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Consider a very large 6 mm thick copper plate in which heat is generated uniformly at a steady rate of 4×10^6 W/m3. Assuming the plate is losing heat from both sides to an ambient condition of 400⁰C, determine the heat flux on the surface of the plate during steady operation. Your answer shall have an accuracy of four places after decimal.?
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Consider a very large 6 mm thick copper plate in which heat is generat...
Problem Statement

Consider a large 6 mm thick copper plate with uniform heat generation at a rate of 4×10^6 W/m3. The plate is losing heat from both sides to an ambient condition of 400⁰C. Determine the heat flux on the surface of the plate during steady operation with an accuracy of four decimal places.

Solution


Assumptions


  • The plate is in steady-state.

  • The heat generation is uniform throughout the plate.

  • The plate is losing heat from both sides to an ambient condition of 400⁰C.

  • The thermal conductivity of copper is constant.

  • The thickness of the plate is constant.



Calculations

The rate of heat generation per unit volume = 4×10^6 W/m3

The thermal conductivity of copper = 401 W/mK

The thickness of the plate = 6 mm = 0.006 m

The temperature difference between the plate and the ambient condition = ΔT = Tp - Ta = 400⁰C

The heat transfer rate through the plate per unit area = q = k * ΔT / t

where k is the thermal conductivity of copper, ΔT is the temperature difference, and t is the thickness of the plate.

Substituting the values, we get q = (401 * 400) / 0.006 = 2.67 x 10^7 W/m2

Answer

The heat flux on the surface of the plate during steady operation is 2.67 x 10^7 W/m2.
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Consider a very large 6 mm thick copper plate in which heat is generated uniformly at a steady rate of 4×10^6 W/m3. Assuming the plate is losing heat from both sides to an ambient condition of 400⁰C, determine the heat flux on the surface of the plate during steady operation. Your answer shall have an accuracy of four places after decimal.?
Question Description
Consider a very large 6 mm thick copper plate in which heat is generated uniformly at a steady rate of 4×10^6 W/m3. Assuming the plate is losing heat from both sides to an ambient condition of 400⁰C, determine the heat flux on the surface of the plate during steady operation. Your answer shall have an accuracy of four places after decimal.? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Consider a very large 6 mm thick copper plate in which heat is generated uniformly at a steady rate of 4×10^6 W/m3. Assuming the plate is losing heat from both sides to an ambient condition of 400⁰C, determine the heat flux on the surface of the plate during steady operation. Your answer shall have an accuracy of four places after decimal.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a very large 6 mm thick copper plate in which heat is generated uniformly at a steady rate of 4×10^6 W/m3. Assuming the plate is losing heat from both sides to an ambient condition of 400⁰C, determine the heat flux on the surface of the plate during steady operation. Your answer shall have an accuracy of four places after decimal.?.
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