Concept explainers
In Section 5.2 we noted that the value of the Biot number significantly influences the nature of the temperature distribution in a solid during a transient conduction process. Reinforce your understanding of this important concept by using the ¡HT model for one-dimensional transient conduction to determine radial temperature distributions in a 30-mm-diameter, stainless steel rod
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Introduction to Heat Transfer
- 2.29 In a cylindrical fuel rod of a nuclear reactor, heat is generated internally according to the equation where = local rate of heat generation per unit volume at r = outside radius = rate of heat generation per unit volume at the centerline Calculate the temperature drop from the centerline to the surface for a 2.5-cm-diameter rod having a thermal conductivity of if the rate of heat removal from its surface is 1.6 .arrow_forward1.10 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 . If a thermocouple at the inner surface of the wall indicates a temperature of 22°C while another at the outer surface shows 6°C, calculate the thermal conductivity of the concrete and compare your result with the value in Appendix 2, Table 11.arrow_forward1.37 Mild steel nails were driven through a solid wood wall consisting of two layers, each 2.5-cm thick, for reinforcement. If the total cross-sectional area of the nails is 0.5% of the wall area, determine the unit thermal conductance of the composite wall and the percent of the total heat flow that passes through the nails when the temperature difference across the wall is 25°C. Neglect contact resistance between the wood layers.arrow_forward
- A square silicon chip 7mm7mm in size and 0.5-mm thick is mounted on a plastic substrate as shown in the sketch below. The top surface of the chip is cooled by a synthetic liquid flowing over it. Electronic circuits on the bottom of the chip generate heat at a rate of 5 W that must be transferred through the chip. Estimate the steady-state temperature difference between the front and back surfaces of the chip. The thermal conductivity of silicon is 150 W/m K. Problem 1.6arrow_forwardContinuous temperature distribution in a semi-permeable material with laser radiation on it, thickness L and with a heat conduction coefficient k, T(x)=-A/k.a^2.e^-ax+Bx+C It is given by equality. Here A, a, B and C are known constants. For this case, the radiation absorption in the material manifests itself in a uniform heat generation term in the form q (x). a) Obtain a relationship for the type that gives the conduction heat fluxes on the front and back surfaces. b) get a correlation for q(x) c) Obtain a relation that gives the radiation energy produced per unit surface area in the whole material.arrow_forwardA certain material has a thickness of 30 cm and a thermal conductivity of 0.04 W/m- °C. At a particular instant in time, the temperature distribution with x, the distance from the left face, is T = 150x ^ 2 - 30x , where x is in meters. Calculate the heat-flow rates atx x = 0 and x = 30 cm . Is the solid heating up or cooling down?arrow_forward
- Consider a solid sphere of radius R with a fixed surface temperature, TR. Heat is generated within the solid at a rate per unit volume given by q = ₁ + ₂r; where ₁ and ₂ are constants. (a) Assuming constant thermal conductivity, use the conduction equation to derive an expression for the steady-state temperature profile, T(r), in the sphere. (b) Calculate the temperature at the center of the sphere for the following parameter values: R=3 m 1₁-20 W/m³ TR-20 °C k-0.5 W/(m K) ₂-10 W/m³arrow_forward67 l all M O 2 o 9:05 the test.pdf Q1/ The thermal contact conductance at the interface of two 1.5-cm-thick copper plates is measured to be 19,000 W/m2 °C. Determine the thickness of the copper plate whose thermal resistance is equal to the thermal resistance of the interface between the plates. The thermal conductivity of copper k = 401 W/m-°C Q2/ A 4-m-internal-diameter spherical tank made of 1.75-cm-thick stainless steel (k 15 W/m °C) is used to store iced water at 0°C. The tank is located in a room whose temperature is 35°C. The walls of the room are also at 35°C. The outer surface of the tank is black, and heat transfer between the outer surface of the tank and the surroundings is by natural convection and radiation. The convection heat transfer coefficients at the inner and the outer surfaces of the tank are 80 W/m2 °C and 10 W/m2 °C, respectively. Determine (a) the rate of heat transfer to the iced water in the tank and (b) the amount of ice at 0°C that melts during a 1-h…arrow_forwardEXAMPLE = wire Consider a long resistance wire of radius ₁ 0.2 cm and thermal conductivity k = 15 W/m . °C in which heat is generated uniformly as a result of resistance heating at a constant rate of g = 50 W/cm3. The wire is embedded in a 0.5-cm-thick layer of ceramic whose thermal conductivity is k = 1.2 W/m °C. If the outer surface temperature of the ceramic layer is measured to be Ts = 45°C, determine the temperatures at the center of the resistance wire and the interface of the wire and the ceramic layer under steady conditions. ceramic 17 Interface Mech. Eng. UOK Wire Ceramic layer T₁=45°C ۳۰/۱۰/۲۰۱۳arrow_forward
- The temperature distribution across a wall 0.3 m thick at a certain instant of time is T(x) = a+ b+cx?, where T is in degrees Celsius and x is in meters, a = 200°C,b = -200°, and c = conductivity of 1 W /m · K. 30°C/m² . The wall has a thermal (a) On a unit surface area basis, determine the rate of heat transfer into and out of the wall and the rate of change of energy stored by the wall. (b) If the cold surface is exposed to a fluid at 100°C, what is the convection coefficient? k=1W/m•k T(x) =200-200x + 30x² 200°C- ĖST 142.7°C q"out | Fluid Too = 100°C,h 9"in |L-0.3marrow_forwardExplain how Fourier's law of conduction (in one-dimensional cartesian system) can be applied to experimentally measure the thermal conductivity of solid materials. What are the necessary conditions and assumptions?arrow_forwardYou are asked to estimate the maximum human body temperature if the metabolic heat produced in your body could escape only by tissue conduction and later on the surface by convection. Simplify the human body as a cylinder of L=1.8 m in height and ro= 0.15 m in radius. Further, simplify the heat transfer process inside the human body as a 1-D situation when the temperature only depends on the radial coordinater from the centerline. The governing dT +q""=0 dr equation is written as 1 d k- r dr r = 0, dT dr =0 dT r=ro -k -=h(T-T) dr (k-0.5 W/m°C), ro is the radius of the cylinder (0.15 m), h is the convection coefficient at the skin surface (15 W/m² °C), Tair is the air temperature (30°C). q" is the average volumetric heat generation rate in the body (W/m³) and is defined as heat generated per unit volume per second. The 1-D (radial) temperature distribution can be derived as: T(r) = q"¹'r² qr qr. + 4k 2h + 4k +T , where k is thermal conductivity of tissue air (A) q" can be calculated…arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning