EXAMPLE 10.6 Discretize the equation =0 at node (i, j) of an interior corner axəy with the convection boundary condition as shown in Fig. 10.8. i, j+ 1 i-1, j i+ 1.j T h i, j-1 Ar
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- 650 °K hair 400°K 300°K 290°K Z777777///, エnSulacien Vair = 5m/s A Free Convection Find the air convection heae transfer knowing coefficiene Chair), that wind speed 5m/s. Surrounding ai cemp occurs is conveceian Where Too= 290OK.A product food with a moisture content of 80% in canned diameter 5 cm want to be frozen. Density product is 1000 kg/m³, the thermal conductivity is 1.0 W/(m K), and initial temperature frozen is -1.75 °C. After 10 hours in medium freezer -25 °C, the temperature of the products be -10 °C. Estimate coefficient heat transfer convection medium freezing. Assume cans as infinite cylinder. a. h = ... W/(m² K).Derive the finite different equations for all the nodes/boundaries in the plate. For this, a small grid is recommended (3x3 at least) T=100 C T=0 C h=200W/m?C q"=100W/m? Insulated pls, do by hand in details by ENERGY BALANCE METHOD
- Solve the heat equation u, = 0.2u on a digital computer using XX the Crank-Nicolson scheme. for the initial condition and boundary conditions TABLE P4.1 Case 1 2 3 4 5 Number of Grid Points 11 11 16 11 11 (x,0) = 100 sin TX L 0.25 0.50 0.50 1.00 2.00 L = 1 u(0,t) = u(L,t) = 0 Compute to t = 0.5 using the parameters in Table P4.1 (if possible) and compare graphically with the exact solution.Made-Up Problem (from class): 20.00 °C along its complete length. One end 60.00 °C, while the other end of the rod is placed in contact with a cold reservoir at T, = 20.00 °C, thus setting up a thermal gradient along the length of the rod. Using An aluminum rod of length L = 1.000m is at an initial temperature of T of the aluminum rod is placed in contact with a hot reservoir at TH the methods outlined in lecture as "Made-up Problem", determine the extension of the aluminum rod under these conditions.Q4/ The cylindrical head of an engine is 1 m long and has an outside diameter of 50 mm. The temperature of outer surface is 150 °C and an ambient temperature 40 °C with a convective coefficient of 80 W/m².'C. The head has been provided with 12 longitudinal straight fine, which are 0.75 mm thick and protrude 25 cm from the cylindrical surface. Calculate the heat dissipation due to addition of fines. Take thermal conductivity is 260 W/m.°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.9:87 A moodle.nct.edu.om A picture window has dimensions of 1.05 m by 2.5 m and is made of glass 7.5 mm thick. On a winter day, the outside temperature is 25.5° C while the inside temperature is a comfortable at 16° C. (k of glass =0.095W/m.K) ((a*1.5)+(b*1.5)+(c*2.0) = 5marks) Calculate the following: a) the area of the window in square metres b) the temperature gradient (AT/Ax)in kelvin/metre b) the rate of heat lost through the window by conduction in watts/metre.kelvin IILTE !!:: خاص A docs.google.com Q2/ An aluminum sphere weighting 7kg and initially at a temperature of 533K is suddenly immersed in a fluid at 283K. if heat transfer coefficient between the sphere and fluid is 50W/m?.°C. Take density=2707kg/m3, specific heat=0.9KJ/kg.°C and thermal conductivity= 204W/m °C. Your answer Determine the Bi number 0.00696 0.000696 0.0052 0.00052 Other: Determine the time required to cool sphere to 263K. * 26.28min 262.8min 52.56 min 525.6 min Other: 2 Request edit access Submit
- A food product with a moisture content of 80% in cans diameter 5 cm to frozen. Mass type of product is 1000 kg/m³, the thermal conductivity is 1.0 W/(m K), and temperature early frozen is -2 °C After 12 hour in the medium freezer -30 °C, the temperature of the products to be -10 °C. Estimate the coefficient of heat transfer convection medium freezing Assume cans as the cylinder is infinite, question a. h =....W/(m²K)Q2/ An aluminum sphere weighting 7kg and initially at a temperature of 533K is suddenly immersed in a fluid at 283K. if heat transfer coefficient between the sphere and fluid is 50W/m?.°C. Take density=2707kg/m3, specific heat=0.9KJ/kg.ºC and thermal conductivity= 204W/m°C. Determine th Bi number and And determine the time required to cool sphere to 263kNatural convection heat coefficient for vertical stainless pipe, outer diameter 100 mm, length 0.25 m. The pipe surface temperature is 125 ° C, and the air temperature is 30 ° C. Convection coefficient = Answer W / m² ° C.