1.1 Consider the fireclay brick wall of Example 1.1 that isoperating under different thermal conditions. The tem-perature distribution, at an instant in time, is T(x) = a+bx where a 1400 K and b = -1000 K/m. Determinethe heat fluxes, q", and heat rates, q, at x = 0 and x = L.Do steady-state conditions exist?

Answered: 1.1 Consider the fireclay brick wall of…

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter4: Numerical Analysis Of Heat Conduction

Section: Chapter Questions

Problem 4.21P

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For flow over a slightly curved isothermal surface, the temperature distribution inside the boundary layer t can be approximated by the polynomial T(y)=a+by+cy2+d3(yt), where y is the distance normal to the surface. (a) By applying appropriate boundary conditions, evaluate the constants a, b, c, and d. Fluid (b) Then obtain a dimensionless relation for the temperature distribution in the boundary layer.
3.9 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 thermocouples, one located in the center and the other near the surface. The two thermocouples registered, within the accuracy of the recording instruments, the same temperature at any given instant. In one test run, the initial temperature of the ball was 66°C, and the temperature decreased by 7°C in 1.15 min. Calculate the heat transfer coefficient for this case.
To determine the thermal conductivity of a structural material, a large 15-cm-thick slab of the material is subjected to a uniform heat flux of 2500 W/m2 while thermocouples embedded in the wall at 2.5 cm. intervals are read over a period of time. After the system had reached equilibrium, an operator recorded the thermocouple readings shown below for two different environmental conditions: Distance from the Surface (cm) Temperature (C) Test 1 0 40 5 65 10 97 15 132 Test 2 0 95 5 130 10 168 15 208 From these data, determine an approximate expression for the thermal conductivity as a function of temperature between 40 and 208C.
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The steady-state temperature distribution in a one-dimensional wall of thermal conductivity k=83 (W/m) °C) and thickness 300 mm is observed to be T(°C) = ax2+bx+c, where a = -2500 °C/m2 , b = 500 °C/m, c = 250 °C and x is in meters. a) What is the heat generation rate ?̇ (W/m3 ) in the wall ? b) Find the maximum and minimum temperatures in the wall. c) Find the amount of heat transferred to the right side of the wall (for 1 m2 surface area.)
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You have a 1-D steady-state conduction problem, constant thermal properties, with energy generation q_dot. The material is 4.0 cm thick and has a constant thermal conductivity of k = 65.0 (W/m-k). The temperature distribution within the object is: T(x) = a + bx^2 a = 100 Celcius b = -1000 Celcius/m^2 Starting with the Heat Diffusion Equation and using the data given above, determine the following: • Determine the heat generation rate q_dot within the wall. • Determine the heat flux q" at x=0 and at x=L.
8. Consider an iron bar, of diameter 4cm and length 1m, with specific heat c = 0.437J/(g K), density p= 7.88 g/cm³, and thermal conductivity K = 0.836 W/(cm K). Suppose that the bar is insulated except at the ends, it is heated to a constant tem- perature of 5 degrees Celsius, and the ends are placed in an ice bath (0 degrees Celsius). Compute the temperature (accurate to 3 digits) at the midpoint of the bar after 20 minutes. (Warning: Be sure to use consistent units.)
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