Concept explainers
What is the physical significance of the Biot number? Is the Biot number more likely to be larger for highly conducting solids or poorly conducting ones?
To discuss: The Physical significance of Biot number and define whether its value is larger for highly conducting solids or poorly conducting solids.
Explanation of Solution
The Biot number is defined as the ratio of internal conduction resistance to the external convection resistance of the body.
The Biot number is used for the analysis of lumped heat capacitive systems, in which thermal internal conduction resistance is much lesser than the external convection resistance. And the condition for its applicability is Bi ? 0.1.
From the formula of Biot number, it can be defined that its value is inversely proportional to the thermal conductivity of the body.
Thus, with a larger value of k, the Biot number will be lesser. Hence, due to lower thermal conductivity, the value of the Biot number will be larger for poorly conducting solids. Also, the poorly conducting materials possess high conduction resistance, resulting in the larger value of the Biot number.
Want to see more full solutions like this?
Chapter 4 Solutions
HEAT+MASS TRANSFER:FUND.+APPL.
- how the mechanisms of heat transfer are applied to the designof structures (materials selection and geometry considerations) for energyconservation and economic purposes. Include illustrations and references.arrow_forwardA glass container has a total wall area (including the lid) of 1.75 m2 and a wall thickness of 1.5 cm. It's filled with 1000 g of ice at 0 C. How many seconds will it take to completely melt all the ice? (Latent heat of fusion is 80 calg and Thermal conductivity of glass is 0.8 W/m K) O 120 s 14, 400 s 2, 800 s 200 sarrow_forwardDetermine the ratio of thermal conductivity for N2 at sea level (T = 300 K, P = 1 atm) versusthe lower stratosphere (T = 230 K, P = 0.25 atm).arrow_forward
- An electric room heater (radiator) element is 25 cm long and 4 cm in diameter. The element dissipates heat to the surroundings at 1500 W mainly by radiation, the surrounding temperature being 15°C. Determine the equilibrium temperature of the element surface in Rankine. Continue >arrow_forwardConsider hotdog being cooked in boiling water in a pan. Would the heat transfer be modeled as one-dimensional or two-dimensional? Would the heat transfer be steady or transient? Explain.arrow_forwardTo warm up milk, it is poured into a thin-walled glass whose dimeter is 6 cm. The height of the milk in the glass is 7 cm. The glass is placed into a large pan filled with hot water at 60o C. The milk is stirred constantly, so that its temperature is always uniform. If the heat transfer coefficient between the water and the glass is 120 W/m2oC, determine how long it will take for the milk to warm up from 3o C to 38o C. Take the properties of the milk to be the same as those of water. Can the milk in this case be treated as a lumped system> Why?arrow_forward
- Two nested spherical tanks with the internal and outer diameters of the 100 cm by 104 cm and 114 cm by 118 cm is used to store hot water at 100 C. Both tanks are made of boron fiber epoxy with different composite compositions. The thermal conductivity of the inner tank is 1.5 W/m K while the outer tank has a thermal conductivity of 0.5 W/m K. The gap between the tanks is filled with air (use properties of air at 50°C). The tank is located in an open environment at 0'C. The outer surface of the tank is white painted and heat transfer between the outer surface of the tank and the surrounding is by natural covection and radiation. The convection heat transfer coefficient at the inner and the outer surface of the pipe is h 20 W/m' K and h 10 W/m K. Determine; a. the rate of heat loss from the tank b. the inside, outside and intermediate surface temperatures. Hint: Take the outer surface temperature as 3°C for radiation calculations.arrow_forwardThe boiling temperature of nitrogen at atmospheric pressure at sea level (1 atm pressure) is -196 °C. Therefore, nitrogen is commonly used in low-temperature scientific studies since the temperature of liquid nitrogen in a tank open to the atmosphere will remain constant at -196 °C until it is depleted. Any heat transfer to the tank will result in the evaporation of some liquid nitrogen, which has a heat of vaporization of 198 kJ/kg and a density of 810 kg/m3 at 1 atm. Consider a 3-m-diameter spherical tank that is initially filled with liquid nitrogen at 1 atm and -196 °C. The tank is exposed to ambient air at 15° C, with a combined convection and radiation heat transfer coefficient of 35 W/m2⋅K. The temperature of the thin-shelled spherical tank is observed to be almost the same as the temperature of the nitrogen inside. Determine the rate of evaporation (in kg/s) of the liquid nitrogen in the tank as a result of the heat transfer from the ambient air if the tank is insulated with…arrow_forwardA pipe 30 m long with an outer diameter of 75 mm is used to carry steam at a rate of 1000 kg / hour. The vapor pressure is 198.53 kPa entering the pipe with a quality of 98%. The pipe needs to be insulated with a thermal conductivity of 0.2 W / (m K) so that the quality of the steam will only slightly decrease to 95%. The outer surface temperature of the insulation is assumed to be 25 ° C. Ignore resistance conductive of the pipe material and it is assumed that there is no pressure drop in the pipe. a. Determine the enthalpy of incoming vapor = Answer kJ / kg. b. Determine the enthalpy of steam coming out = Answer kJ / kg. c. Determine the vapor heat change / loss along the flow = Answer watt. d. Specify the minimum required insulation thickness = Answer cm.arrow_forward
- a. What is the heat flux, q"1 [in W/m2], at the left-hand side of layer B? Express your answer as a negative number if the heat flux goes to the left, and as a positive number if the heat flux goes to the right. b.What is the heat flux, q"2 ( in W/m2) at the right-hand side of layer B? Express your answer as a negative number if the heat flux goes to the left, and as a positive number if the heat flux goes to the right. c. What is the temperature, T1, on the left-hand side of layer B, in Celsius? d. What is the temperature, T2, on the right-hand side of layer B, in Celsius?arrow_forwardHeat Transfer A wall of an oven with a wire in it. Across the wire a voltage of 50 Volts and a current of 2 Amps is applied, and 80% of the electrical power is converted to thermal energy. The oven is a convection oven and has air flowing through it at 240 C and h = 10 W/m^2 K. The wall of the oven is 0.1 m thick and 1.5 m tall and 1.5 m wide and is made of steel (k = 15 W/m K). Find the surface energy balance on the inner wall of the oven and determine the temperature of the ineer wall at steady state. Then do an energy balance on the outer wall, assume that the oven is free standing and has an emissivity, e = 0.6, and the surrounding temperature is 25 C. The air in the surrounding has a convective heat transfer coefficient of 25 W/m^2 K. Just set up the balance equation that would enable to solve, no need to actually solve.arrow_forwardFill in the blanks: An electric room heater (radiator) element is 25 cm long and 4 cm in diameter. The element dissipates heat to the surroundings at 1500 W mainly by radiation, the surrounding temperature being 15°C. Determine the equilibrium temperature of the element surface in Rankine.arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY