torabi

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5 years, 93 days

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These are questions asked by torabi

How  I can use from equations 1-6 and repleacing them into equation 7 to remove qx,qy,qz?

Thank you

simpl2.mw
 

A := q__x(x, y, z, t)+`τ__q`*(diff(q__x(x, y, z, t), t))+(1/2)*`τ__q`^2*(diff(q__x(x, y, z, t), t, t)) = -k*(diff(T(x, y, z, t), x))-k*`τ__T`*(diff(T(x, y, z, t), x, t))-(1/2)*k*`τ__T`^2*(diff(T(x, y, z, t), x, t, t))
NULL

q__x(x, y, z, t)+tau__q*(diff(q__x(x, y, z, t), t))+(1/2)*tau__q^2*(diff(diff(q__x(x, y, z, t), t), t)) = -k*(diff(T(x, y, z, t), x))-k*tau__T*(diff(diff(T(x, y, z, t), t), x))-(1/2)*k*tau__T^2*(diff(diff(diff(T(x, y, z, t), t), t), x))

(1)

A__x := diff(A, x)

diff(q__x(x, y, z, t), x)+tau__q*(diff(diff(q__x(x, y, z, t), t), x))+(1/2)*tau__q^2*(diff(diff(diff(q__x(x, y, z, t), t), t), x)) = -k*(diff(diff(T(x, y, z, t), x), x))-k*tau__T*(diff(diff(diff(T(x, y, z, t), t), x), x))-(1/2)*k*tau__T^2*(diff(diff(diff(diff(T(x, y, z, t), t), t), x), x))

(2)

NULL

B := q__y(x, y, z, t)+`τ__q`*(diff(q__y(x, y, z, t), t))+(1/2)*`τ__q`^2*(diff(q__y(x, y, z, t), t, t)) = -k*(diff(T(x, y, z, t), y))-k*`τ__T`*(diff(T(x, y, z, t), y, t))-(1/2)*k*`τ__T`^2*(diff(T(x, y, z, t), y, t, t))

q__y(x, y, z, t)+tau__q*(diff(q__y(x, y, z, t), t))+(1/2)*tau__q^2*(diff(diff(q__y(x, y, z, t), t), t)) = -k*(diff(T(x, y, z, t), y))-k*tau__T*(diff(diff(T(x, y, z, t), t), y))-(1/2)*k*tau__T^2*(diff(diff(diff(T(x, y, z, t), t), t), y))

(3)

B__y := diff(B, y)

diff(q__y(x, y, z, t), y)+tau__q*(diff(diff(q__y(x, y, z, t), t), y))+(1/2)*tau__q^2*(diff(diff(diff(q__y(x, y, z, t), t), t), y)) = -k*(diff(diff(T(x, y, z, t), y), y))-k*tau__T*(diff(diff(diff(T(x, y, z, t), t), y), y))-(1/2)*k*tau__T^2*(diff(diff(diff(diff(T(x, y, z, t), t), t), y), y))

(4)

NULL

C := q__z(x, y, z, t)+`τ__q`*(diff(q__z(x, y, z, t), t))+(1/2)*`τ__q`^2*(diff(q__z(x, y, z, t), t, t)) = -k*(diff(T(x, y, z, t), z))-k*`τ__T`*(diff(T(x, y, z, t), z, t))-(1/2)*k*`τ__T`^2*(diff(T(x, y, z, t), z, t, t))

q__z(x, y, z, t)+tau__q*(diff(q__z(x, y, z, t), t))+(1/2)*tau__q^2*(diff(diff(q__z(x, y, z, t), t), t)) = -k*(diff(T(x, y, z, t), z))-k*tau__T*(diff(diff(T(x, y, z, t), t), z))-(1/2)*k*tau__T^2*(diff(diff(diff(T(x, y, z, t), t), t), z))

(5)

C__z := diff(C, z)

diff(q__z(x, y, z, t), z)+tau__q*(diff(diff(q__z(x, y, z, t), t), z))+(1/2)*tau__q^2*(diff(diff(diff(q__z(x, y, z, t), t), t), z)) = -k*(diff(diff(T(x, y, z, t), z), z))-k*tau__T*(diff(diff(diff(T(x, y, z, t), t), z), z))-(1/2)*k*tau__T^2*(diff(diff(diff(diff(T(x, y, z, t), t), t), z), z))

(6)

NULL

expand(simplify(-A__x-B__y-C__z+Q = rho*c__p*(diff(T(x, y, z, t), t))))

(-(diff(q__x(x, y, z, t), x))-tau__q*(diff(diff(q__x(x, y, z, t), t), x))-(1/2)*tau__q^2*(diff(diff(diff(q__x(x, y, z, t), t), t), x))-(diff(q__y(x, y, z, t), y))-tau__q*(diff(diff(q__y(x, y, z, t), t), y))-(1/2)*tau__q^2*(diff(diff(diff(q__y(x, y, z, t), t), t), y))-(diff(q__z(x, y, z, t), z))-tau__q*(diff(diff(q__z(x, y, z, t), t), z))-(1/2)*tau__q^2*(diff(diff(diff(q__z(x, y, z, t), t), t), z))+Q = k*(diff(diff(T(x, y, z, t), x), x))+k*tau__T*(diff(diff(diff(T(x, y, z, t), t), x), x))+(1/2)*k*tau__T^2*(diff(diff(diff(diff(T(x, y, z, t), t), t), x), x))+k*(diff(diff(T(x, y, z, t), y), y))+k*tau__T*(diff(diff(diff(T(x, y, z, t), t), y), y))+(1/2)*k*tau__T^2*(diff(diff(diff(diff(T(x, y, z, t), t), t), y), y))+k*(diff(diff(T(x, y, z, t), z), z))+k*tau__T*(diff(diff(diff(T(x, y, z, t), t), z), z))+(1/2)*k*tau__T^2*(diff(diff(diff(diff(T(x, y, z, t), t), t), z), z))+Q) = rho*c__p*(diff(T(x, y, z, t), t))

(7)

NULL

``


 

Download simpl2.mw

 

How I can perform integration by parts, with respect to the x[0..1],y[0..1],t 

PART.mw
 

restart

U := (1/2)*(E*(diff(u(x, y), x)-z*(diff(w(x, y), x, x))+(1/2)*(diff(w(x, y), x))^2)/(-upsilon^2+1)+E*upsilon*(diff(v(x, y), y)-z*(diff(w(x, y), y, y))+(1/2)*(diff(w(x, y), y))^2)/(-upsilon^2+1))*(diff(u(x, y), x)-z*(diff(w(x, y), x, x))+(1/2)*(diff(w(x, y), x))^2)+(1/2)*(E*upsilon*(diff(u(x, y), x)-z*(diff(w(x, y), x, x))+(1/2)*(diff(w(x, y), x))^2)/(-upsilon^2+1)+E*(diff(v(x, y), y)-z*(diff(w(x, y), y, y))+(1/2)*(diff(w(x, y), y))^2)/(-upsilon^2+1))*(diff(v(x, y), y)-z*(diff(w(x, y), y, y))+(1/2)*(diff(w(x, y), y))^2)+E*(1-upsilon)*((1/2)*(diff(v(x, y), x))-z*(diff(w(x, y), x, y))+(1/2)*(diff(u(x, y), y))+(1/2)*(diff(w(x, y), x))*(diff(w(x, y), y)))^2/(-upsilon^2+1)+2*E*l^2*(diff(w(x, y), x, y))^2/(2+2*upsilon)+2*E*l^2*(-(1/2)*(diff(w(x, y), x, x))+(1/2)*(diff(w(x, y), y, y)))^2/(2+2*upsilon)+2*E*l^2*((1/4)*(diff(v(x, y), x, x))-(1/4)*(diff(u(x, y), x, y)))^2/(2+2*upsilon)+2*E*l^2*((1/4)*(diff(v(x, y), x, y))-(1/4)*(diff(u(x, y), y, y)))^2/(2+2*upsilon)

with(IntegrationTools)

``

``


 

Download PART.mw

 

is possible to solvethis equation via maple?

hank you

EQUATION2.mw
 

restartNULL

alpha := 1.2*10^(-4); Betaa := 4.0*log(2); J := 13.4; delta := 15.3*10^(-9); tp := 10^(-13); tq := 8.5*10^(-12); tu := 90.0*10^(-12); kapa := 315; r0 := 2.0*10^(-7); Lx := 5.0*10^(-7); Ly := 5.0*10^(-7); Lz := 1.0*10^(-7); a := 0.7e-1*(Betaa/Pi)^.5*J/(15.3*10^(-22)); bb := exp(-((10^(-7)*x-(1/2)*Lx)^2+(10^(-7)*y-(1/2)*Ly)^2)/(2*r0^2)); print(aa = a); Q := a*exp(-z*10^(-7)/delta)*exp(-1.88*abs(t-2*tp)/tp)*bb

0.1200000000e-3

 

4.0*ln(2)

 

13.4

 

0.1530000000e-7

 

1/10000000000000

 

0.8500000000e-11

 

0.9000000000e-10

 

315

 

0.2000000000e-6

 

0.5000000000e-6

 

0.5000000000e-6

 

0.1000000000e-6

 

0.6917775548e21*ln(2)^.5

 

exp(-0.1250000000e14*((1/10000000)*x-0.2500000000e-6)^2-0.1250000000e14*((1/10000000)*y-0.2500000000e-6)^2)

 

aa = 0.6917775548e21*ln(2)^.5

 

0.6917775548e21*ln(2)^.5*exp(-6.535947712*z)*exp(-0.1880000000e14*abs(t-1/5000000000000))*exp(-0.1250000000e14*((1/10000000)*x-0.2500000000e-6)^2-0.1250000000e14*((1/10000000)*y-0.2500000000e-6)^2)

(1)

(diff(U(x, y, z, t), t)+tq*(diff(U(x, y, z, t), t, t)))/alpha = diff(U(x, y, z, t), x, x)+diff(U(x, y, z, t), y, y)+tu*(diff(U(x, y, z, t), x, x, t)+diff(U(x, y, z, t), y, y, t))+tu*(diff(U(x, y, z, t), z, z, t))+(Q+tq*(diff(Q, t)))/kapa

8333.333333*(diff(U(x, y, z, t), t))+0.7083333333e-7*(diff(diff(U(x, y, z, t), t), t)) = diff(diff(U(x, y, z, t), x), x)+diff(diff(U(x, y, z, t), y), y)+0.9000000000e-10*(diff(diff(diff(U(x, y, z, t), t), x), x))+0.9000000000e-10*(diff(diff(diff(U(x, y, z, t), t), y), y))+0.9000000000e-10*(diff(diff(diff(U(x, y, z, t), t), z), z))+0.2196119222e19*ln(2)^.5*exp(-6.535947712*z)*exp(-0.1880000000e14*abs(t-1/5000000000000))*exp(-0.1250000000e14*((1/10000000)*x-0.2500000000e-6)^2-0.1250000000e14*((1/10000000)*y-0.2500000000e-6)^2)-0.3509398517e21*ln(2)^.5*exp(-6.535947712*z)*abs(1, t-1/5000000000000)*exp(-0.1880000000e14*abs(t-1/5000000000000))*exp(-0.1250000000e14*((1/10000000)*x-0.2500000000e-6)^2-0.1250000000e14*((1/10000000)*y-0.2500000000e-6)^2)

(2)

``

 

Boundary condition:

U(0, y, z, t) = 300; U(Lx, y, z, t) = 300; U(x, 0, z, t) = 300; U(x, Ly, z, t) = 300; U(x, y, 0, t) = 300; U(x, y, Lz, t) = 300

#####################################

INITIAL CONDITIONS:

 

U(x, y, z, 0) = 300; (D[1](U))(x, y, z, 0) = 0

(D[1](U))(x, y, z, 0) = 0

(3)

NULL

 

``


 

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how I can remove this error in dsolve?

Error, (in dsolve/numeric/bvp) singularity encountered
dsolv.mw

Is possible to solve this differential equation by maple?

thaks...

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