A metal cube of 0.1 m sides is being cooled down uniformly from 300°C to 30°C by placing it in cold water at 10°C. The convection coefficient of water around the cube is 40 W/m².K. The properties of the cube material are as follows - thermal conductivity: 137 W/m-K, density: 1600 kg/m³; specific heat: 800 J/kg.K. Neglect radiation. Find the time required for coo cooling. 1426-2

Consider a large plane wall of thickness L = 0.2 m, thermal conductivity k = 1.2 W/mK, and surface area A = 15 m². Internally, the wall is assumed to generate heat at 500 W/m³. The left and right surfaces of the walls are exposed to convective heat transfer. On the left side (at x = 0 m), the wall temperature is maintained at 60°C. On the right surface side (at x = 0.2 m), the surface is exposed to convective heat transfer with an ambient temperature of 20°C. The convective heat transfer coefficient on the right side is assumed to be 200 W/m²K. Please answer the following questions: 1. What are the given material properties and boundary conditions? 2. What is the coordinate system used here? Please draw a schematic with proper coordinates to represent the problem 3. What are the assumptions associated with the problem? 1D, steady state, etc.? 4. Show the full heat conduction equation associated with the problem (including the unsteady term) 5. Show how to reduce it (based on…

A single-cylinder air-cooled lawn mower engine operates under steady conditions. The cylinder temperature cannot exceed 300 ⁰C. To cool the engine, annular fins are placed around the cylinder. The fins are 0.3 cm thick and are 2 cm long from base to tip. The fins are made of cast iron (k = 52 W/mK). The outside diameter of the engine cylinder at the base of the fin is 0.3 m. Assume that the engine operates in 30 ⁰C air and that the heat transfer coefficient on the sides and tip of the fin is 12 Wm^-2K^-1. Determine the number of fins needed to cool a 3 kW engine to the given temperature if the engine has an efficiency of 30 % and 50 % of the total heat given off by the engine actually is dissipated through the fins ?

C A fused-quartz sphere has a thermal diffusivity of 9.5 × 10–7 m²/s, a diameter of 2.5 cm, and a thermal conductivity of 1.52 W/m - °C. The sphere is initially at a uniform temperature of 25°C and is suddenly subjected to a convection environment at 200°C. The convection heat-transfer coefficient is 110 W/m² . °C. Calculate the temperatures at the center and at a radius of 6.4 mm after a time of 3 min. 0ad shot may be manufoctured by dropping molton lond droplots intO wotor Assum

A long aluminum cylinder with a diameter of 5 cm is initially at a temperature of 200oC and is suddenly exposed to 70oC convection and h = 525W /m2 oC Find the 1.25 cm diameter temperature and the heat loss per unit length 1 minute after the cylinder is subjected to convection. Thermal properties of the material k=215 W/moC  a= 8,4x10-5m2/s ρ=2700kg/m3 CP=0.9kJ/kgoC

Troom = 25°C Problem-4: An 8-m-internal-diameter spherical tank made of 1.5-cm-thick stainless steel (k = 15 W/m-K) is used to store iced water at 0°C. The tank is located in a room whose temperature is 25°C. The walls of the room are also at 25°C. The outer surface of the tank is black (emissivity = 1), and heat transfer between the outer surface of the tank and the surroundings is by natural convection and radiation. The convection heat transfer coefficients at the inner and the outer surfaces of the tank are 80 W/m²-K and 10 W/m².K, respectively. Determine (a) the rate of heat transfer to the iced water in the tank and (b) the amount of ice at 0°C that melts during a 24-h period. The heat of the fusion of water at atmospheric pressure is hf5 333.7 kJ/kg. Iced water D D₁= 8 m Tin = 0°C 1.5 cm

Take note that both sides of the plate are exposed to convection.

A thin silicon chip and an 8mm thick aluminum bracket are separated bya 0.02 mm thick epoxy gasket. The chip and bracket are laterally isolated and its surfaces are cooled by air that is at 25°C and has a convective coefficient of 100 W/m².K. If the chip dissipates 100 kW/m² under normal conditions, it will operate below temperature maximum allowable 85°C?Assuming: Steady state; One-dimensional regime (neglect heat transfer to the composite sides); The thermal resistance of the chip is negligible (the chip is isothermal); Thermal exchange by radiation with the surroundings is negligible; Properties are constants; The thermal conductivity of aluminum for this temperature range is 239 W/m.K. Data: Epoxy gasket strength 0.9x10-4 m2 K / W

The concrete slab of a basement is 11 m long, 8 m wide, and 0.5 m thick. During the winter, temperatures are nominally 17°C and 10°C at the top and bottom surfaces, respectively. If the concrete has a thermal conductivity of 1.4 W/m-K, what is the rate of heat loss through the slab, in W? If the basement is heated by a gas furnace operating at an efficiency of 7, = 0.90 and natural gas is priced at = $0.02/MJ, what is the daily cost of the heat loss, in dollars per day? W q = Ca = i $/d