Concept explainers
Consider a medium in which the heat conduction equation is given in its simplest forms as
Is heat transfer steady or transient?
Is heat transfer one-. two-, or thee-dimensional?
Is there heat generation in the medium?
Is the thermal conductivity of the medium constant or variable?
Is the medium a plane wall, a cylinder, or a sphere?
Is this differential equation for heat conduction linear or nonlinear?
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HEAT+MASS TRANSFER:FUND.+APPL.
- 1.60 Two electric resistance heaters with a 20 cm length and a 2 cm diameter are inserted into a well-insulated 40-L tank of water that is initially at 300 K. If each heater dissipates 500 W, what is the time required for bringing the water temperature in the tank to 340 K? State your assumption for your analysis.arrow_forwardHeat is transferred at a rate of 0.1 kW through glass wool insulation (density=100kg/m3) with a 5-cm thickness and 2-m2 area. If the hot surface is at 70C, determine the temperature of the cooler surface.arrow_forwardIn a meat processing plant, 2-cm-thick steaks (k =0.45 W/m·K and a = 0.91 * 1027 m2/s) that are initially at25°C are to be cooled by passing them through a refrigerationroom at 211°C. The heat transfer coefficient on both sides ofthe steaks is 9 W/m2·K. If both surfaces of the steaks are to becooled to 2°C, determine how long the steaks should be keptin the refrigeration room. Solve this problem using analyticalone-term approximation method (not the Heisler charts).arrow_forward
- To defrost ice accumulated on the outer surface of an automobile windshield, warm air is blown over the inner surface of the windshield. Consider an automobile windshield with thickness of 5 mm and thermal conductivity of 1.4 W/m·K. The outside ambient temperature is -10°C and the convection heat transfer coefficient is 200 W/m2·K, while the ambient temperature inside the automobile is 25°C. Determine the value of the convection heat transfer coefficient for the warm air blowing over the inner surface of the windshield necessary to cause the accumulated ice to begin melting.arrow_forward) Consider a solid sphere of radius r=50 cm. The heat is generated steadily inside the sphere at a rate of (15000) W/m3. The conductivity of the sphere is 10 W/m.K. Surface of the sphere is cooled by cooling water whose temperature and convection heat transfer coefficient are 10oC and 125 W/m2.K. Determine the temperatures at the center and surface of the sphere. Find the total heat transfer rate from the surface of the spherearrow_forwardIn a thermal power plant, a horizontal copper pipe of "D" diameter, "L" length and thickness 0.6 cm enters into the boiler that has the thermal conductivity as 0.33 W/mK. The boiler is maintained at 105C and temperature of the water that flows inside the pipe is at 28C. If the energy transfer (Q) is 118922 kJ in 6 hours. Determine the Heat transfer rate, Surface area of the pipe and Diameter & Length of the pipe, if D = 0.016 L. Change in Temperature (in K) = Heat Transfer Rate (in W) = Surface Area of the Pipe (m2) =arrow_forward
- Steam at To1= 320°C flows through a cast iron pipe (k = 80 W/mK) with inner and outer diameters of D1= 5cm and D2 = 5.5 cm, respectively. The pipe is covered with 3-cm-thick glass wool insulation with k = 0.05 W/mk(Figure Q2). Heat is lost to the surroundings (To2 = 5°C) by natural convection and radiation, with a combinedheat transfer coefficient of h2 = 18 W/m2.K.(a) Taking the heat transfer coefficient inside the pipe to be h1 = 60 W/m2 K, Calculate the rate of heat lossfrom steam per unit length of pipe.(b) Calculate the temperature differences between the pipe shell and the insulation. Someone comments that a microwave oven can be viewed as a conventional oven with zero convectionresistance at the surface of the food. Is this a correct statement? Discuss the reason.arrow_forwardA spherical container with an inner radius r1 = 1 m and an outer radius r2 = 1.05 m has its inner surface subjected to a uniform heat flux of q1=7kw/m^2. The outer surface of the container has a temperature T2 = 25°C, and the container wall thermal conductivity is k = 1.5 W/m·K. Show that the variation of temperature in the container wall can be expressed as and determine the temperature of the inner surface of the container at r = r1.arrow_forwardHot water at an average temperature of 70°C is flowing over a 15-m section of a cast iron pipe (k = 52 W/m·K) whose inner and outer diameters are 4 cm and 4.6 cm, respectively. The inner surface of the pipe exchanges heat by convection and radiation to the cold air at 10°C inside the pipe, with a convective heat transfer coefficient of 15 W/m2·K and heat transfer coefficient for radiation is 6.157 W/m2·K. The heat transfer coefficient at the outer surface of the pipe in the hot water side is 120 W/m2·K, Draw the thermal resistance network and determine the rate of heat loss from the hot water.arrow_forward
- A cat has a body temperature of 48 ºC. She stays inside a closed air conditioned room that has an inside wall temperature and inside air temperature of 40 and 35 ºC, respectively. The temperature of the room’s outside wall and the air outside the room are measured to be 45 and 50 ºC, respectively. The convection heat transfer coefficient between the cat and the inside air is 5 W/m2 ºC and the convection heat transfer coefficient between the outside air and outside wall is 35 W/m2 ºC. Use 0 ºC = 273.15 K to calculate the heat losses per unit area (W/m2 ) from the cat if the emissivity of the cat is 0.85.arrow_forwardWater flows through a pipe at an average temperature of T∞ = 70°C. The inner and outer radii of the pipe are r1 = 6 cm and r2 = 6.5 cm, respectively. The outer surface of the pipe is wrapped with a thin electric heater that consumes 300 W per m length of the pipe. The exposed surface of the heater is heavily insulated so that all heat generated in the heater is transferred to the pipe. Heat is transferred from the inner surface of the pipe to the water by convection with a heat transfer coefficient of h = 85 W/m2·K. Assuming constant thermal conductivity and one-dimensional heat transfer, express the mathematical formulation (the differential equation and the boundary conditions) of the heat conduction in the pipe during steady operation. Do not solve.arrow_forwardConsider the process of baking potatoes in a conventional oven. Can the hot air in the oven be treated as a thermal energy reservoir? Explain.arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning