1. An infinite parallel-sided slab of non-dimensional thickness L 1, has an initial (at non-dimensional time t= 0) temperature distribution To (x) given in below. Its left and rightends are subsequently (for t> 0) maintained at temperatures T1, and T2, respectively.The initial temperature distribution is given by T.(x) = 250*x*sin(rx) K, and theboundary temperatures for t> 0 are: T = 50K and T2 = 100K. Use 10 intervals in the x-direction, and At = 0.01.(a) Write the equations you'll be using to solve the problem in matrix form, using theimplicit method. The coefficient matrix and the right-hand-side vector should shownumerical values. Do not write every value, but use the matrix representation given in thepresentation slides so you can fit the answer in the width of the page. Your equationsshould be for solution at time level (n=2), where n = Irepresents time t = 0.

It is asked to generate an implicit model for unsteady-state one-dimensional heat conduction…

An infinite parallel-sided slab of non-dimensional thickness L=1, has an initial (at non- dimensional time t= 0) temperature distribution To (x) given in below. Its left and right ends are subsequently (for t> 0) maintained at temperatures T1, and T2, respectively. %3D !3! The initial temperature distribution is given by T.(x) 250*x*sin(Tx) K, and the boundary temperatures for t> 0 are: T = 50K and T; = 100K. Use 10 intervals in the x- direction, and At = 0.01. %3D %3D Write the equations you'll be using to solve the problem in matrix form, using the implicit method. The coefficient matrix and the right-hand-side vector should show numerical values. Do not write every value, but use the matrix representation given in the presentation slides so you can fit the answer in the width of the page. Your equations should be for solution at time level (n=2), where n = Irepresents time t = 0.

An infinite parallel-sided slab of non-dimensional thickness L=1, has an initial (at non- dimensional time t= 0) temperature distribution To (x) given in below. Its left and right ends are subsequently (for t> 0) maintained at temperatures T1, and T2, respectively. %3D !3! The initial temperature distribution is given by T.(x) 250xsin(Tx) K, and the boundary temperatures for t> 0 are: T = 50K and T; = 100K. Use 10 intervals in the x- direction, and At = 0.01. %3D %3D Write the equations you'll be using to solve the problem in matrix form, using the implicit method. The coefficient matrix and the right-hand-side vector should show numerical values. Do not write every value, but use the matrix representation given in the presentation slides so you can fit the answer in the width of the page. Your equations should be for solution at time level (n=2), where n = Irepresents time t = 0.

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.

Chapter5: Analysis Of Convection Heat Transfer

Section: Chapter Questions

Problem 5.10P: 5.10 Experiments have been performed on the temperature distribution in a homogeneous long cylinder...

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5.10 Experiments have been performed on the temperature distribution in a homogeneous long cylinder (0.1 m diameter, thermal conductivity of 0.2 W/m K) with uniform internal heat generation. By dimensional analysis, determine the relation between the steady-state temperature at the center of the cylinder , the diameter, the thermal conductivity, and the rate of heat generation. Take the temperature at the surface as your datum. What is the equation for the center temperature if the difference between center and surface temperature is when the heat generation is ?
1.63 Liquid oxygen (LOX) for the space shuttle is stored at 90 K prior to launch in a spherical container 4 m in diameter. To reduce the loss of oxygen, the sphere is insulated with superinsulation developed at the U.S. National Institute of Standards and Technology's Cryogenic Division; the superinsulation has an effective thermal conductivity of 0.00012 W/m K. If the outside temperature is on the average and the LOX has a heat of vaporization of 213 J/g, calculate the thickness of insulation required to keep the LOX evaporation rate below 200 g/h.
6. A thin homogeneous metal bar of length 20cm. and made of material with thermal diffusivity 5cm/shas insulated ends and lateral sides. The bar has initial temperature in (C) given by u(x, o) = 10 + 4x 0< x< 10 u( x,0) = = 90 - 4x 10 < x< 20 (a) Model an initial-boundary value problem [IBVP] of the heat equation from the above statement.
2. Consider the temperature distributions associated with a dx differential control volume within the one-dimensional plane walls shown below. T(x,00) T\x,00) * dx * dx (a) (Б) Tx,1) T(x,1) * dx dx (c) (d) (a) Steady-state conditions exist. Is thermal energy being generated within the differential control volume? If so, is the generation rate positive or negative? (b) Steady-state conditions exist as in part (a). Is the volumetric generation rate positive or negative within the differential control volume? (c) Steady-state conditions do not exist, and there is no volumetric thermal energy generation. Is the temperature of the material in the differential control volume increasing or decreasing with time? (d) Transient conditions exist as in part (c). Is the temperature increasing or decreasing with time?
(a) Consider nodal configuration shown below. (a) Derive the finite-difference equations under steady-state conditions if the boundary is insulated. (b) Find the value of Tm,n if you know that Tm, n+1= 12 °C, Tm, n-1 = 8 °C, Tm-1, n = 10 °C, Ax = Ay = 10 mm, and k = W 3 m. k Ay m-1, n 11- m2, 11 m, n+1 m, n-1 The side insulated
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2. Consider the temperature distributions associated with a dx differential control volume within the one-dimensional plane walls shown below. dx dx (b) Tr,1) dx dx le) (d) (a) Steady-state conditions exist. Is thermal energy being generated within the differential control volume? If so, is the generation rate positive or negative? (b) Steady-state conditions exist as in part (a). Is the volumetric generation rate positive or negative within the differential control volume? (c) Steady-state conditions do not exist, and there is no volumetric thermal energy generation. Is the temperature of the material in the differential control volume increasing or decreasing with time? (d) Transient conditions exist as in part (c). Is the temperature increasing or decreasing with time?
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