Question: A thin, flat plate integrated circuit is
A thin, flat plate integrated circuit is cooled on its upper surface by a dielectric liquid. The heat dissipation rate from this chip is 20,000 W/m2 and with the coolant flow at a free-stream temperature of 
, the convective heat transfer coefficient between the chip surface and the liquid is 1000 W/m2. K. On the lower surface, the 5-mm thick chip is attached to a circuit board, where the thermal contact resistance between the chip and the board is 10-4 m2. K/W. The thermal conductivity of the board material is 1.0 W/m. K, and its other surface (away from the chip) is exposed to ambient air at / where it is cooled by natural convection with a heat transfer coefficient of 30 W/m2K. (a) Determine the chip surface temperature under steady-state condition for the described conditions. (b) If the maximum chip temperature is not to exceed 75oC, determine the maximum allowable heat flux that is generated by the chip. (c) A colleague suggests that in order to improve the cooling, you use a high conductivity bonding base at the chip-board interface that would reduce the thermal contact resistance at the interface to 10-5 m2. K/W. Determine the consequent in- crease in the chip heat flux that can be sustained.
> A cryogenic fluid is stored in a 0.3-m-diameter spherical container in still air. If the convection heat transfer coefficient between the outer surface of the container and the air is 6.8 W/m2 K, the temperature of the air is 27°C, and the temperature of
> The heat transfer coefficients for the flow of 26.6°C air over a sphere of 1.25 cm in diameter are measured by observing the temperature-time history of a copper ball the same dimension. The temperature of the copper ball was measured by two
> Green coffee beans, after harvesting, are dried and roasted in a fluidized-bed roaster. This type of roaster has hot air, typically at 250°C, and the air blows through a screen or perforated plate above which the beans float in an agitated suspension (fl
> In a metal wire manufacturing facility, continuously drawn copper wire with a 2.5 mm diameter is annealed by heating it from its initial temperature of 45°C to 400°C in a soaking oven. The oven inside air temperature is 700°C with an average heat transf
> A 0.6-cm-diameter mild steel rod a t 38°C is suddenly immersed in a liquid at 93°C with /Determine the time required for the rod to warm to 88°C.
> In a ball-bearing production facility, steel balls that are each of 15 mm in diameter are annealed by first heating them to 870°C and then slowly cooling in air to 125°C. If the cooling air stream temperature is 60°C, and it has a convective heat transfe
> It is a well-known physiological phenomenon that some materials feel cooler to the touch than others. This is important in the design of instruments for the use of operators, especially in a space station. Experiments conducted at NASA have shown that di
> A large billet of steel initially at 260°C is placed in a radiant furnace where the surface temperature is held at 1200°C. Assuming the billet to be infinite in extent, compute the temperature at point P (see the accompanying sketch
> Estimate the depth in moist soil at which the annual temperature variation is 10% of that at the surface.
> Surface hardening of metallic machine components, such as ball and roller bearings, is carried out in a heat treatment process where the surface temperature is increased to a desirable level without altering the internal temperature substantially. In one
> A thermocouple is made up of a spherical bead bimetallic junction at the end of two very thin wires of different materials. For example, in a type-T thermocouple, a copper wire and a constantan wire, with wire diameters ranging from 0.5 mm to 0.025 mm, a
> The heat transfer coefficient for a gas flowing over a thin flat plate 3-m long and 0.3-m wide varies with distance from the leading edge according to If the plate temperature is 170°C and the gas temperature is 30°C, calculate (a)
> In the experimental determination of the heat transfer coefficient between a heated steel ball and crushed mineral solids, a series of 1.5% carbon steel balls were heated to a temperature of 700°C and the center temperature-time history of each was measu
> An egg, which for the purposes of this problem is assumed to be a 5-cm-diameter sphere having the thermal properties of water, is initially at a temperature of 4°C. It is immersed in boiling water at 100°C for 15 min. The heat transfer coefficient from t
> A monster turnip (assumed spherical) weighing in at 0.45 kg is dropped into a cauldron of water boiling at atmospheric pressure. If the initial temperature of the turnip is 17°C, how long does it take to reach 92°C at the center?
> A steel sphere with a diameter of 7.6 cm is to be hardened by first heating it to a uniform temperature of 870°C and then quenching it in a large bath of water at a temperature of 38°C. The following data apply: Calculate (a) the t
> Estimate the time required to heat the center of a 1.5-kg roast in a 163°C oven to 77°C. State your assumptions carefully and compare your results with cooking instructions in a standard cookbook.
> Ball bearings are to be hardened by quenching them in a water bath at a temperature of 37°C. You are asked to devise a continuous process in which the balls roll from a soaking oven at a uniform temperature of 870°C into the water,
> Consider a heat treatment process in which steel rods with a 10 cm diameter at an initial temperature of 600°C are inserted into an oil bath at 25°C. Assuming a convection coefficient of 400 W/m2. K between the oil and the rod, estimate how long it take
> Repeat Problem 3.31(a), but assume that the billet is only 1.2 m long with the average heat transfer coefficient at both ends equal to 136 W/m2 K.
> A long, 0.6-m-OD 347 stainless steel (k = 14 W/m K) cylindrical billet at 16°C room temperature is placed in an oven where the temperature is 260°C. If the average heat transfer coefficient is 170 W/m2 K, (a) estimate the time required for the center tem
> A solid lead cylinder 0.6 m in diameter and 0.6 m long, initially at a uniform temperature of 121°C, is dropped into a 21°C liquid bath in which the heat transfer coefficient / 1135 W/m2 K. Plot the temperature-time history of the c
> The heat transfer rate from hot air by convection at 100°C flowing over one side of a flat plate with dimensions 0.1 m * 0.5 m is determined to be 125 W when the surface of the plate is kept at 30°C. What is the average convection heat transfer coefficie
> Quenching is a rapid cooling process by which many metallic alloys are hardened. Brass (a copper alloy: 70 Cu, 30 Zn) plates that are 4 mm thick are quenched in a water bath at a heat treating plant. If a brass plate is initially at 450°C, determine the
> A mild-steel cylindrical billet 25 cm in diameter is to be raised to a minimum temperature of 760°C by passing it through a 6-m long strip-type furnace. If the furnace gases are at 1538°C and the overall heat transfer coefficient on the outside of the bi
> A long wooden rod at 38°C with a 2.5-cm-OD is placed into an airstream at 600°C. The heat transfer coefficient between the rod and air is 28.4 W/m2 K. If the ignition temperature of the wood is 427°C, r = 800 kg/m3, k = 0.173 W/m K, and c = 25
> A long copper cylinder 0.6 m in diameter and initially at a uniform temperature of 38°C is placed in a water bath at 93°C. Assuming that the heat transfer coefficient between the copper and the water is 1248 W/m2 K, calculate the time required to heat
> A stainless steel cylindrical billet (k = 14.4 W/m K, ( 5 3.9 * 10-6 m2/s ) is heated to 593°C preparatory to a forming process. If the minimum temperature permissible for forming is 482°C, how long can the billet be exposed to air
> In a curing process for plastic and other polymer- based materials, a plastic sheet, which initially is 25°C, is placed on a hot metal surface that is maintained at 250°C. If the back (or opposite) side of the 5-mm-thick plastic film is considered to be
> A frozen-food company freezes its spinach by first compressing it into large slabs and then exposing the slab of spinach to a low-temperature cooling medium. The large slab of compressed spinach is initially at a uniform temperature of 21°C; it mus
> In the inspection of a sample of meat intended for human consumption, it was found that certain undesirable organisms were present. To make the meat safe for consumption, it is ordered that the meat be kept at a temperature of at least 121°C for a perio
> A 2.5-cm-thick sheet of plastic initially at 21°C is placed between two heated steel plates that are maintained at 138°C. The plastic is to be heated just long enough for its mid plane temperature to reach 132°C. If the thermal conductivity of the p
> In the vulcanization of tires, the carcass is placed into a jig and steam at 149°C is admitted suddenly to both sides. If the tire thickness is 2.5 cm, the initial temperature is 21°C, the heat transfer coefficient between the tire
> Water at a temperature of 77°C is to be evaporated slowly in a vessel. The water is in a low-pressure container surrounded by steam as shown in the sketch below. The steam is condensing at 107°C. The overall heat transfer coefficien
> Dielectric heating, also known as RF or high frequency heating, is a process in which a high-frequency alternating electric field or microwave electromagnetic radiation heats a dielectric material. An important application of this phenomenon is in the he
> High-strength steel is required for use in building structures and equipment (e.g., cranes). It is produced by heat treating quench-hardened steel in a process called tempering that reduces brittleness and imparts toughness. In a production facility, all
> A wire of perimeter P and cross-sectional area A emerges from a die at a temperature T (above the ambient temperature) and with a velocity U. Determine the temperature distribution along the wire in the steady state if the exposed length down-
> A small aluminum sphere of diameter D, initially at a uniform temperature To, is immersed in a liquid whose temperature, T(, varies sinusoidally according to If the heat transfer coefficient between the fluid and the sphere, /is constant and the system c
> A 1.4-kg aluminum household iron has a 500-W heating element. The surface area is 0.046 m2. The ambient temperature is 21°C, and the surface heat transfer coefficient is 11 W/m2 K. How long after the iron is plugged in does its temperature rea
> A large, 2.54-cm.-thick copper plate is placed between two air streams. The heat transfer coefficient on one side is 28 W/m2 K and on the other side is 57 W/m2 K. If the temperature of both streams is suddenly changed from 38°C to 93°C, determine how lo
> A thin-wall jacketed tank heated by condensing steam at one atmosphere contains 91 kg of agitated water. The heat transfer area of the jacket is 0.9 m2 and the over- all heat transfer coefficient U = 227 W/m2 K based on that area. Determine the heating t
> A thin-wall cylindrical vessel (1 m in diameter) is filled to a depth of 1.2 m with water at an initial temperature of 15°C. The water is well stirred by a mechanical agitator. Estimate the time required to heat the water to 50°C if
> A copper wire, 0.8-mm OD, 5 cm long, is placed in an air stream whose temperature rises at a rate given by where t is the time in seconds. If the initial temperature of the wire is 10°C, deter- mine its temperature after 2s, 10s, and 1 min. T
> A spherical stainless steel vessel at 93°C contains 45 kg of water initially at the same temperature. If the entire system is suddenly immersed in ice water, determine (a) the time required for the water in the vessel to cool to 16°C, and (b) the temper
> A thermocouple (0.8-mm-diameter wire) used to measure the temperature of the quiescent gas in a furnace gives a reading of 165°C. It is known, how- ever, that the rate of radiant heat flow per meter length from the hotter furnace walls to the
> In the heat treating process in a sheet-metal manufacturing plant, brass plates are annealed by first heating them in an industrial furnace oven the inside of which is maintained at a constant uniform temperature of 550°C. If the surface of the brass pla
> A spherical shell satellite (3-m-OD, 1.25-cm-thick stainless steel walls) re-enters the atmosphere from outer space. If its original temperature is 38°C, the effective average temperature of the atmosphere is 1093°C, and the effective heat transfer coeff
> Consider a flat plate or a plane wall with a thickness L and a long cylinder of radius ro. Both of these are made of materials such that they can be treated as lumped capacitances (Bi < 0.1) . Show that in each case, the characteristic length lc, defin
> In a large chemical factory, hot gases at 2273 K are cooled by a liquid at 373 K with gas-side and liquid- side convection heat transfer coefficients of 50 and 1000 W/m2. K, respectively. The wall that separates the gas and liquid streams is composed of
> A very thin silicon chip is bonded to a 6-mm thick aluminum substrate by a 0.02-mm thick epoxy glue. Both surfaces of this chip-aluminum system are cooled by air at 258C, where the convective heat transfer coefficient of air flow is 100 W/m2. K. If the h
> Calculate the rate of heat transfer between a 15-cm- OD pipe at 1208C and a 10-cm-OD pipe at 408C. The two pipes are 330 m long and are buried in sand (k = 0.33 W/m K) 12 m below the surface (Ts = 25°C ) . The pipes are parallel and are separated by 23 c
> A 2.5-cm-OD hot steam line at 100oC runs parallel to a 5.0-cm-OD cold water line at 15oC. The pipes are 5 cm apart (center to center) and deeply buried in concrete with a thermal conductivity of 0.87 W/m K. What is the heat transfer per meter of pipe bet
> A 15-cm-OD pipe is buried with its centerline 1.25 m below the surface of the ground (k of soil is 0.35 W/(m K)). An oil having a density of 800 kg/m3 and a specific heat of 2.1 kJ/(kg K) flows in the pipe at 5.6 L/s. Assuming a ground surface temperatur
> A radioactive sample is to be stored in a protective box with 4-cm-thick walls and interior dimensions of 4 cm * 4 cm * 12 cm. The radiation emitted by the sample is completely absorbed at the inner surface of the box, which is made of concrete. If the o
> Using Table 1.4 as a guide, prepare a similar table showing the orders of magnitude of the thermal resistances of a unit area for convection between a surface and various fluids.
> Two long pipes, one having a 10-cm OD and a sur- face temperature of 300oC, the other having a 5-cm OD and a surface temperature of 100oC, are buried deeply in dry sand with their centerlines 15 cm apart. Determine the rate of heat flow from the larger t
> A plane wall of thickness 2L has internal heat sources whose strength varies according to where qo is the heat generated per unit volume at the center of the wall (x = 0) and a is a constant. If both sides of the wall are maintained at a constant tempera
> A 30-cm-OD pipe with a surface temperature of 90oC carries steam over a distance of 100 m. The pipe is buried with its centerline at a depth of 1 m, the ground surface is 26°C, and the mean thermal conductivity of the soil is 0.7 W/m K. Calcul
> Determine the temperature distribution and heat flow rate per meter length in a long concrete block having the shape shown below. The cross-sectional area of the block is square and the hole is centered.
> A long, 1-cm-diameter electric cable is embedded in a concrete wall ( k 5 0.13 W/m K ) that is 1 m * 1 m, as shown in the sketch. If the lower surface is insulated, the surface of the cable is 100oC, and the exposed surface of the concrete is 25oC, estim
> A large number of 3.8-cm-OD pipes carrying hot and cold liquids are embedded in concrete in an equilateral staggered arrangement with centerlines 11.2 cm apart as shown in the sketch. If the pipes in rows A and C are at 16oC while the pipes in rows B and
> A long, 1-cm-diameter electric copper cable is embedded in the center of a 25-cm-square concrete block. If the outside temperature of the concrete is 25oC and the rate of electrical energy dissipation in the cable is 150 W per meter length, determine tem
> Determine the rate of heat flow per meter length from the inner to the outer surface of the molded insulation in the sketch on the next page. Use k = 0.17 W ( m K ) .
> Determine the rate of heat transfer per meter length from a 5-cm-OD pipe at 150oC 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
> Use a flux plot to estimate the rate of heat flow through the object shown in the sketch. The thermal conductivity of the material is 15 W/m K. Assume no heat is lost from the sides.
> If the outer air temperature in Problem 1.11 is 22°C, calculate the convection heat transfer coefficient between the outer surface of the window and the air, assuming radiation is negligible.
> Determine by means of a flux plot the temperatures and heat flow per unit depth in the ribbed insulation shown in the accompanying sketch.
> Compare the rate of heat flow from the bottom to the top of the aluminum structure shown in the sketch below with the rate of heat flow through a solid slab. The top is at -10°C, the bottom at 0oC. The holes are filled with insulation that doe
> Derive an expression for the temperature distribution in a plane wall in which there are uniformly distributed heat sources that vary according to the linear relation where qw is a constant equal to the heat generation per unit volume at the wall tempera
> A 0.3-cm-thick aluminum plate has rectangular fins 0.16 cm * 0.6 cm, on one side, spaced 0.6 cm apart. The finned side is in contact with low pressure air at 38oC, and the average heat transfer coefficient is 28.4 W/m2 K. On the un finned side, water flo
> The handle of a ladle used for pouring molten lead is 30 cm long. Originally the handle was made of 1.9 cm * 1.25 cm 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 s
> The top of a 30-cm I-beam is maintained at a temperature of 260oC, while the bottom is at 93oC. The thick- ness of the web is 1.25 cm. Air at 260oC is blowing along the side of the beam so that / The thermal conductivity of the steel may be assumed const
> The wall of a liquid-to-gas heat exchanger has a sur- face area on the liquid side of 1.8 m2 (0.6 m * 3.0 m)with a heat transfer coefficient of 255 W/m2 K. On the other side of the heat exchanger wall flows a gas, and the wall has 96 thin rectangular ste
> Heat is transferred from water to air through a brass wall (k = 54 W/m K) . The addition of rectangular brass fins, 0.08 cm thick and 2.5 cm long, spaced 1.25 cm apart, is contemplated. Assuming a water-side heat transfer coefficient of 170 W/m2 K and an
> To determine the thermal conductivity of a long, solid 2.5-cm-diameter rod, one half of the rod was inserted into a furnace while the other half was projecting into air at 27oC. After steady state had been reached, the temperatures at two points 7.6 cm a
> A turbine blade 6.3 cm long, with cross-sectional area A = 4.6 3 10-4 m2 and perimeter P = 0.12 m, is made of stainless steel (k = 18 W/m K) . The temperature of the root, Ts, is 482oC. The blade is exposed to a hot gas at 871oC, and the heat transfer co
> A wall with a thickness L is made of a material with a thermal conductivity that varies with its thickness x according to the equation, k=(ax +b) W/mK, where a and b are constants. If the heat flux applied at the surface of one end (x =0) of the wall is
> A circumferential fin of rectangular cross section, 3.7-cm OD and 0.3 cm thick, surrounds a 2.5-cm- diameter tube as shown below. The fin is constructed of mild steel. Air blowing over the fin produces a heat transfer coefficient of 28.4 W/m2 K. If the t
> Both ends of a 0.6-cm copper U-shaped rod are rigidly affixed to a vertical wall as shown in the accompanying sketch. The temperature of the wall is maintained at 93oC. The developed length of the rod is 0.6 m, and it is exposed to air at 38oC. The combi
> One end of a 0.3-m-long steel rod is connected to a wall at 204oC. The other end is connected to a wall that is maintained at 93oC. Air is blown across the rod so that a heat transfer coefficient of 17 W/m2 K is maintained over the entire surface. If the
> A plane wall 15 cm thick has a thermal conductivity given by the relation where T is in kelvin. If one surface of this wall is maintained at 1508C and the other at 508C, determine the rate of heat transfer per square meter. Sketch the temperature distrib
> The tip of a soldering iron consists of a 0.6-cm- diameter copper rod, 7.6 cm long. If the tip must be 204oC, what are the required minimum temperature of the base and the heat flow, in watts, into the base? Assume that W/m2 K and Tair 5 21°C
> The addition of aluminum fins has been suggested to increase the rate of heat dissipation from one side of an electronic device 1 m wide and 1 m tall. The fins are to be rectangular in cross section, 2.5 cm long and 0.25 cm thick, as shown in the figure.
> In cryogenic surgery, a small spherical probe is bought into contact with the diseased tissue which is frozen and thereby destroyed. One such probe can be modeled as a 3-mm diameter sphere whose surface is maintained at 240 K when the surrounding tissue
> The development of contact lenses has transformed the solutions that are available today for vision impairments. However, wearing them also poses several problems that includes the condition of dry eyes due to lack of cooling, oxygenation, and moisturizi
> Liquid oxygen is to be stored on the service module of NASA’s new Orion Spacecraft (NASA, “Orion Quick Facts,” FS-2014-08-004-JSC, Lyndon B. Johnson Space Center, Houston, TX)* in a spherical stainles
> Show that the temperature distribution in a sphere of radius ro, made of a homogeneous material in which energy is released at a uniform rate per unit volume qG , is
> Calculate the heat loss through a 1m*3m glass window 7-mm thick if the inner surface temperature is 20°C and the outer surface temperature is 17°C. Comment on the possible effect of radiation on your answer.
> For the system outlined in Problem 2.31, determine an expression for the critical radius of the insulation in terms of the thermal conductivity of the insulation and the surface coefficient between the exterior surface of the insulation and the surroundi
> The thermal conductivity of a material can be determined in the following manner. Saturated steam at 2.41 * 105 N/m2 is condensed at the rate of 0.68 kg/h inside a hollow iron sphere that is 1.3 cm thick and has an internal diameter of 51 cm. The sphere
> A hollow sphere with inner and outer radii of R1 and R2, respectively, is covered with a layer of insulation having an outer radius of R3. Derive an expression for the rate of heat transfer through the insulated sphere in terms of the radii, the thermal
> An electrical heater capable of generating 10,000 W is to be designed. The heating element is to be a stainless steel wire having an electrical resistivity of 80 * 10-6 ohm-centimeter. The operating temperature of the stainless steel is to be no more tha
> The shield of a nuclear reactor is idealized by a large 25-cm-thick flat plate having a thermal conductivity of 3.5 W/(m K). Radiation from the interior of the reactor penetrates the shield and there produces heat generation that decreases exponentially
> In a cylindrical fuel rod of a nuclear reactor, heat is generated internally according to the equation Calculate the temperature drop from the centerline to the surface for a 2.5-cm-diameter rod having a thermal conductivity of 26 W/(m K) if the rate of
> Heat is generated uniformly in the fuel rod of a nuclear reactor. The rod has a long, hollow cylindrical shape with its inner and outer surfaces at temperatures of Ti and To, respectively. Derive an expression for the temperature distribution.
> Derive an expression for the temperature distribution in an infinitely long rod of uniform cross section within which there is uniform heat generation at the rate of 1 W/m. Assume that the rod is attached to a surface at Ts and is exposed through a conve
> A long, hollow cylinder is constructed from a material whose thermal conductivity is a function of temperature according to = 5 0.15 + 0.0018T, where T is in oC and k is in W/(m K). The inner and outer radii of the cylinder are 12.5 cm and 25 cm, respect
> 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
> A heat flux meter at the outer (cold) wall of a concrete building indicates that the heat loss through a wall of 10-cm thickness is 20 W/m2. If a thermocouple at the inner surface of the wall indicates a temperature of 22°C while another at the outer sur
> On a cold winter day, the outer surface of a 0.2-m-thick concrete wall of a warehouse is exposed to a temperature of 25°C, while the inner surface is kept at 20°C. The thermal conductivity of the concrete is 1.2 W/m K. Determine the
