Department of Chemical Engineering
Department of Chemical Engineering CHEE 315, Heat and Mass Transfer Problem Set #5
Midterm practice problems 1) Derive the equation for the temperature profile for the problem given in Lab 1. 2) A radial disk is mounted on an isothermal rod and is exposed to a fluid at T ∞ , h . At steadystate, the temperature of the fluid exceeds that of the isothermal rod and you may assume that heat entering from all surfaces of the disk flows to the isothermal rod in only the radial direction. The disk has an inner radius of ri, outer radius of ro and a thickness, t. A schematic of the radial disk and rod is given below in figure 2. Disk ro
Isothermal Rod T =T i
t ri
T ∞ ,h Figure 2: Schematic of disk and rod assembly
a) Derive the differential equation that governs the flow of heat through the disk (ri ≤ r ≤ ro). b) Give all the necessary boundary conditions which are required to solve the equation in (a). c) Give the functional form of the temperature profile that is the solution to (a). You do not have to solve for the constants! d) Using the temperature profile from part (c), derive an expression for the amount of heat entering the isothermal rod from the disk. e) Sketch the temperature profile from (ri ≤ r ≤ ro) to the surrounding fluid. End
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Midterm practice problems 1) Derive the equation for the temperature profile for the problem given in Lab 1. 2) A radial disk is mounted on an isothermal rod and is exposed to a fluid at T ∞ , h . At steadystate, the temperature of the fluid exceeds that of the isothermal rod and you may assume that heat entering from all surfaces of the disk flows to the isothermal rod in only the radial direction. The disk has an inner radius of ri, outer radius of ro and a thickness, t. A schematic of the radial disk and rod is given below in figure 2. Disk ro
Isothermal Rod T =T i
t ri
T ∞ ,h Figure 2: Schematic of disk and rod assembly
a) Derive the differential equation that governs the flow of heat through the disk (ri ≤ r ≤ ro). b) Give all the necessary boundary conditions which are required to solve the equation in (a). c) Give the functional form of the temperature profile that is the solution to (a). You do not have to solve for the constants! d) Using the temperature profile from part (c), derive an expression for the amount of heat entering the isothermal rod from the disk. e) Sketch the temperature profile from (ri ≤ r ≤ ro) to the surrounding fluid. End
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