Example 7. The temperature distribution within the thermal boundary layer over a flat plate is as T ( y) = ay² + be. Here, a and b are constant and y is normal distance measured from the plate. If liquid flowing over the plate has temperature 25°C and K= 0.1W/m-K, then calculate the value of b. %3D Given, hocal = 2.0 W/m2-K, T. = 85°C %3D Jocal
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- t = 30 + 0.9563 (62.2- 30) = 60.79°C (Ans.) Example 4.14. A very thin glass walled 3 mm diameter mercury thermometer is placed in a stream of air, where heat transfer coefficient is 55 W/m2°C, for measuring the unsteady temperature of air. Consider cylindrical thermometer bulb to consist of mercury only for which k and a = 0.0166 m2/h. Calculate the time required for the temperature change to reach half its final or, %3D 8.8 W/m C %3D value.J 6 A semi-infinite solid, with a boundary condition of convection on the surface (Tfluid = 100°, h = 220 W/m2-°C) has at t=0s, a uniform temperature of Ti = 0°C, draw the isotherm of 60°C, at time t = 2h. Consider the solid to be cast iron.A:Find the amount of heat transferred through an iron fin of thickness 5 mm, length 10 cm and width 100 cm. Also determine the temperature difference e at the tip of the fin at: 1- adiabatic tip, 2-heat convection at the tip. Assuming the atmospheric temperature of 28°C K=50 w/mK, h=10 w/m’K, O,=80°C. B-Why is the dimensional heat flow assumption important in the analysis of fins problems? C- Why are the annular fins more efficiency than others?.
- 19 mm diameter steel balls are quenched by heating to 989 K followed by slow cooling to 400 K in an environment with air at T∞ = 325 K and h = 39 W/m2.K. Assuming that the steel properties are k = 40 W/m.K, ρ = 7800 kg/m3 and C = 600 J/kg.K, estimate the time (in "minutes") required for the cooling process. Bolas de aço com 19 mm de diâmetro são temperadas pelo aquecimento a 989 K seguido pelo resfriamento lento até 400 K em um ambiente com ar a T∞ = 325 K e h = 39 W/m2.K. Admitindo que as propriedades do aço sejam k = 40 W/m.K, ρ = 7800 kg/m3 e C = 600 J/kg.K, estime o tempo (em "minutos") necessário para o processo de resfriamento.A composite plane wall consisting of materials, 1.5-in steel (k = 312 BTU-in/HR.ft2.0F) and 2-in aluminum (k = 1400 BTU-in/HR.ft2.0F), separates a hot gas at Ti = 2000F, hi = 2 BTU/HR.ft2.0F, from cold gas at To = 80 deg F, ho = 5. If the hot fluid is on the aluminum side, find: a) Transmittance, U; b) The heat through 100 sq. ft of the surface under steady state condition and c) The interface temperature at the junction of the metals.An ordinary egg can be approximated as a 5.5-cm-diameter sphere whose thermal conductivity of roughly k = 0.6- W mk overall density of p = 1000; and heat capacity of C₂ = 3000- kg m² The egg is initially at a uniform temperature of T₂ = 10°C and is dropped into boiling water at T.. = 90°C W - determine how long it will take for the egg to m²K Taking the convective heat transfer coefficient to be h reach T = 70°C. In solving the problem, please follow the steps below. For the Lump Model In solving this problem, please use the lump model method (ignoring the requirement of small Biot number and discuss the outcomes, 1. 2. Compute the characteristic length Lc Compute the volume and surface area of the sphere (as the egg model) Vol As 3. Compute the diffusivity α = = 10- k p Cp = J kgk Compute non-dimensional excessive temperature 0 = h Lc k 4. Compute the Biot number using the characteristic length found above Bi = T-Too 5. Ti-Too 6. Calculate the Fourier number from the equation =…
- Q3: In iron whose base plaet is mad aluminum alloy is turn on : The time for the plate temperature to reach 140°C. Determine the plate temperature which is to be uniform at all times . Take for the aluminum p=2770 kg/m, C,-875 kJ/kg."C , a=7.3 m/s. The thermal conductivity of the plate k=177 W/m."C Air 22°C Ans : 51.8 °C IRON 1000 W ttt t tSteel is sequentially heated and cooled to relieve stresses and to make it less brittle. Consider a 100 mm thick plate that is initially at a uniform temperature of 300 °C and is heated on both sides in a gas fired furnace for which To 700 °C and h=500 W/m². K. How long will it take the coldest spot to reach 550 °C in the plate? Materials properties are given in this graph. == = Steel plate: 11 T₁ = 300°C T(0,t) = 550°C L = 50 mm Combustion gases p=7800 kg/m3 Cp = 500 J/kg-K k = 45 W/m-K T∞ = 700°C h = 500 W/m²-KA metallic ball of radius ro = 5 mm, is initially in equilibrium at 400 C in a furnace. It is suddenly dropped to water at 20 C ( hw = 11003 W/m^2). The properties of the sphere are density= 3000 kg/m3, k = 20 W/m_ K, c = 1000 J/kg K, and α= 6.66E-6 m2/s. Calculate the time required for the center of the sphere to cool to 50 C.
- Q1-A block as sphere made of Teflon initially at a temperature of 90 C is suddenly immersed in a fluid at 20 C. The convection heat- transfer coefficient is 15 W/m2 C. Determine the dimension of the block that it is just considered as lumped-capacity system. Calculate : (1) the time the center of the sphere reaches the half value of initial temperature and, (2) the heat loss from the block at that time.4.) A 15-cm-diameter steam line carries saturated steam at 6 MPa and is located in a tunnel with stagnant air with a temperature of 50oC. The outside unit convective coefficient is 8.5 W/m2-K. The steam line is covered with 3 cm of 85% magnesia insulation. It is decided to reduce the heat loss by one-half. How much 85% magnesia insulation is required? Neglect thermal resistance of pipe and inside surface.Steel balls 12 mm in diameter are annealed by heating to 1100 K and then slowly cooling to 360 K in an air environment for which T. = 325 Kand h = 20 W/m2-K. Assuming the properties of the steel to be k = 40 W/m-K,p = 7800 kg/m, and c = 600 J/kg-K, estimate the time required for the cooling process. The time required for the cooling process isi h.