Heat Transfer by Convection

Convection The flow of heat associated with the movement of a fluid, such as when hot air from a furnace enters a room, or to the transfer of heat from a hot surface to a flowing fluid.

Math. Model by convection The convection flux is usually proportional to the difference between the surface temperature and temperature of the fluid, as stated in Newton’s law of cooling (牛顿冷却定律) Where: q: heat transfer rate, w A: heat transfer area, m2 Ts : surface (wall) temperature, K Tf: fluid temperature, K h: heat-transfer coefficient , w/(m2 .K ) h is not a physical property of the fluid, but depends on the flow patterns determined by fluid mechanics as well as on the thermal properties of the fluid. (对流传热膜系数 film coefficient)

Note that the linear dependence on the temperature driving force ts-tf is the same as that for pure conduction in a solid of constant thermal conductivity.

Two Kinds of Convections First one is natural (free) convection 自然对流 Definition: If the currents are the result of buoyancy forces generated by differences in density and the differences in density are in turn caused by temperature gradients in the fluid mass, the action is called natural convection.

Second is Forced Convection 强制对流 Definition: If the currents are set in motion by the action of a mechanical device such as a pump or agitator, the flow is independent of density gradients, and is called forced convection.

Types of Convection Temperature gradient Nature convection Without phase change With phase change Density gradient Forced convection Without phase change With phase change

Important physical properties in convection Nusselt number Nu 赛努尔数 Dimensionless group (P179) h: film coefficient , W/(m2 .K ) D: diameter or length k: thermal conductivity, W/(m .K ) Prandtl number Pr 普朗特数 (P186) is the ratio of the diffusivity of momentum ν or μ/ρ to the thermal diffusivity α or k /ρcp cp: specific heat 比热 , J/(kg·℃ ) μ: viscosity of fluid, Pa·s k: thermal conductivity, W/(m .K )

Graetz number Gz 格雷兹数 (P189) is commonly used in treating heat transfer to fluids Peclet number Pe 佩克莱特数 (P189) α: thermal diffusivity k/ρcp Grashof number Gr 格拉斯霍夫数 (P200)

Empirical equations For laminar flow heat transfer in tube for air and moderate-viscosity liquids for viscous liquids Heat Transfer by forced convection in turbulent flow 0.4 when the fluid is being heated n= 0.3 when the fluid is being cooled

Example 4.7 Benzene at 20℃ flows through the pipe of a 1-2 pass shell-tube exchanger cosisting of 48 steel tubes (Φ25×2.5 mm) with flow rate of 9.5 kg/s and is heated to 80℃ by saturated vapor which goes through shell-side. What is the heat transfer coefficient hi between benzene pipe wall? If benzene flow rate is double and other conditions are unchanged, what is the heat transfer coefficient between benzene pipe wall? If the pipe diameter is decreased to the half of origin and other conditions are similar to case (1), what is the heat transfer coefficient between benezene and pipe wall?

Double pipe heat exchanger（双管式换热器）

Shell-tube heat exchanger(壳管式热交换器)

A point temperature difference approaches Temperature range

Energy Balance In heat exchangers there is no shaft work, and mechanical, potential, and kinetic energies are small in comparison with the other terms in the energy-balance equation. where =flow rate of stream q=Q/t= rate of heat transfer into stream Ha、Hb= enthalpies焓 per unit mass of stream at entrance and exit, respectively. Overall enthalpy balance

If only sensible heat is transferred and constant specific heats 比热 are assumed, For a condenser with saturated vapor (no superheat) enter the condenser and the condensate leaves at condensing temperature without being further cooled. λ=latent heat 潜热 of vaporization of vapor If the condensate leaves at a temperature Thb that is less than Th, the condensing temperature of the vapor, thus

Countercurrent (逆流)and parallel (并流) flows countercurrent flow 逆流 parallel flow 并流 Logarithmic mean temperature difference （LMTD）对数平均温差

For the inside of tube (the warm side) For the outside of tube (the cold side) inside The rate of heat transfer through the tube wall outside

overall coefficient

Fouling factors (污垢系数） In actual service, heat-transfer surfaces do not remain clean. Scale, dirt, and other solid deposits form on one or both sides of the tubes, provide additional resistances to heat flow, and reduce the over all coefficient.

Example 4.4 The butyl alcohol with flow rate 1930 kg/h and specific heat cp 2.98 kJ/(kg·℃) is cooled from 90 ℃ to 50 ℃ in a 6 m2 exchanger having overall heat transfer coefficient 230 W/(m2 ·℃). Water at 18 ℃ is used as a cooling medium. If the exchanger is operated with countercurrent flow and heat loss can be ignored, what are the outlet temperature and flow rate of cooling water?

Conclusion Conduction（热传导） （4.2-1）P163 Steady-State Conduction k thermal conductivity热导率 W/(m ·℃) R thermal resistance热阻 (m2 ·℃)/W ☆Calculating about k 1、 pick up k at the arithmetic average (算术平均)of the temperature

2、 for large temperature range for most liquid k decreases by 3-4% for a 10℃ rise in temperature, except water For monatomic(单原子) gases, a hard-sphere model gives the theoretical equation: ☆Calculating in series (4.2-11) P167 a flat wall a cylinder

Convection（对流传热） (4.1-2) P162 Nusselt number Nu 赛努尔数 (P179) Prandtl number Pr 普朗特数 (P186) Graetz number Gz 格雷兹数 (P189) Peclet number Pe 佩克莱特数 (P189) laminar flow (4.4-19) P190 0.4 being heated turbulent flow n= 0.3 being cooled P191

countercurrent flow 逆流 Enthalpy balance Logarithmic mean temperature difference （LMTD）对数平均温差 countercurrent flow 逆流 parallel flow 并流 (4.3-36) P181 overall resistance overall coefficient

Problem 4.7 Air at the normal pressure passes through the pipe (di 20mm) and is heated from 20℃ to 100℃. What is the film heat transfer coefficient hi between the air and pipe wall if the average velocity of air is 10 m/s? The properties of air at 60℃ are as follows. Air: density ρ 1.06 kg/m3, viscosity μ 0.02 cP, conductivity k 0.0289 W/(m·℃), and heat capacity cp 1 kJ/(kg·K).

Problem 4.9 Benzene with mass flow 1800 kg·h-1 flows through the annulus of double pipe exchanger. Its temperature changes from 20℃ to 80℃. The dimension of inner tube is Φ19×2.5mm, and the dimension of outer tube is Φ38×3mm. What is individual heat transfer coefficient of benzene?

Problem 4.12 A hot fluid with a mass flow rate 2250 kg/h passes through a Φ25×2.5mm tube. The physical properties of fluid are as follows: k=0.5 W/(m·℃), cp=4 kJ/(kg·K), viscosity 10-3 N·s/m2, density 1000 kg/m3 Find: Heat transfer film coefficient hi, in W/(m·K). If the flow rate decreases to 1125 kg/h and other conditions are the same, what is the hi? If the diameter of tube (inside diameter) decreases to 10 mm, and the velocity u keeps the same as that of case a, calculate hi. When the average temperature of fluid and quantity of heat flow per meter of tube are 40 ℃ and 400 W/m, respectively, what is the average temperature of pipe wall for case a? From this problem, in order to increase the heat transfer film coefficient and enhance heat transfer, what kinds of methods can you use and which is better, explain?

Problem 4.14 In a double pipe exchange (Φ23×2mm), the cold fluid [cp=1 kJ/(kg·K), flow rate 500 kg/h] passes through the pipe and the hot fluid goes through the annular. The inlet and outlet temperatures of cold fluid are 20℃ and 80℃, and the inlet and outlet temperatures of hot fluid are 150℃ and 90℃, respectively. The hi (heat transfer coefficient inside a pipe) is 700 W/(m2·℃) and overall heat transfer coefficient Uo (based on the outside surface of pipe) is 300 W/(m2·℃), respectively. If the heat loss is ignored and the conductivity of pipe wall (steel) is taken as 45 W/(m·℃), find: Heat transfer coefficient outside the pipe ho? The pipe length required for counter flow, in m? What is the pipe length required if the heating medium changes to saturated vapor (140℃) which condenses to saturated liquid and other conditions keep unchanged? When the exchanger is used for a year, it is found that it cannot meet the need of production (the outlet temperature of cold fluid cannot reach 80℃), explain why?

Problem 4.19 Water flows through the pipe of a Φ25×2.5mm shell-tube exchanger from 20℃ to 50℃. The hot fluid (cp 1.9 kJ/(kg·K), flow rate 1.25 kg/s) goes along the shell and the temperatures change from 80℃ to 30℃. Heat transfer coefficients of water and hot fluid are 0.85 kW/(m2·℃) and 1.7kW/(m2·℃). What is the overall heat transfer coefficient Uo (based on outer surface area of tube) and heat transfer area if the scale resistance can be ignored? (The conductivity of steel is 45 W/(m·℃)).

Problem 4.20 Heated oil (heat capacity cp=3.35 kJ/(kg·℃)) is cooled by water (heat capacity cp=4.187 kJ/(kg·℃)) and they flow countercurrently through a double pipe exchanger with inner pipe dimension Φ180×10mm. Water at 15℃ of inlet temperature goes through the pipe and leaves at 55℃. Oil passes through the annulus with mass flow rate 500kg/h and inlet and outlet temperatures of oil are 90℃ and 40℃, respectively. The heat transfer coefficients hi and ho for water and oil are 1000 W/(m2·℃) and 299 W/(m2·℃), and heat resistances of pipe wall and fouling as well as heat loss can be ignored. Find: Water flow rate, in kg/h. Overall heat transfer coefficient Uo based on outer surface of pipe. LMTD △tm and pipe length of pipe, in m. If inlet temperature of water becomes 20℃ and oil inlet temperature keeps the same, what happens to that? In order to enhance heat transfer, what ways can be employed?