## Vm 335 Heat Transfer

## Final Exam

Heat Transfer代考 A cold rectangular plate, of length a and width b with a > b, is hanged vertically in saturated water vapor.

**Problem 1 (30 points) **

**Part A (10 pts) **

A scientist conducts wind tunnel experiments with air flow on the model of an aircraft. The actual aircraft is 10 times larger than the model and is expected to experience air flow velocity of *u**∞ *while in operation. Assuming the characteristic length of the model to be *L*, answer the following questions

(a) What should be the air velocity *U*1 inside the wind tunnel to preserve hydrodynamic similarity?

(b) What will be the heat transfer coefficient experienced for the actual aircraft if the measured heat transfer coefficient on the model inside the wind tunnel is *h*? Assume that the Prandtl number of air remains the same. Heat Transfer代考

**Part B (10 points) **

Consider a flow of water inside a tube. The heat transfer from the tube wall to the fluid is given to be *q**s ’ **=ax*^{2} (W/m).

(a) Derive the expression for the mean fluid temperature *T**m*(*x*) as a function of tube length *x*, mass flow rate, specific heat *c**p *and the inlet mean temperature *T**m,i*.

(b) On the *T-x *diagram, sketch the mean fluid temperature *T**m*(*x*) as a function of distance along the tube. Note that *x**fd,t *is the thermal entry length.

**Part C (10 points) **

A cold rectangular plate, of length *a *and width *b *with *a *> *b*, is hanged vertically in saturated water vapor. The vertical side can be either along *b *(Case 1) or a (Case 2), as illustrated. Laminar film condensation occurs on the cold plate. What is the condensation rate ratio of Case 1 to Case 2?

Please provide brief explanation to your result below.

**Problem 2 (20 pts) **

A shell-and-tube heat exchanger is consisted of *N *tubes. The heat exchanger is used to condense saturated stream at 340 K at rate of 2.73 kg/s. Condensation occurs on the outer tube surfaces, and the corresponding convection coefficient is 10000 W/m2 K. The temperature of the cooling water enters at 15ºC and exit at 30 ºC. The tubes are thin-walled, having a length *L* 0.8 m and diameter of *D* 0.019 m. The mass flow rate in a *single tube *is 0.141 kg/s. Heat Transfer代考

Material properties may be useful:

Saturated water at 340 K, latent heat *h*_{fg}= 2.342× 10^{6}J/kg

Cooling water at 22.5 ºC, heat capacity *c*_{p}= 4181J/kg·K

(a) **(5 pts) **Calculate the total heat exchange rate *q *of this heat exchanger.

(b) **(5 pts) **Estimate the number of tubes *N *of the heat exchanger.

(c) **(10 pts) **Estimate the overall heat transfer coefficient *U*

**Problem 3 (30 pts) Heat Transfer代考**

A laser-materials-processing apparatus encloses a sample in the form of a thin disk. The sample has an opaque and diffuse surface for which the spectral distribution of the emissivity *ε**λ *is shown below.The apparatus enclosure is large, with isothermal walls at *T*w = 400 K. The sample is maintained at an operating temperature of *T**s **= *1500 K.

(a) **(7 pts) **Determine the total emissivity *ε *of the sample.

(b) **(7 pts) **Determine the total absorptivity *α *of the sample for irradiation from the enclosure walls.

(c) **(10 pts) **A parallel laser beam with a wavelength of λ 3 μm irradiates the upper surface of the sample. To reduce oxidation, an inert gas stream of temperature *T*∞ = 300 K and convection coefficient *h = *70 W/m2 K flows over the sample. Determine the laser irradiation, *G*laser, required to maintain the sample at *T**s *= 1500 K.

(d) **(6 pts) **Consider a cool-down process, when the laser and the inert gas flow are suddenly turned off. Sketch the total emissivity of the sample as a function of time during the process. Identify the emissivity for the initial and final conditions.

**Problem 4 (30 pts) Heat Transfer代考**

As shown in the left figure below, a cylindrical furnace with a diameter of *D* 1 m and a length of *L *0.8 m is located on the combustion chamber. A plate at the top of the furnace with a thermal conductivity *k* 75 W/mK and a thickness of *H* 0.1 m is heated up whose upper and lower surface temperatures are measures as *T*0 and *T*1, respectively. The lower surface of the plate is a diffuse, gray surface with an emissivity of *ε*1 0.8. The side wall of the furnace with temperature *T*2 is diffuse, gray and perfectly insulated. The inlet temperature of the furnace (as shown by the dashed line, which can be regarded as an imaginary black surface) is measured at *T*3 1000 K.

(a) **(5 pts) **Find the view factor of the lower surface of the plate with respect to the wall, *F*12.

(b) **(5 pts) **Sketch the radiation network for the system and label all pertinent resistances and potentials. Heat Transfer代考

(c) **(6 pts) **If *T*1 600 K, calculate the radiative heat transfer to the plate *q*1.

(d) **(6 pts) **If *T*1 600 K, calculate the wall temperature *T*2.

(e) **(8 pts) **As shown in the figure on the right, considering heat convection near the lower surface of the plate, where the hot air near the lower surface of the plate has a temperature of *T**a* 750K with a convection coefficient of *h*. If *T*1 600 K, *T*0 550K, find the convection coefficient *h*.