An engineer seeks to study the effect of temperature on the curingof concrete by controlling the curing temperature in the followingway. A sample slab of thickness L is subjected to a heat flux, qw,on one side, and it is cooled to temperature T1 on the other. Derivea dimensionless expression for the steady temperature in the slab.Plot the expression and offer a criterion for neglecting the internalheat generation in the slab.

Given : An engineers want to learn and study the effect of temperature on the curing of concrete by…

An engineer seeks to study the effect of temperature on the curir of concrete by controlling the curing temperature in the followir way. A sample slab of thickness L is subjected to a heat flux, q on one side, and it is cooled to temperature T1 on the other. Deri a dimensionless expression for the steady temperature in the sla Dlo amit ing

An engineer seeks to study the effect of temperature on the curir of concrete by controlling the curing temperature in the followir way. A sample slab of thickness L is subjected to a heat flux, q on one side, and it is cooled to temperature T1 on the other. Deri a dimensionless expression for the steady temperature in the sla Dlo amit ing

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.

Chapter5: Analysis Of Convection Heat Transfer

Section: Chapter Questions

Problem 5.10P: 5.10 Experiments have been performed on the temperature distribution in a homogeneous long cylinder...

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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.
1.3 A furnace wall is to be constructed of brick having standard dimensions of Two kinds of material are available. One has a maximum usable temperature of 1040°C and a thermal conductivity of 1.7 W/(m K), and the other has a maximum temperature limit of 870°C and a thermal conductivity of 0.85 W/(m K). The bricks have the same cost and are laid in any manner, but we wish to design the most economical wall for a furnace with a temperature of 1040°C on the hot side and 200°C on the cold side. If the maximum amount of heat transfer permissible is 950 , determine the most economical arrangement using the available bricks.
A plane wall of thickness 2L has internal heat sources whose strength varies according to qG=qocos(ax) 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 temperature of Tw, derive an expression for the total heat loss from the wall per unit surface area.
5.10 Experiments have been performed on the temperature distribution in a homogeneous long cylinder (0.1 m diameter, thermal conductivity of 0.2 W/m K) with uniform internal heat generation. By dimensional analysis, determine the relation between the steady-state temperature at the center of the cylinder , the diameter, the thermal conductivity, and the rate of heat generation. Take the temperature at the surface as your datum. What is the equation for the center temperature if the difference between center and surface temperature is when the heat generation is ?
1.63 Liquid oxygen (LOX) for the space shuttle is stored at 90 K prior to launch in a spherical container 4 m in diameter. To reduce the loss of oxygen, the sphere is insulated with superinsulation developed at the U.S. National Institute of Standards and Technology's Cryogenic Division; the superinsulation has an effective thermal conductivity of 0.00012 W/m K. If the outside temperature is on the average and the LOX has a heat of vaporization of 213 J/g, calculate the thickness of insulation required to keep the LOX evaporation rate below 200 g/h.
Derive a formula for the thermal resistance, R₁, for a spherical shell assuming one- dimensional heat flux in the radial direction. The inside and outside radii of the spherical shell are r; and r., respectively, and the shell is made of a material having thermal conductivity k. Assume the temperatures at the inside and outside surfaces of the shell are T and T., respectively. The thermal resistance formula assumes the rate of heat transfer through the spherical shell, Q, is constant. The heat flux is in the radial direction for this one-dimensional case, and the dT heat flux is given by Fourier's law: q, = -k The rate of heat transfer through a dr spherical surface is Q =q₁A where A = 4лr². Derive the formula for the thermal 1 ++)) r = resistance for a spherical shell answer: R₁ 1 1 4лk ri
(3-5) A composite furnace wall has an inside wall temperature of 1100 C and an outside wall temperature of 38 C. The types of bricks are available as follows: brick k, W/m-k Thickness, cm Max allowable temp, °C 1. 1.45 10.5 2 0.18 5.5 875 3 0.50 7.0 200 The heat loss must not exceed 0.73 kw/ m?. 3. Determine the minimum wall thickness 4. The actual heat loss for (6) 5. The temperature between the last two bricks counting from the inside.
Question 2: Air at the temperature of T1 is being heated with the help of a cylindrical cooling fin shown in the figure below. A hot fluid at temperature To passes through the pipe with radius Rc. a) Derive the mathematical model that gives the variation of the temperature inside the fin at the dynamic conditions. b) Determine the initial and boundary conditions to solve the equation derived in (a). air To Re Assumptions: 1. Temperature is a function of only r direction 2. There is no heat loss from the surface of A 3. Convective heat transfer coefficient is constant
The principles of Newton’s Law of Cooling. You can imagine and create your own data. Discuss the nature and origin of the four (4) types of coffee where it originates. Various settings, formulations, containers, and the number of trials will be properly discussed in their methodology. Once the experimentation has been done, the thermal coefficient shall be computed and recorded. The temperature coefficient acquired at t=0 and t= 5 mins, will be tested at t = 6,7,8,9 and 10 minutes.
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.)
Question 2: Air at the temperature of T1 is being heated with the help of a cylindrical cooling fin shown in the figure below. A hot fluid at temperature To passes through the pipe with radius Rc. a) Derive the mathematical model that gives the variation of the temperature inside the fin at the dynamic conditions. b) Determine the initial and boundary conditions to solve the equation derived in (a). air T1 Re Assumptions: 1. Temperature is a function of onlyr direction 2. There is no heat loss from the surface of A 3. Convective heat transfer coefficient is constant
Using Gauss-Seidel iteration method, determine the temperatures at nodes 1, 2, 3 and 4.Estimate the midpoint temperature.