高等传热学课程作业1

1、高等传热学 课程作业Homework 5.21. Slug flow in a tube(u(r) = V) with a fully developed temperature profile:- Constant heat flux- What is T(r)?·Remember dTm/dx = constant·Use dT/dr = 0 at r = 0 and Tw at r = R to get ingration constants- What is Nu?A: 根据能量方程， (1)对于充分发展的管内弹状流，u=0, 且由于 = constant，因此(1

2、)式可化简为： (2)解之可得， (3)根据边界条件，代入(3)中，得到C1=0, 平均温度因此，得到2. Fully developed Poiseuille flow between parallel plates- Constant heat flux- Top and bottom at the same temperature- Neglect viscous dissipation- What is T(y)?·Remember dTm/dx = constant·Use Tw at y = 0 and y = h to get integration cons

3、tants- What is Nu?A: 根据能量方程， (1)对于x方向充分发展的Poiseuille流，v=w=0由于 = constant，(1)式可化为： (2)根据，且，代入得到解得温度分布为 (3)根据Poiseuille流边界条件：带入(3)式中解得，, 因此，得到温度分布为根据 Nu Homework 5.31. Find the equation for the boundary layer thickness and for Cf for:Compare to the exact values and the fourth order equation solutions.

4、A: 对于，根据边界条件， a = 0， 1 = b + c + d对于平板，有， c = 0根据， b + 3d = 0由此可得，a = 0, b = 1.5, c = 0, d = -0.5.对于U = constant，积分后得到，与精确解相差7.2%，与4级近似解相差20.5%，且与精确解相差2.6%，与4级近似解相差5.5%2. Derive the ordinary differential equation and the boundary conditions for the Blasius solution energy equation for flow over a fl

5、at plate. (See pages 29-30)A: 根据能量方程，常壁温边界条件：根据Blasius solution 代入能量方程中得到，即 边界条件为3. Start from the local friction coefficient for flow over a flat plate, Cf, on slide 31 and derive the average friction coefficient over the entire plate, CL. Show your work.A: 4. A projectile in the form of a bluff-en

6、ded cylinder 20 cm in diameter and 60 cm long, moves through the air in the direction of its long axis at a velocity U of 100 m/s. The drag coefficient, C, is equal to 1.0 for this object. Frontal area=pD2/4, FD= total dragAssuming that the boundary layer thickness over the cylindrical surface of th

7、e projectile at a distance x from the leading edge is given by:and that the momentum thickness of the boundary layer is given by: Find what proportion of the total drag on the projectile is attributable to skin friction over the curved surface, assuming no pressure gradient in the boundary layer in

8、the streamline direction. Data. Air kinematic viscosity is 0.15 cm2/sAir density is 1.15 Kg/m3Assumptions: Assume this is like a flat plate, then use the equation on slide 15. A: 若将圆柱表面看成平板，U = constant, ，则因为12.16N180.64N6.7%Homework 5.41. Derive the equation relating q” to the temperature differenc

9、e for natural convection driven flow in a round tube (like on slide 19 for parallel plates).- water properties at 25 C- tube length = 100 cm- tube diameter = 1 mm- constant heat flux- fully developed flow in a tube (from the first homework)a) Plot DT and Q (m3/s) versus heat flux for fluxes of 500 t

10、o 5000 W/m2 b) Is the assumption of fully developed flow valid?- hint: is L/(D Re) > 0.05c) Is the Boussinesq approximation valid here?A: 圆管内充分发展的流体，其速度分布为平均速度体积流量为根据能量平衡，即 将代入，得到，a) 根据以上推导过程可以得到，分别作出当时与Q随q变化的曲线，如下图所示。b) 125.4 > 0.05 满足充分发展的假设c) 热膨胀系数0.085 < 1满足Boussinesq假设2. a) Derive the similarity solution equation for