8) Which of the following equation represents the cooling rate derived from Rosenthal's 3D equation on a semi-infinite body? Where: Q is the heat input, k is the thermal conductivity, V is the velocity of the heat source in x -direction, T and To are the temperature generated and ambient temperature respectively. (T-T.) a. -27k: Q а. (T-To)² b. -2rkV- (T-To) c. -27Q k d. -27QVT-T.)²
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- NUMBER 4 A food product wants to be produced in a small round shape (pellet) by freezing it in a water blast freezer freezer. Air freezer operates at -40 ° C. The initial product temperature is 25 ° C. The pellet has a diameter of 1 cm, and a density of 980 kg / m³. The initial freezing temperature is -2.5 ° C. The latent heat of freezing of the product is 280 kJ / kg. The thermal conductivity of the frozen product is 1.9 W / (m ° C). The convective heat transfer coefficient is 50 W / (m² K). Calculate the freeze time. t f = hourQ1 Passage of an electric current through a long conducting rod of radius r; and thermal conductivity k, results in uniform volumetric heating at a rate of ġ. The conduct- ing rod is wrapped in an electrically nonconducting cladding material of outer radius r, and thermal conduc- tivity k, and convection cooling is provided by an adjoining fluid. Conducting rod, ġ, k, 11 To Čladding, ke For steady-state conditions, write appropriate forms of the heat equations for the rod and cladding. Express ap- propriate boundary conditions for the solution of these equations.Specific Heat, Cp Water Thermal Thermal Content, Temperature, T Density, p Conductivity, k Ibm/ft3 Diffusivity, a ft2/s Food %(mass) °F Btu/h-ft.°F Btu/lbm-R Fruits/Vegetables Apple juice Apples Apples, dried Apricots, dried Bananas, fresh 1.51 x 10-6 1.47 x 10-6 87 68 62.4 0.323 0.922 85 32-86 52.4 0.242 0.910 41.6 73 53.4 0.127 1.03 x 10-6 0.650 1.22 x 10-6 1.51 × 10-6 43.6 73 82.4 0.217 0.662 76 41 61.2 0.278 0.856 Broccoli 21 35.0 0.223 | 1.42 x 10-6 Cherries, fresh Figs Grape juice 92 32-86 65.5 0.315 0.952 40.4 73 77.5 0.179 1.03 x 10-6 0.642 1.51 × 10-6 1.51 × 10-6 89 68 62.4 0.328 0.934 Peaches 36-90 2-32 59.9 0.304 0.934 Plums 3 38.1 0.143 | Potatoes 32-158 0-70 65.7 0.288 1.40 x 10-6 0.868 Raisins 32 73 86.2 0.217 1.18 x 10-6 0.592 Meats Beef, ground Beef, lean 67 43 59.3 0.235 1.40 x 10-6 0.802 74 37 68.0 0.272 1.40 x 10-6 0.844 Beef fat 95 50.5 0.110 72 95 73 Beef liver 0.259 0.832 1.18 x 10-6 1.40 x 10-6 Cat food 39.7 71.2 0.188 0.638 Chicken breast 75 32 65.5 0.275 0.850
- Newtons laws of cooling proposes that the rate of change of temperature is proportional to the temperature difference to the ambient (room) temperature. And can be modelled using the equation: dT/dt = -k (T-Ta)It can also be written as dT/T-Ta = -k dtWhere:T = Temperature of materialTa = Ambient (room) temperaturek = A cooling constanta) integrate both sides of the equation and show that the temperature difference is given by:(T-Ta) = CoE^-kt(Co is a constant for this problem)B) calculate Co if the initial temperature is 70 degrees C and Ta = 20 degrees C?36 -S 42 2. Metal castings can sometimes develop a gap between the casting and mold as the molten metal hardens. The result can be a substantially altered cooling process. Set up a simple heat-transfer model that would let you look at the effect of the gap on the cooling process. Assume the casting and mold are square in shape, with an air gap of thickness das shown in the figure. The mold sits in some ambient room temperature. State clearly all assumptions and develop a corresponding model of the heat transfer problem. Assuming that the casting is aluminum, the mold is diatomaceous earth and the gap is filled with air, see if you can arrive at and summarize some insight into the effect of the gap and its size on the heat transfer process.ng/19:HupCeX-7fb1 TjKjAnHHIrQ7-ussXeH9Kbx8 lo-gK_PM1@thread.tacv2 R Search WODOGA Vote 40000 00 Brushes Color Color Edit colors Edit with Paint 30 Shapes Colors Steam is generated at 4.1O MPa and 440C and condensation occurs at 0.105 MPa. Find the thermal efficiency of the cycl the T-S diagram. Draw the schematic diagram and
- You are tasked to design a cooling system for an ice rink. A standard ice rink has surface area ofArink = 1580 m2 . In this design, a technologically advanced solid state thermoelectric generatingcooling plate is placed in between concrete slabs. The following diagram contains the dimensionalparameters of the design (a) In the space below, with your best effort to correspond to the above diagram, draw a thermalcircuit that establishes the relationship between the cooling plate’s heat rate, Q, and the system’stemperatures and thermal resistances. Label the appropriate dimensions, thermal conductivities,convection coefficient, and temperatures. Ignore effects from contact resistance. (b) Given that the temperature at the top surface of the ice must be T ice = -5°C, obtain the requiredheat rate Q that must be drawn by the cooling plate in units Kilowatts. Be careful of +/- sign.Answer: ____________________________ [kW] c) Using the thermal circuit you established in Part (a), obtain the…Pls answer 4-10show complete step by step solution1 The temperature of the outer surface of the container T5,0 2 The temperature of the inside surface of the container Ts,i 3 The temperature at the center of the waste sphere (r = 0) °℃ °℃ °℃
- After a thorough derivation by Doraemon to establish an equation for cylindrical fuel rod of a nuclear reactor. Here he was able to come up an equation of heat generated internally as shown below. 96 = 9. where qG is the local rate of heat generation per unit volume at radius r, ro is the outside radius, and qo is the rate of heat generation per unit volume at the centre line. Calculate the temperature drop from the centre line to the surface for a 2.5 cm outer diameter rod having k = 25 W/m K, if the rate of heat removal from the surface is 1650 kW/m2 A 619 °C 719 °C C) 819 °C 919 °C E 1019 °C F None of theseEXL/ Calculate Cooling load temperature di fference (CLTD) for Sonth wall from grouPDat 32° North latitude Assume darK Colour,design outoor temperature 35 ,desion Îndoor temperature TR=25.5 è, mean outdoor temperature Tm= 29.4 c and daily range DR=.6¢ at hour 14. on october21.The schematic below illustrates a tank formed from two zones, i.e. liquid and solid. The tank is heated from the left-side with a time-varying solar heat radiation g,ol =f(t) (Wim), while the right-side is kept at a low temperature T. The top surface of the tank is subjected to the ambient conditions, i.e. (hair & Tair ), while its bottom is thermally insulated. Conjugate heat transfer takes place between the two-physically different zones through the fluid-solid interface separating them, while fluid flow is induced due to buoyancy effects where the buoyancy force is approximated according to Boussinesq formulation Fiuoyaney=P0 Bg(T-To). Explain the following: 1- The assumptions required to simulate the below problem. 2- The conservation equations governing the transport phenomena in each zone. 3- The boundary conditions closing the mathematical model. 4- The discretized form of each conservation equation stated in (point 2) above. 5- The appropriate differencing scheme to be used for…