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- Show that the rate of heat conduction per unit length through a long, hollow cylinder of inner radius ri and outer radius ro, made of a material whose thermal conductivity varies linearly with temperature, is given by qkL=TiTo(rori)/kmA where Ti = temperature at the inner surface To = temperature at the outer surface A=2(rori)/ln(ro/ri)km=ko[1+k(Ti+To)/2]L=lenthofcyclinder3.16 A large, 2.54-cm.-thick copper plate is placed between two air streams. The heat transfer coefficient on one side is and on the other side is . If the temperature of both streams is suddenly changed from 38°C to 93°C, determine how long it takes for the copper plate to reach a temperature of 82°C.A 0.6-cm diameter mild steel rod at 38C is suddenly immersed in a liquid at 93C with hc=110W/m2K. Determine the time required for the rod to warm to 88C.
- Determine the rate of heat transfer per meter length from a 5-cm-OD pipe at 150C placed eccentrically within a larger cylinder of 85 magnesia wool as shown in the sketch. The outside diameter of the larger cylinder is 15 cm and the surface temperature is 50C.The handle of a ladle used for pouring molten lead is 30 cm long. Originally the handle was made of 1.9cm1.25cm mild steel bar stock. To reduce the grip temperature, it is proposed to form the handle of tubing 0.15 cm thick to the same rectangular shape. If the average heat transfer coefficient over the handle surface is 14 W/m K, estimate the reduction of the temperature at the grip in air at 21C.2.43 A turbine blade 6.3 cm long, with cross-sectional area and perimeter , is made of stainless steel . The temperature of the root, , is . The blade is exposed to a hot gas at , and the heat transfer coefficient is K. Determine the temperature of the blade tip and the rate of heat flow at the root of the blade. Assume that the tip is insulated.
- 2.29 In a cylindrical fuel rod of a nuclear reactor, heat is generated internally according to the equation where = local rate of heat generation per unit volume at r = outside radius = rate of heat generation per unit volume at the centerline Calculate the temperature drop from the centerline to the surface for a 2.5-cm-diameter rod having a thermal conductivity of if the rate of heat removal from its surface is 1.6 .A food product with 80% water content in a 10 cm diameter can be frozen. Mass of the product type is 1000 kg / m³, thermal conductivity is 1.0 w / (m k), and the frozen early temperature is -1.75 ° C.After 15 hours in the freezing medium -25 ° C, the temperature of the product becomes -10 ° C. Estimating the coefficient of moving the heat of the medium freezing convection. Assume cans as an unlimited cylinder. H = Answerw / (m² k).Number 3A food product with 73% moisture content in a 7 cm diameter can wants to be frozen. The density of the product is 970 kg/m³, the thermal conductivity is 1.2W/(m K), and the initial freezing temperature is -2.5°C. After 11 hours in the freezing medium -40°C, the product temperature becomes -10°C. Estimate the convection heat transfer coefficient of the freezing medium. Assume the can as an infinite cylinder. h= answer in W/(m²K)
- Water at 5°C is being used to cool apples from an initial temperature of 25° to 10°C. Thewater flow over the surface of the apple creates a convective heat-transfer coefficientof 15 W/(m2-K). Assume the apple can be described as a sphere with a 10 cm diameterand the geometric center is to be reduced to 10°C. The apple properties include thermalconductivity of 0.45 W/(m-K), specific heat of 3.950 kJ/(kg-K), and density of 940 kg/m3.a. Determine the time that the apples must be exposed to the water.b. If the apple is submerged only for 2 hours, what will be its center temperature?Citrus fruits are very susceptible to cold weather as extended exposure to subfreezingtemperatures can destroy them. Consider an 8-cm-diameter orange, that is initially at 10°C. A cold front moves inand the temperature drops to -2°C, with a heat transfer coefficient of 25 W/m2K. Using the properties of water for theorange, and given the ambient conditions remain constant for 7 hours, to what depth r will the orange freeze, if itdoes at all. Ignore any latent heat of solidification effects as the orange freezes.3. A food product with 80% moisture content in a 7 cm diameter can wants to be frozen. The density of the product is 1000 kg / m³, the thermal conductivity is 1.0 W / (m K), and the initial freezing temperature is -2 ° C. After 11 hours in the freezing medium -30 ° C, the product temperature becomes -10 ° C. Estimate the convection heat transfer coefficient of the freezing medium. Assume the can as an infinite cylinder. h = Answer W / (m² K).