【Daily Question】Theoretical Foundation 2020.11.16
Thread Content
Multiple-choice question: The question is shown in the image ( ). Answer: A. Hint: Extra rewards will be given to those who can explain the solution process; the answer can be submitted there
The heat conservation method states that the algebraic sum of the heat fluxes entering any node is zero. It has a wide range of applicability; in cases where the thermal conductivity is a function of temperature or where the internal heat sources are unevenly distributed, it is easy to formulate differential equations. Therefore, the heat conservation method is frequently used in numerical calculations of heat conduction； In the implicit difference scheme, the second derivative of temperature with respect to x is expressed using a central difference formula, while the first derivative of temperature with respect to time is expressed using a backward difference formula ； When solving unstable heat conduction problems, the central difference scheme should not be used for the first derivative of temperature with respect to time, as this will lead to numerical instability.
The correct answer is A. The law of heat conservation states that the algebraic sum of the heat fluxes entering any node is zero. It has a wide range of applicability; in cases where the thermal conductivity is a function of temperature or where the internal heat sources are unevenly distributed, it is easy to establish differential equations. Therefore, the law of heat conservation is frequently used in numerical calculations of heat conduction ； In the implicit difference scheme, the second derivative of temperature with respect to x is expressed using a central difference formula, while the first derivative of temperature with respect to time is expressed using a backward difference formula ； When solving unstable heat conduction problems, the central difference scheme should not be used for the first derivative of temperature with respect to time, as this will lead to numerical instability.
The heat conservation method states that the algebraic sum of the heat fluxes entering any node is zero. It has a wide range of applicability; in cases where the thermal conductivity is a function of temperature or where the internal heat sources are unevenly distributed, it is easy to formulate differential equations. Therefore, the heat conservation method is frequently used in numerical calculations of heat conduction； In the implicit difference scheme, the second derivative of temperature with respect to x is expressed using a central difference formula, while the first derivative of temperature with respect to time is expressed using a backward difference formula ； When solving unstable heat conduction problems, the central difference scheme should not be used for the first derivative of temperature with respect to time, as this will lead to numerical instability.