heat is generated in the wire
uniformly at a rate of g = 5 x 107 W/m³ as a result of resistance heating. If the
temperature of the outer surface of the wire remains at 180°C, determine the
temperature atr= 2 mm after steady operation conditions are reached. Take the
thermal conductivity of the wire to be k = 8 W/m · °C. Answer: 212.8°C
180°C
rol
-.-.-
Resistance wire

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

The inner diameter of a pipe made of %1 C steel used in the drying machine of a textile factory is D1 = 160 mm and the thread diameter is D₂= 170 mm. The pipe is insulated with 25 mm thick glass wool. The heat transfer coefficient between the air and the pipe surface at 90 °C temperature inside the pipe is 80 W/m²K. The temperature of the ambient air outside the insulation is 20 °C and the air comes perpendicular to the cat wool surface at a speed of 10 m/s. Find the total heat transfer coefficient according to the inside diameter of the pipe. Calculate the heat transfer per unit length of pipe per unit time ?
the plane Wall seen in the figure is L=20 cm and the heat conduction coefficient is 57 W/mK. Inside the wall there is a uniform distributed volumetric heat generation of 120 kW/m3. One surface of the wall is a fluid alloy with a temperature of 15 Co, the otherits surface is subjected to heat flux of Q0 = 50 kW/m2. Since the heat transfer coefficient between the wall and the fluid is 400 W / m2 K, accepting the temperature change within the wall as one-dimensional and continuous,a) draw the temperature change curve by finding the correlation that gives the temperature distribution inside the Wall b) find the maximum temperature inside the Wall? E) find in x=L?
Consider a permanent one-dimensional heat conduction on a flat wall of length L = 0.4 m and constant thermal conductivity equal to 0.9 W/m.K, without heat generation. a) If the inner wall is T(0) = 140°C and receives a constant thermal flux of q', = 400 W/m?, what is the temperature at the outer surface, T(L) = ? b) If T(0) = 50°C and the outside of the wall is exposed to air convection at 25°C and h=10 W/k.m?, what is the temperature on the outside surface, T(L)?
A long rod with a thermal conductivity of 1 W / m · K is subjected to the boundary conditions given in the figure. Find the temperature distribution in the steady state with the energy balance method for ∆x = ∆y = 0.2m. Also calculate the heat transfer between rod and fluid per unit length.
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.
Q3. A small electric heating application uses wire of 2 mm diameter with 0.8 mm thick insulation (k = 0.15 W/m°C). The heat transfer coefficient (ho) on the insulated surface is 31 W/m2°C. Determine the critical thickness of insulation in this case and the percentage change in the heat transfer rate if the critical thickness is used, assuming the temperature difference between the surfaces of the wire and surrounding air remains unchanged. - Wire Insulator air 12 0.8 mm
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.
The rate of heat generation per unit volume in a plane wall of thickness 30 mm can be modeled as: q=1000-7000x? If the temperature of wall at x = 0 is 100 °C and at x = 30 mm is 70 °C, then find the mid-plane temperature. Take thermal conductivity of plane wall equal to 5W/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.
1 - A square chip, with side w = 5 mm, operates under isothermal conditions.The chip is positioned on a substrate so that its side and bottom surfaces are thermally insulated, while its top surface is exposed to theflow of a refrigerant at T∞ = 15°C. From reliability considerations, the chip temperature cannot exceed T = 85°C. The refrigerant being air, with a convection heat transfer coefficientcorresponding h = 200 W/(m2K), what is the maximum allowable power for the chip? Since the coolant is a dielectric liquid for which h = 3000 W/(m²K), what is the maximum allowed power?
Consider a homogeneous spherical piece of radioactive material of radius r0 = 5 cm that is generating heat at a constant rate of q.= 3.8x107 W/m3 The heat generated is dissipated to the environment T∞= 27°C and h = 110 W/m2°C steadily. The outer surface of the sphere is maintained at a uniform temperature (Ts) and the thermal conductivity of the sphere is k = 25 W/m°C. Assuming steady one-dimensional heat transfer, (a) express the differential equation and the boundary conditions for heat conduction through the sphere, (b) obtain a relation for the variation of temperature in the sphere by solving the differential equation, and (c) determine the temperature at the center of the sphere