1). What is the value of ∂T/∂t (partial derivative of temperature with time) in 3D steady...
1). What is the value of ∂T/∂t (partial derivative of temperature with time) in 3D steady state conductionthrough an object.
2). Sketch an internal node for 2D conduction affected by 4 adjacent points. Write the nodal temperature equation for this internal node.
Homework Answers
no idea about 2 questionAdd Answer to:
1). What is the value of ∂T/∂t (partial derivative of
temperature with time) in 3D steady...
Consider two-dimensional, steady-state conduction in a square cross section with prescribed surfa...
need help with c and d
Consider two-dimensional, steady-state conduction in a square cross section with prescribed surface temperatures shown in the figure. 2) 100°C a) Determine the temperatures at nodes 1, 2, 3, and 4 Estimate the midpoint temperature. Reducing the mesh size by a factor of 2, determine the corresponding nodal temperatures. Compare your results with those from the coarser grid. b) 50°C 200°c c) If the body generates heat at a rate of 20,000 W/m determine the...
(i) Explain the meaning of the Lagrangian derivative or total derivative, de noted by the symbol...
(i) Explain the meaning of the Lagrangian derivative or total derivative, de noted by the symbol D/Dt (ii) What happens to the Lagrangian derivative in a steady flow? (iii) Consider a 3D flow whose velocity field and temperature fields are given by: V (1,4, 2, t) = (x² - y)i + (yt j - (2+ 2), T(x, y, z,t) = 100(1 – 0.02zy), Determine if the temperature of a fluid element A located at (1,-1,2) at time t=1sec is increasing...
Computer assignment Computer assignment Consider two dimensional, steady state conduction in a square cross section. Discretization...
Computer assignment
Computer assignment Consider two dimensional, steady state conduction in a square cross section. Discretization is as shown Δx=Δy Requires 1- determine temperature at node 1 through 16. 2-determine heat transfer rates. 3-determine location and value of T"max" 4-check energy balance. The details for boundary conditions in the picture Need code written in EES ( engineering equation solver) Will be helpful if there is: Mathematical formulation and Numerical solution procedure. Thanks
(1 point) For partial derivatives of a function use the subscript notation, so for the second par...
(1 point) For partial derivatives of a function use the subscript notation, so for the second partial derivative of the function u(x,t) with respect to x use uxx. For ordinary differential equations use the prime notation, so the second derivative of the function f(x) is f" Solve the heat equation 14 1502,>0 a(0,t) = 92,21(2, t) 87, t > 0 using a steady-state and transient solution: ie write u(z, 1) _ u(z,t) + S(z) with u a solution of the...
Project: 2D, S/S Heat Conduction in a Rectangle with Heat Generation Write a code in MATLAB that ...
Project: 2D, S/S Heat Conduction in a Rectangle with Heat Generation Write a code in MATLAB that can calculate the temperature inside a thin, rectangular, metal plate, T(x, y) at some selected points as shown in the figure. The temperatures at the boundaries are constant and there is heat generation inside the plate. The problem is steady- state and k = 100 W/(m·K) with L = 1m and H = 0.5 m. The equation to be solved is, 50 °C...
3. (20 points) Denote u(ar, y) the steady-state temperature in a rectangle area 0 z 10,...
3. (20 points) Denote u(ar, y) the steady-state temperature in a rectangle area 0 z 10, 0yS 1. Find the temperature in the rectangle if the temperature on the up side is kept at 0°, the lower side at 10° while the temperature on the left side is S0)= sin(y) and the right side is insulated. Answer the following questions. (a) (10 points) Write the Dirichlet problem including the Laplace's equation in two dimensions and the boundary conditions. (b) (10...
Problem 2(30 points) Consider the steady-state temperature distribution in a square plate with dimensions 2 m...
Problem 2(30 points) Consider the steady-state temperature distribution in a square plate with dimensions 2 m x 2 m. There is a heat generation of ġ(x.y)=6x [W/my], and the thermal conductivity of k=1[W/(m-°C)]. The temperature on the top boundary is given by a piecewise function, f(x), which is defined below. x(4- x²)+10 0<x<1 | x(4- x?) + 20, 1<x<2 The bottom boundary is insulated. The temperatures on left-handed and right-handed boundary are maintained at constants 10[°C] and 20 [°C] as...
1. Consider a thin rectangular plate in the ry-plane, the figure. The PDE describing the temperature...
1. Consider a thin rectangular plate in the ry-plane, the figure. The PDE describing the temperature of the plate is the heat equation shown in as 0 xa, 0< y < b, t>0. D + at where u(x, y, t) is the temperature at point (x, y) diffusivity at time t andD> 0 is the thermal (a) Suppose that the solution to the PDE (once we impose initial and boundary con ditions) reaches equilibrium when t o, that is there...
the previous problem set was this one, its the solution to the steady state temperature distribution...
the previous problem set was this one, its the solution to the
steady state temperature distribution on the left of problem
2
2. In the last problem set you found the steady-state temperature distribution for the situation on the left. What is the steady state temperature distribution for the situation on right? Hint: make use of your previous solution. 100°C 120°C Extra credit: Make a plot of the temperature distribution 100°C 120°c T 100°C 2. Find the steady-state temperature distribution...
Steady state temperatures at three nodal points of a long rectangular rod are as shown. The...
Steady state temperatures at three nodal points of a long rectangular rod are as shown. The rod experiences a uniform volumetric generation rate of 4 x 107 W/m3 and has a thermal conductivity of 20W/mK. Several other nodal temperatures are given as shown. TA = 398K, Tg = 374.6K, and T = 348.5K. Two of its sides (top and right) are insulated as shown. -5 mm 300K 2 TA 5 mm 300K TC 3 ТВ 300K Submitting your answer in...
need help with c and d
Consider two-dimensional, steady-state conduction in a square cross section with prescribed surface temperatures shown in the figure. 2) 100°C a) Determine the temperatures at nodes 1, 2, 3, and 4 Estimate the midpoint temperature. Reducing the mesh size by a factor of 2, determine the corresponding nodal temperatures. Compare your results with those from the coarser grid. b) 50°C 200°c c) If the body generates heat at a rate of 20,000 W/m determine the...
(i) Explain the meaning of the Lagrangian derivative or total derivative, de noted by the symbol D/Dt (ii) What happens to the Lagrangian derivative in a steady flow? (iii) Consider a 3D flow whose velocity field and temperature fields are given by: V (1,4, 2, t) = (x² - y)i + (yt j - (2+ 2), T(x, y, z,t) = 100(1 – 0.02zy), Determine if the temperature of a fluid element A located at (1,-1,2) at time t=1sec is increasing...
Computer assignment
Computer assignment Consider two dimensional, steady state conduction in a square cross section. Discretization is as shown Δx=Δy Requires 1- determine temperature at node 1 through 16. 2-determine heat transfer rates. 3-determine location and value of T"max" 4-check energy balance. The details for boundary conditions in the picture Need code written in EES ( engineering equation solver) Will be helpful if there is: Mathematical formulation and Numerical solution procedure. Thanks
(1 point) For partial derivatives of a function use the subscript notation, so for the second partial derivative of the function u(x,t) with respect to x use uxx. For ordinary differential equations use the prime notation, so the second derivative of the function f(x) is f" Solve the heat equation 14 1502,>0 a(0,t) = 92,21(2, t) 87, t > 0 using a steady-state and transient solution: ie write u(z, 1) _ u(z,t) + S(z) with u a solution of the...
Project: 2D, S/S Heat Conduction in a Rectangle with Heat Generation Write a code in MATLAB that can calculate the temperature inside a thin, rectangular, metal plate, T(x, y) at some selected points as shown in the figure. The temperatures at the boundaries are constant and there is heat generation inside the plate. The problem is steady- state and k = 100 W/(m·K) with L = 1m and H = 0.5 m. The equation to be solved is, 50 °C...
3. (20 points) Denote u(ar, y) the steady-state temperature in a rectangle area 0 z 10, 0yS 1. Find the temperature in the rectangle if the temperature on the up side is kept at 0°, the lower side at 10° while the temperature on the left side is S0)= sin(y) and the right side is insulated. Answer the following questions. (a) (10 points) Write the Dirichlet problem including the Laplace's equation in two dimensions and the boundary conditions. (b) (10...
Problem 2(30 points) Consider the steady-state temperature distribution in a square plate with dimensions 2 m x 2 m. There is a heat generation of ġ(x.y)=6x [W/my], and the thermal conductivity of k=1[W/(m-°C)]. The temperature on the top boundary is given by a piecewise function, f(x), which is defined below. x(4- x²)+10 0<x<1 | x(4- x?) + 20, 1<x<2 The bottom boundary is insulated. The temperatures on left-handed and right-handed boundary are maintained at constants 10[°C] and 20 [°C] as...
1. Consider a thin rectangular plate in the ry-plane, the figure. The PDE describing the temperature of the plate is the heat equation shown in as 0 xa, 0< y < b, t>0. D + at where u(x, y, t) is the temperature at point (x, y) diffusivity at time t andD> 0 is the thermal (a) Suppose that the solution to the PDE (once we impose initial and boundary con ditions) reaches equilibrium when t o, that is there...
the previous problem set was this one, its the solution to the
steady state temperature distribution on the left of problem
2
2. In the last problem set you found the steady-state temperature distribution for the situation on the left. What is the steady state temperature distribution for the situation on right? Hint: make use of your previous solution. 100°C 120°C Extra credit: Make a plot of the temperature distribution 100°C 120°c T 100°C 2. Find the steady-state temperature distribution...
Steady state temperatures at three nodal points of a long rectangular rod are as shown. The rod experiences a uniform volumetric generation rate of 4 x 107 W/m3 and has a thermal conductivity of 20W/mK. Several other nodal temperatures are given as shown. TA = 398K, Tg = 374.6K, and T = 348.5K. Two of its sides (top and right) are insulated as shown. -5 mm 300K 2 TA 5 mm 300K TC 3 ТВ 300K Submitting your answer in...
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