KNOWN: Copper sphere, 10 mm diameter, initially at a prescribed elevated temperature is quenched in a saturated (1 atm) water bath. FIND: The time for the sphere to cool (a) from Ti = 130 to 110°C and (b) from Ti = 550°C to 220°C . ASSUMPTIONS: (1) Sphere approximates lumped capacitance, (2) Water

KNOWN: Surface temperature and emissivity of strip steel. FIND: Heat flux across vapor blanket. ASSUMPTIONS: (1) Steady-state conditions, (2) Vapor/jet interface is at Tsat for p = 1 atm, (3) Negligible effect of jet and strip motion. PROPERTIES: Table A-6, Saturated water (100°C):

KNOWN: Inner and outer diameters, outer surface temperature and thermal conductivity of a tube. Saturation pressure of surrounding water and convection coefficient associated with gas flow through the tube. FIND: (a) Heat rate per unit tube length, (b) Mean temperature of gas flow through tube.

KNOWN: Horizontal, stainless steel bar submerged in water at 25°C. FIND: Heat rate per unit length of the bar. ASSUMPTIONS: (1) Steady-state conditions, (2) Film pool boiling, (3) Water at 1 atm. PROPERTIES: Table A-6, Water, liquid (1 atm, Tsat = 100°C): ρl = 957.9 kg/m3, hfg = 2257 kJ/kg; Table

KNOWN: Electrical conductor with prescribed surface temperature immersed in water. FIND: (a) Power dissipation per unit length, q′s and (b) Compute and plot q′s as a function of surface temperature 250 ≤ Ts ≤ 650°C for conductor diameters of 1.5, 2.0, and 2.5 mm; separately plot the percentage

KNOWN: Cylinder of 120 mm diameter at 1000K quenched in saturated water at 1 atm FIND: Describe the quenching process and estimate the maximum heat removal rate per unit length during cooling. ASSUMPTIONS: Water exposed to 1 atm pressure, Tsat = 100°C.

KNOWN: Steel bar upon removal from a furnace immersed in water bath. FIND: Initial heat transfer rate from bar. ASSUMPTIONS: (1) Uniform bar surface temperature, (2) Film pool boiling conditions. PROPERTIES: Table A-6, Water, liquid (1 atm, Tsat = 100°C): ρl = 957.9 kg/m³, hfg = 2257 kJ/kg; Table

KNOWN: A sphere (aluminum alloy 2024) with a uniform temperature of 500°C and emissivity of 0.25 is suddenly immersed in a saturated water bath maintained at atmospheric pressure. FIND: (a) The total heat transfer coefficient for the initial condition; fraction of the total coefficient contributed

KNOWN: Operating conditions of apparatus used to determine surface boiling characteristics. FIND: (a) Nucleate boiling coefficient for special coating, (b) Surface temperature as a function of heat flux; apparatus temperatures for a prescribed heat flux; applicability of nucleate boiling

KNOWN: Thickness and thermal conductivity of a silicon chip. Properties of saturated fluorocarbon liquid. FIND: (a) Temperature at bottom surface of chip for a prescribed heat flux and 90% of CHF, (b) Effect of heat flux on chip surface temperatures; maximum allowable heat flux. ASSUMPTIONS: (1)

KNOWN: Small copper sphere, initially at a uniform temperature, Ti, greater than that corresponding to the Leidenfrost point, TD, suddenly immersed in a large fluid bath maintained at Tsat. FIND: (a) Sketch the temperature-time history, T(t), during the quenching process; indicate temperature

KNOWN: Concentric stainless steel tubes packed with dense boron nitride powder. Inner tube has heat generation while outer tube surface is exposed to boiling heat flux, q″s = C(Ts – Tsat)³. Saturation temperature of boiling liquid and temperature of the outer tube surface. FIND: Expressions for the

KNOWN: Boiling water at 1 atm pressure on moon where the gravitational field is 1/6 that of the earth. FIND: Critical heat flux. ASSUMPTIONS: Nucleate pool boiling conditions. PROPERTIES: Table A-6, Water (1 atm): Tsat = 100°C, ρl = 957.9 kg/m³, ρv = 0.5955 kg/m³, hfg = 2257 kJ/kg, σ = 58.9 × 10^-3

KNOWN: Lienhard-Dhir critical heat flux correlation for small horizontal cylinders. FIND: Critical heat flux for 1 mm and 3 mm diameter horizontal cylinders in water at 1 atm. ASSUMPTIONS: Nucleate pool boiling. PROPERTIES: Table A-6, Water (1 atm): ρl = 957.9 kg/m³, ρv = 0.5955 kg/m³,

KNOWN: Kutateladze’s dimensional analysis and the bubble diameter parameter. FIND: (a) Verify the dimensional consistency of the critical heat flux expression, and (b) Estimate heater size with water at 1 atm required such that the Bond number will exceed 3, i.e., Bo ≥ 3. ASSUMPTIONS: Nucleate

KNOWN: Zuber-Kutateladze correlation for critical heat flux, q″max. FIND: Pressure dependence of q″max for water; demonstrate maximum value occurs at approximately 1/3 pcrit; suggest coordinates for a universal curve to represent other fluids. ASSUMPTIONS: Nucleate pool boiling conditions.

KNOWN: Saturated water boiling on a brass plate maintained at 115°C. FIND: Power required (W/m²) for pressures of 1 and 10 atm; fraction of critical heat flux at which plate is operating. ASSUMPTIONS: (1) Nucleate pool boiling, (2) ΔTe = 15°C for both pressure levels. PROPERTIES: Table A-6,

KNOWN: Diameter and length of tube submerged in pressurized water. Flowrate and inlet temperature of gas flow through the tube. FIND: Tube wall and gas outlet temperatures. ASSUMPTIONS: (1) Steady-state, (2) Uniform tube wall temperature, (3) Nucleate boiling at outer surface of tube, (4) Fully

KNOWN: Copper tubes, 25 mm diameter × 0.75 m long, used to boil saturated water at 1 atm operating at 75% of the critical heat flux. FIND: (a) Number of tubes, N, required to evaporate at a rate of 750 kg/h; tube surface temperature, Ts, for these conditions, and (b) Compute and plot Ts and N

KNOWN: Nickel wire passing current while submerged in water at atmospheric pressure. FIND: Current at which wire burns out. ASSUMPTIONS: (1) Steady-state conditions, (2) Pool boiling.