EGEE304Spring2018_Quiz1_Solutions.pdf - EGEE 304 Spring 2018 Heat and Mass Transfer Quiz 1 Introduction to Heat Transfer Name PSUID 1 You have a plane

EGEE304Spring2018_Quiz1_Solutions.pdf - EGEE 304 Spring...

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Unformatted text preview: EGEE 304 Spring 2018 Heat and Mass Transfer Quiz 1: Introduction to Heat Transfer Name: __________________________ PSUID: ____________________ 1. You have a plane wall that contains a heat source, as shown in the figure. Using your knowledge of heat transfer, and the information in this figure: a) What is an energy balance on a “thin” volume element in words. Hint: there are four terms as suggested in the equation – write the energy balance with one term in each ( ) set – 1 point each term (4 points total): A · Qx 0 ( )–( )+( · Egen Volume element · Qx + ∆ x x )=( x + ∆x L Ax = Ax + ∆ x = A 2. What is the driving force for heat transfer (1 point)? 3. Draw a thermal circuit for the situation below labeling all resistances; note T1 > T2 (2 points). T!1 Wall T1 T2 T!2 · Q R T R T R ) FIGURE 2–13 One-dimensional heat conduction through a volume element in a large plane wall. b) Write the heat equation that is represented by your energy balance in simplified form. State any assumptions you made to write this equation (3 points). 135 CHAPTER 3 x (%/%t " 0 and e·gen " 0) dr !r dr " " 0 (2–29) EGEE 304 Spring 2018· Egen Note that we again replaced the partial derivatives by ordinary derivatives inHeat and Mass Transfer the one-dimensional steady heat conduction case since the partial and ordinary Quizare 1: Introduction to Heat Transferdepends (Make up) derivatives of a function identical when the function on a single variable only [T " T(r) in this case]. –31) PSUID: ____________________ 0 –20. Name: __________________________ n be Heat Conduction Equation in a Sphere Now consider a sphere with wall density #,below. specific heat c, the andtemperatures outer radius R.are The 1. Draw a thermal circuit for the plane shown Please note that given in this picture, area of the sphere normal to the direction of heat transfer at any location is and be sure to draw and label all resistances (3 points). A " 4Insulation pr 2, where r is the value of the radius at that location. Note that the heat –32) transfer area A depends on r in this case also, and thus it varies with location. One-dimension By considering a thin spherical shell element of thickness $r and repeating A1 2 through a volume e the approach described above for the cylinder by using A " 4 pr instead of 1 k1 A3 transient heat conduction equation for a T1 A " 2prL, the one-dimensional 3 –33) 2 isk2determined to be (Fig. 2–17) sphere k3 A2 h, T$ ! " %T 1 % 2 %T r k ! e·gen " rc 2 %r %r %t r Variable conductivity: (2–30) which, inL1the thermal conductivity, reduces to = L 2case of constant L3 –34) . egen 1 % 2 %T 1 %T r conductivity: ! " (2–31) 2 %r %r a and 2. QIs· it possible to over-insulate a· pipe? Why or r why not? Explain based k on %t your knowledge of heat transfer (2 points). Q ons hird lay- onal the ! · Q1 Constant " R T1 1 where · again the property a " k/rc is the thermal diffusivity of the material. It Q2 $ R3 Rconv Tunder reduces to the following forms specified conditions: . R2 egen (1) Steady-state: 1 d 2 dT r ! "0 FIGUREr 23–20 (%/%t " 0) dr dr k Thermal resistance network for (2) Transient, combined series-parallel arrangement. 1 % 2 %T 1 %T r " no heat generation: 2 %r %r a %t r (e· " 0) gen ! " (2–32) ! " (2–33) (3) Steady-state, dT d dT d 2T " by 0 the form: or r 2 !2 "0 no heat generation: 3. For a given medium, the heat equation ris2satisfied dr dr dr dr · (%/%t " 0 and egen " 0) ! " (2–34) where again we replaced the partial derivatives by ordinary derivatives in the a) Is heat transfer steady or transient (1 point)? ________________________ one-dimensional steady heat conduction case. b) Is there generation in the medium (1 point)? ________________________ c) Which coordinate system are we using (1 point)? ________________________ 4. How are flux and rate of heat transfer related (2 points)? ...
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