The temperature within a thin plate with thermal conductivity of 10 W/m/K depends on position as given by the following expression: TT=(100 K)????????−xx2/????????xx 2cos�yy/????????yy�+300 K Where, Lx = 1 m, and Ly = 2 m. At the point (0.4 m, 1 m), find: a. The magnitude of the heat flux b. The direction of the heat flux


Answer 1


Heat flux = (598.3î + 204.3j) W/m²

a) Magnitude of the heat flux = 632.22 W/m²

b) Direction of the heat flux = 18.85°


- The correct question is the first image attached to this solution.

- The solution to this question is contained on the second and third images attached to this solution respectively.

Hope this Helps!!!

Related Questions

Anatomy of a Wave worksheet can someone help me out with the answers????
If a freely falling object were somehow equipped with a speedometer, its speedreading would increase each second bya) about 15 m/s.b) a rate that depends on its initial speed.c) a variable amount.d) about 5 m/s.e) about 10 m/s.
When it is at rotating at full speed, a disk drive in a certain old computer game system revolves once every 0.050 seconds. Starting from rest, it takes two revolutions for the disk to reach full speed. Assuming that the angular acceleration of the disk is constant, what is its angular acceleration while it is speeding up
You wish to buy a motor that will be used to lift a 10-kg bundle of shingles from the ground to the roof of a house. The shingles are to have a 1.5-m/s2 upward acceleration at the start of the lift. The very light pulley on the motor has a radius of 0.17 m . Part A Determine the minimum torque that the motor must be able to provide. Express your answer with
Singing that is off-pitch by more than about 1% sounds bad. How fast would a singer have to be moving relative to the rest of a band to make this much of a change in pitch due to the Doppler effect

1. A mass suspended from a spring oscillates vertically with amplitude of 15 cm. At what distance from the equilibrium position will the speed of the mass be 25% of its maximum speed?



The value of the distance is \bf{14.52~cm}.


The velocity of a particle(v) executing SHM is

v = \omega \sqrt{A^(2) - x^(2)}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`~(1)

where, \omega is the angular frequency, A is the amplitude of the oscillation and x is the displacement of the particle at any instant of time.

The velocity of the particle will be maximum when the particle will cross its equilibrium position, i.e., x = 0.

The maximum velocity(\bf{v_(m)}) is

v_(m) = \omega A~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(2)

Divide equation (1) by equation(2).

(v)/(v_(m)) = \frac{\sqrt{A^(2) - x^(2)}}{A}~~~~~~~~~~~~~~~~~~~~~~~~~~~(3)

Given, v = 0.25 v_(m) and A = 15~cm. Substitute these values in equation (3).

&& (1)/(4) = \frac{\sqrt{15^(2) - x^(2)}}{15}\n&or,& A = 14.52~cm

What type of circuit measurement is made by placing a meters test leads in parallel with a deenergized component


If the component is DE-energized, meaning the whole device is
powered down, then the only thing you can measure with the meter-
probes on both ends of the component is its resistance.

If you have a fancy, expensive meter, then maybe you could measure
the component's capacitance or inductance.  I never had one of those. 

The normal meter measures volts, amps, and ohms.  If you touch
the probes to both ends of the component and the circuit is energized,
then you measure the voltage across the component.  If the circuit is
DE-energized, then you're measuring the component's resistance.

(Note:  You have to know which one you're measuring, and set up the
meter properly.  For example, if the circuit is energized and you try to
measure resistance, it's possible that you could fry your meter.)

25% part (c) assume that d is the distance the cheetah is away from the gazelle when it reaches full speed. Derive an expression in terms of the variables d, vcmax and vg for the time, tc, it takes the cheetah to catch the gazelle.


maximum speed of cheetah is

v_1 = v_(max)

speed of gazelle is given as

v_2 = v_(g)

Now the relative speed of Cheetah with respect to Gazelle

v_(12) = v_1 - v_2

v_(12) = v_(max) - v_g

now the relative distance between Cheetah and Gazelle is given initially as "d"

now the time taken by Cheetah to catch the Gazelle is given as

d = v_(12)* t

so by rearranging the terms we can say

t = (d)/(v_(12))

t = (d)/(v_(max) - v_g)

so above is the relation between all given variable

A 10 kg block moving at 10 m/s in a direction 45 degrees above the horizontal. When it has fallen to a point that is 10 m below the initial point measured vertically (without air friction), the block's kinetic energy is closest to


The block's kinetic energy is closest to 1500 Joules.

Kinetic energy :

The energy is always conserved.

So that, the total kinetic energy will be sum of initial potential energy and kinetic energy during falling.

Given that, mass(m)=10kg, v=10m/s, h=10m,g=10m/s^2

              K.E=(1/2)mv^2 + mgh

              K.E=(1/2)*10*100 + (10*10*10)

              K.E=500 + 1000=1500Joule

The  block's kinetic energy is closest to 1500 Joules.

Learn more about the kinetic energy here:


Kinetic energy = 1500 J


The computation of the block's kinetic energy is shown below:

As we know that

Conservation of energy is

PE_i + KE_i = PE_f + KE_f


Initial Potential energy = PE_i = m gh = 10kg× 10m/s^2 × 10m = 1000 J

Initial Kinetic energy = KE_i = (0.5) m V^2 = (0.5) (10 kg) (10 m/s)^2 = 500 J

Final potential energy = PE_f = mgh = 0      

As h = 0 which is at reference line


PE_i + KE_i = PE_f + KE_f

Now put these valeus to the above formulas

1000 J + 500 J = 0 + KE_f

After solving this

Kinetic energy = 1500 J

An ideal gas is at a temperature of 320 K. What is the average translational kinetic energy of one of its molecules



6.624 x 10^-21 J


The temperature of the ideal gas = 320 K

The average translational energy of an ideal gas is gotten as

K_(ave) = (3)/(2)K_(b)T


K_(ave)  is the average translational energy of the molecules

K_(b) = Boltzmann constant = 1.38 × 10^-23 m^2 kg s^-2 K^-1

T is the temperature of the gas = 320 K

substituting value, we have

K_(ave) = (3)/(2) * 1.38*10^(-23) * 320 = 6.624 x 10^-21 J

If you travel 2 km north, then travel 5 km south, what is your displacement?



This is a vector addition problem which requires magnitude and direction as the answer. First is to resolve the southbound vector and the northbound vector. Since they are opposite in directions their vector sum is their algebraic sum. 3 km north + 5 km south = 2 km south.

We then add 2 km west and 2 km south using Pythagorean theorem since west and south form a right angle. (2 km)^2 west + (2 km)^2 south gives (4 + 4) km^2 southwest = 8 (km)^2 45 degrees south of west

Extracting the square root of 8 gives us about 2.83 km 45 degrees south of west.


I hope it will help you...

Other Questions