a critical evaluation of the engineering applications solutions of the Leibnitz-Maclaurin method and the Euler’s method. In terms of their first order and second order differential equation solutions, highlight and show two (2) advantages and disadvantages over each other with reference to the particular problems they were intended to solve. In addition to the above critical evaluation, make a comparison between two (2) engineering models, by evaluating how the different models use first-order differential equations

a critical evaluation of the engineering applications solutions of the Leibnitz-Maclaurin method and the Euler’s method. In terms of their first order and second order differential equation solutions, highlight and show two (2) advantages and disadvantages over each other with reference to the particular problems they were intended to solve. In addition to the above critical evaluation, make a comparison between two (2) engineering models, by evaluating how the different models use first-order differential equations

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter4: Numerical Analysis Of Heat Conduction

Section: Chapter Questions

Problem 4.21P

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Let's assume that the outdoor temperature in your region was 1 C on 26.12.2002. Let's assume that you use a 2088 W heater in the room in order to keep the indoor temperature of the room at 20 ° C. In the meantime, a 68 W light bulb for lighting, a computer you use to solve this question and load it into the system (let's assume it consumes 217 W of energy), you and your two friends (three people in total) are in the room to assist you in solving the questions. A person radiates 45 J of heat per second to his environment. When you consider all these conditions, calculate the exergy destruction caused by the heat loss from the exterior wall of your room.
First 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.
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Which procedure provides a method that may be used to apply Cstigliano's second theorem?
One-dimensional, steady-state conduction with uniform internal energy generation occurs in a plane wall which is subject to convection on the left side at x = 0 and being well-insulated on the other.a) Specify the mathematical model defining T(x): provide a governing differential equation and appropriate boundary conditions. Express your answer in terms of defined variables rather than numerical values with units. b) Solve for the temperature profile T(x) referencing the x-origin as shown on the left surface (again expressing your answer in terms of defined variables rather than numericalvalues.) c) Find the maximum temperature in the wall and the wall surface temperature if the volumetric generation is qdot = 1 MW/m^3 with the remaining parameters as specified in the figure.
Do not actually solve the problem numerically or algebraically, just pick the one equation and define the relevant knowns and single unknown. Don’t forget to include direction when called for by a vector variable 12) The air conditioner removes 2.7 kJ of heat from inside a house with 450 m3 of air in it. At a typical air density of 1.3 kg/m3 that means 585 kg of air. If the specific heat of air is 1.01 kJ/(kg oC), by how much would this cool the house if no heat got in through the rest of the house during that time?
a) Separate the rod into 4 control sections, each with a node in the centre, then use finite-volume analysis to estimate the temperature along the length of the rod. b) Separate the rod into 4 sections and repeat (a) with equal both temperature values and beginning conditions using the finite difference method (if necessary). c) Write down and analytically compare with (a) and (b) differential equation for the temperature distribution along the rod. d) Compare the results (a), (b) and (c) by using a graph and differences.e) How to improve the results from (a) and (b)? Show it.
We are seeing statically indeterminate cases. We need to find a compatibility equation and solve from there, or at least that is my understanding...
Differential equation THE LAPLACE METHOD CANNOT BE USED. When two springs in series, with constants k1 and k2 respectively,support a mass, the effective spring constant is calculated as:k = k1*k2 / k1+k2 A 420 g object stretches a spring 7 cm, and that same object stretches 2.8 cmanother spring. Both springs are attached to a common rigid support and then toa metal plate, as shown in the figure of springs in series. Then the object joins thecenter of the plate (figure of springs in series). Determine: (a) the effective spring constant.(b) the position of the object at any time t, if the object is initially releasedfrom a point 60 cm below the position ofequilibrium and with an upward velocity of 1.2 m / s.Consider the acceleration of gravity as 9.8 m / s2.
We performed the experiment to measure the thermal conductivity of 2 materials (Brass & Steel) in the laboratory and measured the following tabulated values: Material 1 - BRASS (Diameter = 25mm) Power Temperature (°C) Q' (W) 2 3 4 6 7 8 1 5 9 14.6 78.9 77.5 76 50.2 46.7 42.4 36.1 34.6 33.6 Material 2 - STEEL (Diameter = 25mm) Power Temperature (°C) 7 Q' (W) 14.25 2 3 1 9 88.6 87.4 85 34.1 33.4 32.7 CALCULATE THE FOLLOWING: MATERIAL 1 - BRASS Calculation for Brass Quantities Calculated Values Power (Q') W Area of cross section (A) m2 Difference in Temperature between two points (AT) °C Difference in distance between two points (Ax) m Thermal conductivity of brass (k,) W/m'C MATERIAL 2 - STEEL Calculation for Steel Quantities Calculated Values Power (Q') W Area of cross section (A) m? Difference in Temperature between two points (AT) "C Difference in distance between two points (Ax) m Thermal conductivity of steel (k,) W/m°C
1. A spring mass system serving as a shock absorber under a car's suspension, supports the M 1000 kg mass of the car. For this shock absorber, k = 1 × 10°N /m and c = 2 × 10° N s/m. The car drives over a corrugated road with force %3| F = 2× 10° sin(@t) N . Use your notes to model the second order differential equation suited to this application. Simplify the equation with the coefficient of x'" as one. Solve x (the general solution) in terms of w using the complimentary and particular solution method. In determining the coefficients of your particular solution, it will be required that you assume w – 1z w or 1 – o z -w. Do not use Matlab as its solution will not be identifiable in the solution entry. Do not determine the value of w. You must indicate in your solution: 1. The simplified differential equation in terms of the displacement x you will be solving 2. The m equation and complimentary solution xe 3. The choice for the particular solution and the actual particular solution x,…
I am able to find the first row and the first column of by hand. However, When I do the 2nd row and 2nd column, my answer doesnt match my matlab code. Would someone be able to help me? Thank you! Use the explicit method to solve by hand the 1D heat equation for the temperature distribution in a laterally insulated wire with a length of 1 cm, whose ends are kept at T(0) = 0 0C and T(1) = 0 0C, for 0 ≤ x ≤ 1 and 0 ≤ t ≤ 0.5. At t = 0, the temperature of the wire is subjected to initial condition T(x) = 100sin(πx). Use the following values of k = 0.15 cm2/s, Δx = 0.25 cm, and Δt = 0.1 s. Calculate by hand the values of temperature at the internal mesh points only for the first time row at t = 0.1 s. Verify the values of temperature at t = 0.1 s calculated by hand. Use Heat1DCN.m M-file to solve the 1D heat equation within the space-time domain 0 ≤ x ≤ 1 and 0 ≤ t ≤ 2 with Δx = 0.05 cm and Δt = 0.1 s. Make the plot of temperature surface.