In a particular application involving airflow over a heated surface, the boundary layer temperature distribution may be approximated as
where y is the distance normal to the surface and the Prandtl number,
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Introduction to Heat Transfer
- The properties of mercury at 300 K are Density = 13529 kg/m³. c = 0 1393 kJ/kgk dynamic viscosity = 0 1523 x 102 Ns/m² and thermal conductivity = 8 540 W/mK . What is the Prandtl number of the mercury at 300 K?arrow_forwardThe data listed below is from a passenger hot air balloon. The balloon is designed to lift 10-people (80 kg each person). The balloon consists of a basket, a burner- propane tank system. It will lift up when the cold air trapped inside warms up by the burner. Density of air inside the balloon is 99°C: 0.9486 kg/m³, density of air outside balloon is 20°C (ambient): 1.2041 kg/m³ Mass (kg) Balloon Basket Burner Propane tank 113.4 kg 63.5 kg 22.7 kg 183.7 kg Assume the balloon is a sphere shape, volume =(4/3)pi R3. a. Determine the minimum diameter of the balloon that would have a total lifting force to balance the weight of balloon, basket, burner, propane tank and 10 people? b. If the balloon is converted to survey the weather, it will be filled with hydrogen gas (H2). Assume the weight of the people (800kg) is now replaced by onboard equipment, what is minimum diameter needed to keep it afloat at 18km above the surface of the earth?arrow_forwardՁ Ա 12h fluid with f. **>x u Figure 1: Parallel Plates, top plate moving to the right at 2U and the bottom plate moving to the left at U. / ני ди suly)=? Figure 2: Angled Plate with a free surface 3. Figure 1 shows two infinite parallel plates separated by a distance 2h where the top plate is moving at a velocity 2U to the right and the bottom plate is moving to the left at a speed U. Noting that the coordinate system starts at the midpoint between the plates find the following: (a) Use continuity and boundary conditions to show v = 0 everywhere. (b) Derive the velocity profile u (y) using Navier-Stokes Equation. (c) At what position between the two plates is u (y) = 0?arrow_forward
- Q5/A 400 m² light-colored swimming pool is located in a normal suburban site, where the measured wind speed at 10 m height is 2 m/s. The water temperature is 25 °C, the ambient air temperature is 10 °C, and relative humidity is 60%. There are no swimmers in the pool, the temperature of the make-up water is 20 °C, and the solar irradiation on a horizontal surface for the day is 15 MJ/m2-d. Neglect heat losses due to evaporation and radiation. How much energy must the solar system supply (Qss) to the pool to keep its temperature to 25 °C? Take: a = Solar absorptance (a = 0.85 for light-colored pools; a = 0.90 for dark colored pools).arrow_forwardAir flows over a flat plate at 38 m/s, 25°C and 1 atm pressure. The kinematic viscosity of air at 25°C is ν = 1.562 × 10−5 m2/s. What plate length should be used to achieve a Reynolds number of 1 × 108 at the end of the plate? (Round the final answer to two decimal places.)arrow_forwardFor most gases at standard or near standard conditions, the relationshipamong pressure, density, and temperature is given by the perfect gasequation of state: p = ρRT, where R is the specific gas constant. For airat near standard conditions, R = 287 J/(kg · K) in the International System of Units and R = 1716 ft · lb/(slug · ◦R) in the English Engineering System of Units. Using the above information, consider the following two cases: a. At a given point on the wing of a Boeing 727, the pressure andtemperature of the air are 1.9 × 104 N/m2 and 203 K, respectively.Calculate the density at this point.b. At a point in the test section of a supersonic wind tunnel, the pressureand density of the air are 1058 lb/ft2 and 1.23 × 10−3 slug/ft3,respectively. Calculate the temperature at this point.arrow_forward
- Fluid Mechanicsarrow_forwardThe heat flux for stable film boiling on the outside of a horizontal cylinder or sphere of diameter D, in m, is given below. What should be the value of "n", for the equation above to be dimensionally consistent? Use dimensional analysis: q=heat flux, W m² W k = thermal conductivity of vapor, 'm °C hgf - [g kỷ Pv(P₁ − Pv)[hfg + 0.4 Cpv (Ts − Tsat)]] à = Cf MyD (Ts - Tsat) Pv = density of vapor, P₁ = density of liquid,- kg m³ kg 'm³ Cpv = enthalpy of vaporization, kg g = gravitatioinal acceleration, C = experimental constant, dimensionless m J kg °C Ts = surface temperature of the heater, °C Tsat = saturation temperature of vapor, °C kg Hv = viscosity of vapor, ms = specific hear of vapor, (Ts - Tsat)arrow_forwardA steel ball with the density of 6229 kg/m and the radius of 0,65 cm was dropped into the oil whose viscosity was to be measured as isseen in the figure. When the ball attains a constant velocity, the distance that the ball travelled was measured as 99 cm within the time interval of 4,7 sec. Before the experiment, the mass of the 100 ml-oil was measured as 2,1 gr. According to the data given above, find; a) the density of the oil (in kg/m ). (Please do not use any decimal digit.) b) the speed of the steel ball after the ball attains a constant velocity (in m/s). (Please use 4 decimal digits.) c) the dynamic viscosity of the oil (in Pa.s) (Please use 3 decimal digits.) d) the flow Reynolds number. (Please use 4 decimal digits.) Please solve this question step by step to reach correct answers. correct answers: a) 21 b) 0,2106 c) 2,715 d) 0,0212arrow_forward
- A cube of side (a) and mass (M) is initially sitting fully submerged at the bottom of a container filled with a liquid of kinematic viscosity v and density p. The container has a square cross-section of side (a+a/5) and the cube is sitting right at the middle of the container base. (a) A force (F) starts pulling the cube up at a constant velocity (U). Develop an expression for the force in terms of (U, M. a. g, p and v). You may assume that the velocity in the gap between the cube's sides and the container walls is linear. The expression for (F) is to be valid as long as the cube remains submerged. (b) After the cube reaches the water surface, it continues to be pulled up by the same force. Develop a differential equation for the variation with time of the fraction of the cube that is submerged in water.arrow_forwardA compressed air tank is designed to contain 50 standard cubic feet of air when Ölled to a gaugepressure of 200 atm at an ambient temperature of 70 F. Calculate the interior volume of thetank. One standard cubic foot of air occupies one cubic foot at standard temperature and pressure(T = 59 F and p = 2116 lb/ft2).arrow_forwardFor the flow of a viscous fluid, with the velocity V = f(x)g(y)h(z)i (where f, g, h are arbitrary functions), the following conditions are given: . The flow is adiabatic. • The quantities v = 2 and 3 = $ are constants. • The velocity circulation is conserved for the flow, irrespective of the values of vand 3. What is the general solution for the functions f, g, h?arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning