A small dam, which may be idealized by a large slab 1.2 m thick, is to be completely poured in a short period of time. The hydration of the concrete results in the equivalent of a distributed source of constant strength of 100 W/m3 . If both dam surfaces are at 16°C, determine the maximum temperature to which the concrete will be subjected, assuming steady-state conditions. The thermal conductivity of the wet concrete may be taken as 0.84 W/(m K).

GIVEN



FIND

The maximum temperature (Tmax)

ASSUMPTIONS

Steady state conditions prevail

SKETCH


The dam is symmetric. Therefore, x will be measured from the centerline of the dam. The equation for one

dimensional conduction is given



This is subject to the following boundary conditions





The constant C1 can be evaluated using the first boundary condition



Integrating once again



The constant C2 can be evaluated using the second boundary condition



Therefore, the temperature distribution in the dam is



The maximum temperature occurs at x = 0

Physics & Space Science

You might also like to view...

Which of these was NOT seen telescopically by Galileo?

A) sunspots B) Venus' phase cycle C) stellar parallax D) four moons around Jupiter E) craters and mare on the Moon

Physics & Space Science

Water, ImageO, and methane, CImage, have about the same mass and differ by only one type of atom. Why is the boiling point of water so much higher than that of methane?

A) The water molecule is less symmetrical than is the methane molecule. B) The oxygen of a water molecule has two lone pairs of electrons. C) The electronegativity difference between oxygen and hydrogen is greater than the electronegativity difference between carbon and hydrogen. D) all of the above

Physics & Space Science

For a projectile launched horizontally, the vertical component of a projectile's velocity

A) is zero. B) remains a non-zero constant. C) continuously increases. D) continuously decreases. E) any of the above, depending on position.

Physics & Space Science

If the U-tube in Problem 4 is rotated about the right leg, what maximum rpm will result in the 20°C water being thrown from the tube?

(A) 741 rpm (B) 672 rpm (C) 569 rpm (D) 432 rpm

Physics & Space Science