Simplify the general form of the equation for a 1-dimensional steady-state systemUwithout heat generation. Note: Steady state means that the temperature of the systemdoes not change with time. :Hint: Equation will be reduced into an ordinary differential equation.Obtain an expression for the variation of temperature in the object. :Consider the heating plate of a 15cm x 15cm ceramic coated laboratory hotplate withmagnetic stirrer that has a thickness of 1 cm, and average thermal conductivity of 10W/m-K. The inner surface of the heating plate is subjected to a uniform heat flux of 1200W/m? and the outer surface loses heat to the surroundings at T= 298 K by convectionwith convection coefficient of 80 W/m:K (schematic diagram shown below). Obtain anexpression for the variation of temperature in the heating plate and use the derivedexpression to determine the inner and outer temperatures of the plate. Schematicdiagram is shown below., aTат(*) + (*) + )+ g = pc,kдудуazp dtaxdz

Disclaimer: “Since you have asked multiple question, we will solve the first question for you. That…

Simplify the general form of the equation for a 1-dimensional steady-state system without heat generation. Note: Steady state means that the temperature of the system does not change with time. :; Hint: Equation will be reduced into an ordinary differential equation.

Simplify the general form of the equation for a 1-dimensional steady-state system without heat generation. Note: Steady state means that the temperature of the system does not change with time. :; Hint: Equation will be reduced into an ordinary differential equation.

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

Similar questions

A solid rectangular parallelepiped is made of aluminum and is initially at 20 C. The base is a 2 cm by 3 cm rectangle and the height of the parallelepiped is 5 cm. The parallelepiped is now dropped into hot oil at 150 C. Find: a) the temperature of point P and b) the temperature of the center of the parallelepiped after 2 min of exposure to hot oil. Point P is located 1 cm above the center plane and1 cm from each side.
2) Design a chain link (meaning find its diameter) made out of a ductile cast iron which needs to operate in a furnace that is used to fire ceramic bricks. The chain will be used for five years at 600°C with an applied load of 5000 lbs. Below is a diagram of the chain link and the Larson-Miller parameter graph for this particular cast iron. Be sure to use the specific equation for the Larson-Miller parameter provided on the x-axis of the graph. Furthermore, for your calculations assume a Safety Factor of 2. Stress (psi) 20,000 10,000 8,000 6,000 4,000 2,000 1,000 32 34 36 Larson-Miller parameter = 30 38 40 42 (36+0.78 ln 1) T(K) 1000 1200 dis SH ER
1. Suppose you have a 4-foot metal rod, made out of steel which has a thermal conductive factor of a = 4 Assume the temperature on the ends of the rod is always 0 degrees. a) Filling in the numerical parameters mentioned above in the problem, write down the general solution to this heat equation, which should include some unknown coefficients (c,'s), in addition to t's and x's.
d²u d²u u(x,t) is solution to steady state 2-D heat equation, + dx² ду2 -=0,with following parameters for numerical approximation: u = u(0,0), u(0,y)=0, u(1,y)=y(1-y), 0
The Laws of Physics are written for a Lagrangian system, a well-defined system which we follow around – we will refer to this as a control system (CSys). For our engineering problems we are more interested in an Eulerian system where we have a fixed control volume, CV, (like a pipe or a room) and matter can flow into or out of the CV. We previously derived the material or substantial derivative which is the differential transformation for properties which are functions of x,y,z, t. We now introduce the Reynold’s Transport Theorem (RTT) which gives the transformation for a macroscopic finite size CV. At any instant in time the material inside a control volume can be identified as a control System and we could then follow this System as it leaves the control volume and flows along streamlines by a Lagrangian analysis. RTT:DBsys/Dt = ∂/∂t ʃCV (ρb dVol) + ʃCS ρbV•n dA; uses the RTT to apply the laws for conservation of mass, momentum (Newton's Law), and energy (1st Law of…
A piece of metal is initially heated to 850°C and is quenched in water which temperature is kept at 50°C. The temperature decay constant of the system is 0.30/min. a.) Determine the temperature of the metal at any time, T(t), using Laplace Transforms. b.) Determine the time needed for the metal to be at 80°C.
A conditioned space has a calculated heat loss at the design maximum heating day of 10,000 BTUs / Hr to maintain an interior temperature of 70 F. We will use a hydronic baseboard style convector to heat the space. The style we have chosen comes in standard lengths. At rated temperature and flow of hydronic heating fluid for each 1 foot of length the heater will add 750 BTUs /Hr to the room. What length of heater can just maintain the temperature on the worst day? For this example we are ignoring other sources of heat loss such as ventilation or drafts.
non homogeneous system using the Laplace transform
Insulated Ax h, T» 1 2 3 4 5
The steady-state distribution of temperature on a heated plate can be modeled by the Laplace equation, a²T ²T + a²x a²y If the plate is represented by a series of nodes as illustrated in Figure, centered finite-divided differences can be substituted for the second derivatives, which results in a system of linear algebraic equations. Use the Gauss-Seidel method to solve for the temperatures of the nodes in Figure. 0= Submission date: 09/01/2024 25°C T12 T₂2 250°C # T₁1 T₂1 250 CO 75°C 25°C 75°C 0°C 0°C
1. A motor coil can be modeled as a hollow copper cylinder with an outer diameter of 0 50 mm, an inner diameter of 40 mm, and a length of 60 mm. The motor stalls at time t = 0 and, at this point, the copper experiences a step input in electrical heating of Po u(t), where Po is 350 W. Assume that there is little time for significant heat loss to the environment so that the copper cylinder can be considered to be insulated. If the initial temperature is 30 °C, find the temperature as a function of time, T(t), analytically using Laplace transforms. Calculate the time required to reach the breakdown temperature of the wire insulation, which is approximately 250 °C. Write a script file in MATLAB® to: (a) determine the time for the copper to reach 250 °C using the command find; and (b) plot T(t) over this time interval. Copper has a density of 8960 kg/m³ and a specific heat of 390 J/kg-°C. 25 mm 20 mm P(t) = Pou(t)
Question 4 Iterative methods of solution for simultaneous equations include successive over relaxation (SOR) Gauss-Seidel iteration O Jacobi iteration LU decomposition Householder decomposition