A cylindrical carrot of radius R and length L with an initial temperature of T0 is...
A cylindrical carrot of radius R and length L with an initial temperature of T0 is placed into boiling water (TH). Note that the initial temperature is lower than the boiling water. The radius of the carrot is equal to that of half the length. The boiling water has a surface average heat transfer coefficient of h across the entire surface of the carrot. Use the center of the carrot to represent z = 0 and r = 0.
1. What are the non-dimensional boundary conditions of this system?
2. What is the radial average non-dimensional heat transfer equation for the carrot? Solve the PDE obtained in question 1 and apply the boundary conditions, you will need to transform the boundary conditions found in question 1 to fit the new form of the PDE in question 2
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A cylindrical carrot of radius R and length L with an initial
temperature of T0 is...
3. (Cotal: 30 pts) Consider a cylinder of radius R and length L. The thermal "Gonductivity ofthe eyǐnaeris R. The temperature is fixed at the left end at TO and the other end is subject to co...
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The conductive heat transfer in a rod of length L is described by the equation au ди əraat ,0<r<L,+20 where u(x, t) is the local temperature of the rod, t is time, and a is a positive constant describing the thermal conductivity of the rod. The initial and boundary conditions are: T(r, 0) = 0, T(L, t) = 0, and T (0, 1) = 1 for > 0 (1) Find the general solution of this PDE. (11) Find the eigenvalues...
Two large parallel plates with surface conditions approximating those of a blackbody are maintained at 800°C...
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Please provide very detailed steps Find the temperature u(x, t) in a bar of length T...
Please provide very detailed steps
Find the temperature u(x, t) in a bar of length T with thermoconductivity coefficient c2 1 (all the quantities are non-dimensional) under adiabatic boundary conditions (zero heat flux) at ends of the bar if the initial tem- perature u(z, 0) . 130 cos(3x)
Find the temperature u(x, t) in a bar of length T with thermoconductivity coefficient c2 1 (all the quantities are non-dimensional) under adiabatic boundary conditions (zero heat flux) at ends of the...
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We are trying to solve for the temperature distribution of a sphere in boiling water. The...
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2. In the figure below a cylindrical pipe with radius R and length L is shown....
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Consider a uniform bar of length L having an initial temperature distribution given by f(x), 0...
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3. (Cotal: 30 pts) Consider a cylinder of radius R and length L. The thermal "Gonductivity ofthe eyǐnaeris R. The temperature is fixed at the left end at TO and the other end is subject to convective heat transfer with heat transfer coefficient h and environment temperature of To. The side surface of the cylinder is subject to radiative heat transfer to environment of To. Assume there is no heat generation in the cylinder. (10 pts) starting with energy balance,...
The conductive heat transfer in a rod of length L is described by the equation au ди əraat ,0<r<L,+20 where u(x, t) is the local temperature of the rod, t is time, and a is a positive constant describing the thermal conductivity of the rod. The initial and boundary conditions are: T(r, 0) = 0, T(L, t) = 0, and T (0, 1) = 1 for > 0 (1) Find the general solution of this PDE. (11) Find the eigenvalues...
Two large parallel plates with surface conditions approximating those of a blackbody are maintained at 800°C and 100°C, respectively. Determine the rate of heal transfer by radiation between the plates in Wim and the radiative heat transfer coefficient in W/m K ) 12 Write down the one-dimensional sent heal conduction equation for a plane wall with constant thermal conductivity and heat generation in its simplest form, and indicate what each variable represents 13 Write down the one-dimensional transient heat conduction...
Please provide very detailed steps
Find the temperature u(x, t) in a bar of length T with thermoconductivity coefficient c2 1 (all the quantities are non-dimensional) under adiabatic boundary conditions (zero heat flux) at ends of the bar if the initial tem- perature u(z, 0) . 130 cos(3x)
Find the temperature u(x, t) in a bar of length T with thermoconductivity coefficient c2 1 (all the quantities are non-dimensional) under adiabatic boundary conditions (zero heat flux) at ends of the...
A long, cylindrical non-conductor of radius R and length L is placed with it long axis along the Z-axis as shown The cylinder has a total charge Q distributed non-uniformly thrpughout its volume. The charge density is only a function of the radial distance "r" from the cylinder axis and varies as ρ(r):- where α is a constant Vr. 2 +9R2 c) What coordinate system will you use? L (xy,z), (p,o,Z), (,o,)) d) What variables will the magnitude of the...
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2. (25 points) A spherical metal ball of radius ris heated in an oven to a temperature of T; throughout and is then taken out of the oven and dropped into a large body of water at To where it is cooled by convection with an average convection heat transfer coefficient of h. It is given that there is no internal heat generation, that the thermal conductivity is constant, and that there are no temperature variations in the transient one-dimensional...
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