A simplified representation for cooling in very large-scale integration (VLSI) of microelectronics is shown in the sketch. A silicon chip is mounted in a dielectric substrate, and one surface of the system is convectively cooled, while the remaining surfaces are well insulated from the surroundings. The problem is rendered two-dimensional by the system to be very long in the direction perpendicular to the paper. Under steady-state operation, electric power dissipation in the chip provides for uniform volumetric heating at a rate of
For the conditions shown on the sketch, will the maximum temperature in the chip exceed 85°C, the maximum allowable operating temperature set by industry standards? A grid spacing of 3 mm is suggested.
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Fundamentals of Heat and Mass Transfer
- 1. A simple cavity wall consists of two brick layers separated by an air gap of 50 mm. If the inside air temperature is 20oC and the ambient outside temperature is 5 oC, calculate the heat flux through the wall. Bricks are 100 mm thick with thermal conductivity kbrick = 0.5 W/m K, hin = 10 W/m2 K, hout = 20 W/m2 K. The internal air cavity can be considered still (no convection) with kair = 0.015 W/m K. 2. On a day in winter, the outside air temperature drops to -5 oC and the outside convective heat transfer changes to hout = (2 x V) + 8.9 W/m2 K. If the outside wind speed gusts at 50 kph, calculate the change in heat flux for the wall in question 3.arrow_forwardA warehouse is being built that will have neither heating nor cooling. Depending on the amount of insulation, the time constant for the building may range from 1 to 4 hr. To illustrate the effect insulation will have on the temperature inside the warehouse, assume the outside temperature varies as a sine wave, with a minimum of 12°C at 2:00 A.M. and a maximum of 32°C at 2:00 P.M. Assuming the exponential term (which involves the initial temperature To) has died off, what is the lowest temperature inside the building if the time constant is 1 hr? If it is 4 hr? What is the highest temperature inside the building if the time constant is 1 hr? If it is 4 hr? If the time constant is 1 hr, then the lowest temperature inside the building is about °C. (Round to the nearest tenth as needed.)arrow_forwardExperiment: A cooling tower uses forced air and column packing to cool downward-flowing water. Inlet water temperature and water flow rate are varied to investigate effects on outlet water temperature, outlet air temperature, and outlet air humidity. The system is first observed operating with ambient room temperature water. A heat load is then applied to the water tank, and the system response is observed. This is to simulate a power plant starting up and placing a cooling load on the cooling water supply. The aim is to compare the system response with and without the load. Data from the Experiment and the make-up water mass flow rate are both shown in the following tables below. For the load cases, determine the net rate of water evaporation from the cooling water to the air using the equation for air flow rate. Compare this with the rate at which make-up water enters the system. For the load cases, determine the rate of work supplied by the pump and compare it to the pump power…arrow_forward
- An underwater sonar that maps the ocean bathymetry is encapsulated in a sphere with a diameter of 85 mm. During operation, the sonar generates heat at a rate of 300W. What is the sonar surface temperature when it’s located in a water column where the temperature is 15o C and the water current is 1 m/sec? The sonar was pulled out of the water without turning it off, thus, it was still working. The air temperature was 15o C and the air speed was 3 m/sec. What was the sonar surface temperature? Was there any reason for concern?arrow_forwardNUMBER 4 A food product wants to be produced in a small round shape (pellet) by freezing it in a water blast freezer freezer. Air freezer operates at -40 ° C. The initial product temperature is 25 ° C. The pellet has a diameter of 1 cm, and a density of 980 kg / m³. The initial freezing temperature is -2.5 ° C. The latent heat of freezing of the product is 280 kJ / kg. The thermal conductivity of the frozen product is 1.9 W / (m ° C). The convective heat transfer coefficient is 50 W / (m² K). Calculate the freeze time. t f = hourarrow_forwardShape Factor Conduction Problem A cylindrical pipeline that is used for the transport of crude oil is buried in the soil horizontally such that its centerline is 1.5 m (z) below the surface. The pipe has the outer diameter of 0.5 m (D) and is coated with a 100 mm thick layer of glass insulation on the outside. Assume that heated oil at 120 °C flows through the pipe and the soil surface temperature is at 0 °C (T:). The soil thermal conductivity is known as 0.5 W/m-K, and the glass insulation thermal conductivity is known as 0.07 W/m-K. What is the rate of heat loss per unit length of the pipe (W/m)? T2 Soil Glass insulation Oil, T1arrow_forward
- For each of the following cases, determine an appropriate characteristic length Lc and the corresponding Biot Bi number that is associated with the transient thermal response of the solid object. Say if the global capacitance approximation is va lid. If temperature information is not provided, evaluate properties T = 300K a)oroidal shape with diameter D = 50mm and cross-sectional area AC = 5 mm², with thermal conductivity k = 2.3W / (mK) The surface of the toroid is exposed to a refrigerant corresponding to a convective coefficient eta = 50 W/( m2.k) b)A long stainless steel heated bar (AISI 304), with rectangular cross section, and dimensions w = 3mm , W = 5mm and L = 100mm . the bar issubjected to a refrigerant that provides a heat transfer coefficient of h =15 W/(m2 K) on all exposed surfaces. c)A long extruded aluminum tube (2024 Alloy) with internal dimensions and external w = 20 mm and W = 24 mm , respectively, suddenly submerged in water, with a convective coefficient of h =…arrow_forward5. A current of 200 A is passed through a stainless-steel wire [k=19 W/mK] 3 mm in diameter. The resistance of the steel may be taken as 0.099 ohm, and the length of the wire is 1 m. The wire is submerged in a liquid at 110 C and experiences a convection heat-transfer coefficient of 4 kW/m?K. Calculate the center and surface temperatures of the wire. Resistance heaterarrow_forwardAn electrical resistance wire made of tungsten dissipates heat to the surroundings at a constant rate. Which of the following equations are you going to use to compute for the temperature at any point within the wire when the temperature throughout the whole wire no longer changes with time? Assume that the wire can be approximated as a thin cylinder. a. Fourier-Biot equation b. Poisson equation c. Diffusion equation d. Laplace equationarrow_forward
- The schematic below illustrates a tank formed from two zones, i.e. liquid and solid. The tank is heated from the left-side with a time-varying solar heat radiation g,ol =f(t) (Wim), while the right-side is kept at a low temperature T. The top surface of the tank is subjected to the ambient conditions, i.e. (hair & Tair ), while its bottom is thermally insulated. Conjugate heat transfer takes place between the two-physically different zones through the fluid-solid interface separating them, while fluid flow is induced due to buoyancy effects where the buoyancy force is approximated according to Boussinesq formulation Fiuoyaney=P0 Bg(T-To). Explain the following: 1- The assumptions required to simulate the below problem. 2- The conservation equations governing the transport phenomena in each zone. 3- The boundary conditions closing the mathematical model. 4- The discretized form of each conservation equation stated in (point 2) above. 5- The appropriate differencing scheme to be used for…arrow_forwardQ1 Passage of an electric current through a long conducting rod of radius r; and thermal conductivity k, results in uniform volumetric heating at a rate of ġ. The conduct- ing rod is wrapped in an electrically nonconducting cladding material of outer radius r, and thermal conduc- tivity k, and convection cooling is provided by an adjoining fluid. Conducting rod, ġ, k, 11 To Čladding, ke For steady-state conditions, write appropriate forms of the heat equations for the rod and cladding. Express ap- propriate boundary conditions for the solution of these equations.arrow_forward1- The energy transferred from the anterior chamber of the eye through the cornea varies considerably depending on whether a contact lens is worn. Treat the eye as a spherical system and assume the system to be at steady state. The convection coefficient ho is unchanged with and without the contact lens in place. The cornea and the lens cover one-third of the spherical surface area. T he T h Anterior chamber Contact lens Cornea are as follows: Values of the parameters representing this situation r 10.2mm, r 12.7 mm, r3= 16.5 mm, Teoj= 37°C, Teoo = 21°C, ki = 0.35 W/m.K, k2 0.80 W/m.K, h 12 W/m2.K, ho 12 W/m2.K. (a) Construct the thermal circuits, labeling all potential and flows form the systems excluding the contact lens and including the contact lens. Write resistance elements in terms of appropriate parameters (b) Determine the heat loss from the interior chamber with and without the contact lens in place (c) Discuss the implication of your results.arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning