Just as Fourier's law and the heat balance can be employed to characterize temperature distribution, analogous relationships are available to model field problems in other areas of engineering. For example, electrical engineers use a similar approach when modeling electrostatic fields. Under a number of simplifying assumptions, an analog of Fourier's law can be represented in one-dimensional form as
whereD is called the electric flux density
where
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EBK NUMERICAL METHODS FOR ENGINEERS
- The stress profile shown below is applied to six different biological materials: Log Time (s] The mechanical behavior of each of the materials can be modeled as a Voigt body. In response to o,= 20 Pa applied to each of the six materials, the following responses are obtained: 2 of Maferial 6 Material 5 0.12 0.10 Material 4 0.08 Material 3 0.06 0.04 Material 2 0.02 Material 1 (a) Which of the materials has the highest Young's Modulus (E)? Why? Log Time (s) (b) Using strain value of 0.06, estimate the coefficient of viscosity (n) for Material 6. Stress (kPa) Strainarrow_forwardFirst Order Differential Equations are inherent in almost all aspects of engineering, e.g., electronics (RC/RL circuits or charge/discharge of capacitors), thermodynamics (i.e., Newton’s Law of Cooling), mechanical systems (stress/strain) etc. In fact, virtually anywhere there are time varying dynamics. You need to demonstrate how different engineering systems models are used to solve them using first-order differential equations.arrow_forwardTranscribe the hamiltonian onto the Heisenberg square [き] V3 В 2а H-arrow_forward
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- How can the Bode plot be used to analyze and design control systems in mechanical engineering applications?arrow_forwardA higher-order differential equation given as y" + p(x)y' g (x)y = O is a homogenous equation, even if p(x) = 0. A higher-order differential equation given as y" + p(x)y' + q(x)y = 0 is also a homogenous equation, even if g(x) = 0. O Only first statement is true. O Only second statement is true. O Both first and second statements are true. O Both first and second statements are false.arrow_forwardmechanical engineering dynamics please solve question 7arrow_forward
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