1-D, steady-state conduction with uniform internal energy generation occurs in a plane wall with a thickness of 50 mm and a constant thermal conductivity of 5 W/m/K. The temperature distribution has the form T = a + bx + cx2 °C. The surface at x=0 has a temperature of To = 120 °C and experiences convection with a fluid for which To = 20 °C and h = 500 W/m² K. The surface at x= 50 mm is well insulated (no heat transfer). Find: (a) The volumetric energy generation rate q. (b) Determine the coefficients a, b, and c. T= 120°C T= 20°C h = 500 W/m2.K Fluid Lex T(x)- q, k = 5 W/m.K L = 50 mm

1-D, steady-state conduction with uniform internal energy generation occurs in a plane wall with a thickness of 50 mm and a constant thermal conductivity of 5 W/m/K. The temperature distribution has the form T = a + bx + cx2 °C. The surface at x=0 has a temperature of To = 120 °C and experiences convection with a fluid for which To = 20 °C and h = 500 W/m² K. The surface at x= 50 mm is well insulated (no heat transfer). Find: (a) The volumetric energy generation rate q. (b) Determine the coefficients a, b, and c. T= 120°C T= 20°C h = 500 W/m2.K Fluid Lex T(x)- q, k = 5 W/m.K L = 50 mm

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: H +x L→∞0 B The temperature at the base is 498 K, and the temperature of the surrounding fluid is…

Q: Find the steady state temperature distribution in the semi infinite plate shown below. The 2D steady…

A: For T assuming a product so;ution…

Q: A 1-D conduction in a plane composite wall. The outer surfaces are exposed to a fluid at 25 °C and a…

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: Consider steady-state conditions for one-dimensional conduction in a plane wall having a thermal…

Q: A long steel cylinder of diameter 60 cm is placed in a hot water bath of 50°C. The convection…

A: Given information k=15.1 W/m.C, q=1250 w/m^3 Find Temperature at centre

Q: -T2 L Determine the heat flux, in kW/m², and the unknown quantity for each case. T1 (°C) T2(°C)…

Q: An AISI stainless steel spherical canister is bath-cooled to store chemicals. The properties of the…

Q: HEAT CONDUCTION ON PLANE WALLS 15. A composite slab is made from three layers of 15 cm, 10 cm and 12…

A: Givenlayer 1t1=15cm =0.15mk1=1.45W/mK with A1=60%k2=2.5W/mK with A2=100-60=40%layer 2t2=10cm…

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

Q: 12 = 40 cm and 13 = 80 cm, respectively. The leng is 1 meter. The thermal conductivity of the wall…

Q: A dormitory at a large university, built 50 years ago, has exterior walls constructed of L. = 25-…

Q: A = 1m² T1 = 1 K h₁=1 W/m²K T₁ x=0 q=0W/m³ k= 1W/mK L=1m x=im Ton2 = 1 K h₂=1 W/m²K (4) Consider a…

Q: Plaster Insulation Brick Inside Air Outside Air le ra A particular house wall consists of three…

A: CONDUCTION COVEVECTION HEAT TRANFER THROGH A COMPOSITE LAB Heat move through a plane mass of…

Q: A heat pack can be modeled as a plane wall of thickness L=2cm. Assume that the pack has a constant…

A: Given:To find:a. Reduce the heat equation with clearly stated assumptionsb. Find the steady-state…

Q: Steel pipe 5 cm thick, 1.0 m long and 12 cm deep, covered with 8 cm thick insulation. The wall…

Q: A 6 in thick concrete wall, having thermal conductivity k =0.50 Btu/h-ft-º F, is exposed to air at…

A: Given:thickness of wall, t=6 in =0.5ftThermal conductivity, k=0.50 Btu/h.ft.°FT1=70°FT2=20°Fhi=2.0…

Q: A steel plate 30 mm thick with a thermal conductivity k = 50 W/m K has a heat transfer rate of 125…

Concept explainers

Conduction and Convection

When energy travels from one object to another it is said to have undergone heat transfer. Heat transfer is nothing but the transfer of thermal energy or internal energy from one thing to another, like e.g., when a vessel with water, kept on top of a burner, heats up because of the flame underneath it.

Question

1-D, steady-state conduction with uniform internal energy generation occurs in a plane wall with
a thickness of 50 mm and a constant thermal conductivity of 5 W/m/K. The temperature
distribution has the form T = a + bx + cx² °C. The surface at x=0 has a temperature of To =
120 °C and experiences convection with a fluid for which T..
surface at x= 50 mm is well insulated (no heat transfer). Find:
(a) The volumetric energy generation rate q. (15)
(b) Determine the coefficients a, b, and c.
20 °C and h 500 W/m² K. The
To:
= 120°C
T = 20°C
h = 500 W/m².K
111
Fluid
T(x)-
=
q, k = 5 W/m.K
L = 50 mm

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: a) Evaluate heat generation rate.

VIEW

Step 2: b) Evaluate coefficients

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 17 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

#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
3- A large plane wall has a thickness L=50 cm and thermal conductivity k=25 W/m.K. On the left surface (x=0), it is subjected to a uniform heat flux go, while the surface temperature To is constant. On the right surface, it experiences convection and radiation heat transfer while the surface temperature is TL = 225°C and surrounding temperature is 25°C. The emissivity and the convection heat transfer coefficient on the right surface are 0.7 and 15 W/m²K, respectively. (a) Derive the temperature distribution equation for the wall parametrically (based on x, T₁, qo, L, and k). Plane wall Tsurr = 25°C T% = 25°C k = 25 W/m.K h = 15 W/m²K 90 ε = 0.7 T₁ = 225°C (b) Determine the temperature of the left surface of the wall at x=0? L x
Steel pipe 5 cm thick, 1.0 m long and 12 cm deep, covered with 8 cm thick insulation. The wall temperature in the steel pipe is 100 ° C. The ambient temperature around the insulated pipe is 24 ° C. The convection heat transfer coefficient outside the insulation surface is 50 W / (m² K). The thermal conductivity of steel is 54 W / (m K), and the thermal conductivity of the insulation is 0.04 W / (m K). Count; a. Heat loss per meter of pipe = watt. b. Temperature between steel pipe and insulation. = ° C.
A plane wall of an oven with an insulation coating is attached to an insulated wall. The thermal conductivity and thickness of the insulation coating are 0.1 W/(m K) and 1 mm, respectively. The material of the plane wall is stainless steel 304. The density, thermal conductivity, and specific heat capacity of the stainless steel 304 are 7900 kg/m³, 74.9 W/(mK), and 477 J/(kg K), respectively. The wall thickness of the stainless steel 304 is 15 mm. The temperature of the plane wall with the insulated coating is initially maintained at 30 °C. Suddenly, hot gas with a temperature of 1000 °C enters the oven. The convection heat transfer coefficient at the insulation coating surface is 70 W/(m²K). Insulation Coating Stainless Steel 304 Oven Gas Perfectly Insulated Wall 3-1) What is the overall heat transfer coefficient per unit area from the gas to the surface of the stainless steel? The answer should be given in the unit of W/(m²K). 3-2) What is the value of the Biot number?
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?
6. a. The heat flux applied to the walls of the biomass combustion furnace is 20 W/m2. The furnace walls have a thickness of 10 mm and a thermal conductivity of 12 W/m.K. If the wall surface temperature is measured to be 50oC on the left and 30oC on the right, prove that conduction heat transfer occurs at a steady state!b. Heating the iron cylinder on the bottom side is done by placing the iron on the hotplate. This iron has a length of 20 cm. The surface temperature of the hotplate is set at 300oC while the top side of the iron is in contact with the still outside air. To reach the desired hotplate temperature, it takes 5 minutes. Then it takes 15 minutes to measure the temperature of the upper side of the iron cylinder at 300oC. Show 3 proofs that heat transfer occurs transiently
Consider 1D heat conduction in a Cu rod with an average temperature of 25C. Does there exist a maximum (or upper-limit value) temperature gradient for heat conduction. If so, what is that value with justification on the derivation/scientific reasoning. The thermal conductivity is k=385 W/m*K. The diameter of the rod is left in terms of d.
Shown in the figure below is an insulated copper block that receives energy at a rate of 200 W from an embedded resistor. The temperature of the resistor is 34°C above the temperature of the copper block. Insulation Δt = Resistor 5000000000000000000000 oooooooooooooo....... Copper block If the block has a volume of 10-3 m³ and an initial temperature of 20°C, how long would it take, in minutes, for the temperature to reach 88°C? -V=10-³ m³ T₁ = 20°C min
a. The wall of a building has a surface area of 50 m2. The outside layer of the wall is 20 cm thick concrete with thermal conductivity kcon = .8 W/m-K. The inner layer is 10 cm thick balsa wood (kbalsa = .048 W/m-K) as an insulator. Outside temperatures of 47o C are expected, while an inside temperature of 21o C is maintained by the cooling system. Find the rate of heat transfer through the wall.