Explanation Given: The length of the mussel layer is L m = 30 mm . The thickness of the skin layer is L s f = 3 mm . The heat loss rate from the body is q 1 = 142 W . The temperature of the infinity is T ∞ = 15 °C . The thermal conductivity of the mussel layer is k m = 0.5 W / m ⋅ K . The frequency is ω = 0.0005 s -1 . The density of body is ρ b = 1000 kg / m 3 . The specific heat of the body is c b = 3600 J / kg ⋅ K . The area of the body is A = 1.8 m 2 . The temperature of the arterial is T a = 37 °C . The core body temperature is T c = 37 °C . The comfortable body temperature of the body is T s = 33 °C . The convective heat transfer coefficient is h = 2 W / m 2 ⋅ K . The emissivity is ε = 0.95 . The Stefan Boltzmann constant is σ = 5.67 × 10 − 8 W / m 2 ⋅ K 4 . The surrounding temperature is T s u r r = 15 °C . Formula used: The expression for the heat loss rate from the skin surface to environment is given as, q = h A ( T s − T ∞ ) + ε σ A ( T s 4 − T s u r r 4 ) The expression for the temperature of the skin layer is given as, T i = T s − q L s f k s f A The expression for the parameter m is given as, m = ω ρ b c b k m The expression for the metabolism heat generation rate is given as, q ˙ m = ω ρ b c b [ q k m A m sin ( m L m ) + ( T i − T a ) cosh ( m L m ) + ( T c − T a ) cosh ( m L m ) + 1 ] Calculation: The heat loss rate from the skin surface to environment can be calculated as, q = h A ( T s − T ∞ ) + ε σ A ( T s 4 − T s u r r 4 ) q = { 2 W / m 2 ⋅ K × 1.8 m 2 [ 33 °C ( °C + 273 ) K − 15 °C ( °C + 273 ) K ] + 0.95 × 5.67 × 10 − 8 W / m 2 ⋅ K 4 × 1.8 m 2 [ { 33 °C ( °C + 273 ) K } 4 − { 15 °C ( °C + 273 ) K } 4 ] } q = 247

6th Edition

ISBN: 9780470501962

Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine

Publisher: Wiley, John & Sons, Incorporated

See similar textbooks

Videos

Question

Chapter 3, Problem 3.166P

To determine

The metabolic heat generation rate.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 3, Problem 3.165P

Chapter 3, Problem 3.167P

Students have asked these similar questions

For the 21.5-cm thick multilayer assembly as listed below, please estimate the temperature on the interface between material layers 3 and 4 Material layers - counted from the interior side: (1) 1.5 - cm gypsum board; (2) 4.0-cm - concrete of density - 2400-kg/m3; (3) 10-cm of XPS foam; (4) 6.0-cm - concrete of density - 2400-kg/m3 Interior film resistance is Ri = 0.121 m2K/W Exterior film resistance is Re - 0.029 m2K/W Internal temperature +20 degC External Temperature - 20 degC

There are 2 options to be considered to form the insulation layer between the refractory brick and air space, which are fiberglass and firebrick. Calculate the minimum thickness required for the both fiberglass and firebrick. Which option do you recommend? Comment. State the assumption in your calculation. Based on your recommendation, calculate the temperature at each interface throughout the wall and draw a temperature variation diagram from inside wall surface to outside wall surface. * Refractory brick Fiberglass or firebrick? 0.5" Plaster Heat Ambient source Air spáce 4 Concrete block Figure 2

Chapter 3 Solutions

Introduction to Heat Transfer

Ch. 3 - Consider the plane wall of Figure 3.1, separating...Ch. 3 - A new building to be located in a cold climate is...Ch. 3 - The rear window of an automobile is defogged by...Ch. 3 - The rear window of an automobile is defogged by...Ch. 3 - A dormitory at a large university, built 50 years...Ch. 3 - In a manufacturing process, a transparent film is...Ch. 3 - Prob. 3.7P Ch. 3 - A t=10-mm-thick horizontal layer of water has a...Ch. 3 - Prob. 3.9P Ch. 3 - The wind chill, which is experienced on a cold,...

Ch. 3 - Prob. 3.11P Ch. 3 - A thermopane window consists of two pieces of...Ch. 3 - A house has a composite wall of wood, fiberglass...Ch. 3 - Prob. 3.14P Ch. 3 - Prob. 3.15P Ch. 3 - Work Problem 3.15 assuming surfaces parallel to...Ch. 3 - Consider the oven of Problem 1.54. The walls of...Ch. 3 - The composite wall of an oven consists of three...Ch. 3 - The wall of a drying oven is constructed by...Ch. 3 - The t=4-mm-thick glass windows of an...Ch. 3 - Prob. 3.21P Ch. 3 - In the design of buildings, energy conservation...Ch. 3 - Prob. 3.23P Ch. 3 - Prob. 3.24P Ch. 3 - Prob. 3.25P Ch. 3 - A composite wall separates combustion gases at...Ch. 3 - Prob. 3.27P Ch. 3 - Prob. 3.28P Ch. 3 - Prob. 3.29P Ch. 3 - The performance of gas turbine engines may...Ch. 3 - A commercial grade cubical freezer, 3 m on a...Ch. 3 - Prob. 3.32P Ch. 3 - Prob. 3.33P Ch. 3 - Prob. 3.34P Ch. 3 - A batt of glass fiber insulation is of density...Ch. 3 - Air usually constitutes up to half of the volume...Ch. 3 - Prob. 3.37P Ch. 3 - Prob. 3.38P Ch. 3 - The diagram shows a conical section fabricatedfrom...Ch. 3 - Prob. 3.40P Ch. 3 - From Figure 2.5 it is evident that, over a wide...Ch. 3 - Consider a tube wall of inner and outer radii ri...Ch. 3 - Prob. 3.43P Ch. 3 - Prob. 3.44P Ch. 3 - Prob. 3.45P Ch. 3 - Prob. 3.46P Ch. 3 - To maximize production and minimize pumping...Ch. 3 - A thin electrical heater is wrapped around the...Ch. 3 - Prob. 3.50P Ch. 3 - Prob. 3.51P Ch. 3 - Prob. 3.52P Ch. 3 - A wire of diameter D=2mm and uniform temperatureT...Ch. 3 - Prob. 3.54P Ch. 3 - Electric current flows through a long rod...Ch. 3 - Prob. 3.56P Ch. 3 - A long, highly polished aluminum rod of diameter...Ch. 3 - Prob. 3.58P Ch. 3 - Prob. 3.59P Ch. 3 - Prob. 3.60P Ch. 3 - Prob. 3.61P Ch. 3 - Prob. 3.62P Ch. 3 - Consider the series solution, Equation 5.42, for...Ch. 3 - Prob. 3.64P Ch. 3 - Copper-coated, epoxy-filled fiberglass circuit...Ch. 3 - Prob. 3.66P Ch. 3 - A constant-property, one-dimensional Plane slab of...Ch. 3 - Referring to the semiconductor processing tool of...Ch. 3 - Prob. 3.69P Ch. 3 - Prob. 3.70P Ch. 3 - Prob. 3.71P Ch. 3 - The 150-mm-thick wall of a gas-fired furnace is...Ch. 3 - Steel is sequentially heated and cooled (annealed)...Ch. 3 - Prob. 3.74P Ch. 3 - Prob. 3.75P Ch. 3 - Prob. 3.76P Ch. 3 - Prob. 3.77P Ch. 3 - Prob. 3.78P Ch. 3 - The strength and stability of tires may be...Ch. 3 - Prob. 3.80P Ch. 3 - Prob. 3.81P Ch. 3 - A long rod of 60-mm diameter and thermophysical...Ch. 3 - A long cylinder of 30-min diameter, initially at a...Ch. 3 - Work Problem 5.47 for a cylinder of radius r0 and...Ch. 3 - Prob. 3.85P Ch. 3 - Prob. 3.86P Ch. 3 - Prob. 3.87P Ch. 3 - Prob. 3.88P Ch. 3 - Prob. 3.89P Ch. 3 - Prob. 3.90P Ch. 3 - Prob. 3.91P Ch. 3 - Prob. 3.92P Ch. 3 - In Section 5.2 we noted that the value of the Biot...Ch. 3 - Prob. 3.94P Ch. 3 - Prob. 3.95P Ch. 3 - Prob. 3.96P Ch. 3 - Prob. 3.97P Ch. 3 - Prob. 3.98P Ch. 3 - Work Problem 5.47 for the case of a sphere of...Ch. 3 - Prob. 3.100P Ch. 3 - Prob. 3.101P Ch. 3 - Prob. 3.102P Ch. 3 - Prob. 3.103P Ch. 3 - Consider the plane wall of thickness 2L, the...Ch. 3 - Problem 4.9 addressed radioactive wastes stored...Ch. 3 - Prob. 3.106P Ch. 3 - Prob. 3.107P Ch. 3 - Prob. 3.108P Ch. 3 - Prob. 3.109P Ch. 3 - Prob. 3.110P Ch. 3 - A one-dimensional slab of thickness 2L is...Ch. 3 - Prob. 3.112P Ch. 3 - Prob. 3.113P Ch. 3 - Prob. 3.114P Ch. 3 - Prob. 3.115P Ch. 3 - Derive the transient, two-dimensional...Ch. 3 - Prob. 3.117P Ch. 3 - Prob. 3.118P Ch. 3 - Prob. 3.119P Ch. 3 - Prob. 3.120P Ch. 3 - Prob. 3.121P Ch. 3 - Prob. 3.122P Ch. 3 - Consider two plates, A and B, that are each...Ch. 3 - Consider the fuel element of Example 5.11, which...Ch. 3 - Prob. 3.125P Ch. 3 - Prob. 3.126P Ch. 3 - Prob. 3.127P Ch. 3 - Prob. 3.128P Ch. 3 - Prob. 3.129P Ch. 3 - Consider the thick slab of copper in Example 5.12,...Ch. 3 - In Section 5.5, the one-term approximation to the...Ch. 3 - Thermal energy storage systems commonly involve a...Ch. 3 - Prob. 3.133P Ch. 3 - Prob. 3.134P Ch. 3 - Prob. 3.135P Ch. 3 - A tantalum rod of diameter 3 mm and length 120 mm...Ch. 3 - A support rod k=15W/mK,=4.0106m2/s of diameter...Ch. 3 - Prob. 3.138P Ch. 3 - Prob. 3.139P Ch. 3 - A thin circular disk is subjected to induction...Ch. 3 - An electrical cable, experiencing uniform...Ch. 3 - Prob. 3.142P Ch. 3 - Prob. 3.145P Ch. 3 - Consider the fuel element of Example 5.11, which...Ch. 3 - Prob. 3.147P Ch. 3 - Prob. 3.148P Ch. 3 - Prob. 3.149P Ch. 3 - Prob. 3.150P Ch. 3 - In a manufacturing process, stainless steel...Ch. 3 - Prob. 3.153P Ch. 3 - Carbon steel (AISI 1010) shafts of 0.1-m diameter...Ch. 3 - A thermal energy storage unit consists of a large...Ch. 3 - Small spherical particles of diameter D=50m...Ch. 3 - A spherical vessel used as a reactor for producing...Ch. 3 - Batch processes are often used in chemical and...Ch. 3 - Consider a thin electrical heater attached to a...Ch. 3 - An electronic device, such as a power transistor...Ch. 3 - Prob. 3.161P Ch. 3 - In a material processing experiment conducted...Ch. 3 - Prob. 3.165P Ch. 3 - Prob. 3.166P Ch. 3 - Prob. 3.167P Ch. 3 - Prob. 3.168P Ch. 3 - Prob. 3.173P Ch. 3 - Prob. 3.174P Ch. 3 - Prob. 3.175P Ch. 3 - Prob. 3.176P Ch. 3 - Prob. 3.177P

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The metabolic heat generation rate.

Solution Summary: The author explains the metabolic heat generation rate, the thermal conductivity of the mussel layer, and the convective heat transfer coefficient.

Videos

The metabolic heat generation rate.

Want to see the full answer?

Chapter 3 Solutions