Correction to: A study for multi-layer skin burn injuries based on DPL bioheat model
- PDF / 447,611 Bytes
- 2 Pages / 595.276 x 790.866 pts Page_size
- 34 Downloads / 192 Views
CORRECTION
Correction to: A study for multi‑layer skin burn injuries based on DPL bioheat model Rajneesh Kumar Chaudhary1 · Kabindra Nath Rai2 · Jitendra Singh1
© Akadémiai Kiadó, Budapest, Hungary 2020
Correction to: Journal of Thermal Analysis and Calorimetry https://doi.org/10.1007/s10973-020-09967-3
In the original publication of the article, the following equations has been incorrectly published. The corrected equations are given below:
Df cρW (𝜌s − 𝜌c )
Qd =
(Δr)2
Δm =
Dv MW Ra 𝛿c
[(
PW TW
(11)
(T(r, t) − T0 ),
)
− s
(
PW TW
)
a
] RH ,
(13)
⎧ l = 1 for first kind non-Fourier boundary condition, ⎪ M = Ml ⎨ l = 2 for second kind non-Fourier boundary condition, ⎪ l = 3 for third kind non-Fourier boundary condition. ⎩
[
N1 = Pmo − Qvo +
Fl (Fo ) h2
Pmo − Qvo ⋯ Pmo − Qvo
]T
[
Rajneesh Kumar Chaudhary [email protected] Kabindra Nath Rai [email protected] 1
Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India
Department of Mathematical Sciences, IIT-BHU, Varanasi 221005, India
2
U1,1 (U1,2 + 1)V1
[
−(U1,2 + U1,3 )Qdo 𝜃w
[(
(60)
) U2,2 + U2,3 Qdo 𝜃w
1 U2,1 (U2,2 + 1)V2 ( (( )( ) ) ) + P2f U2,2 − U2,1 −1 + U2,1 𝜃b + U2,2 + U2,3 𝜃w (( )( ) ( ) )] + Pmo U2,2 − U2,1 −1 + U2,1 − U2,2 + U2,3 𝛼𝜃w
𝜃(x, Fo ) = −
∞ ∑
) 1 [ Fo V2,n −U2,4 (x+2) (( 2U2,4 x + e2U2,4 e e U V n = 0 2,4 2,n ( ) (( )( ) 𝜃w Qdo + V2,n + P2f e2U2,4 − eU2,4 x eU2,4 x − 1 𝜃b ( ) ) (( ) + e2U2,4 x + e2U2,4 𝜃w + Pmo e2U2,4 − eU2,4 x ( U x ) ) )] e 2,4 − 1 − (e2U2,4 x + e2U2,4 𝛼𝜃w ) , +
(45) ]T
(49)
1
+ Pmo (𝛼(U1,2 + U1,3 )𝜃w + (U1,1 − 1)(U1,1 − U1,2 )) ] + (U1,2 − U1,1 )(U1,1 − 1)Qvo ) ∞ ( ∑ ) [ F V −U (x+2) (( 2U x 1 + e 1,4 + e2U1,4 𝜃w (Qdo + V1,n ) e o 1,n 1,4 U V 1,4 1,n n=0 (( ) ) + Pmo e2U1,4 − eU1,4 x (eU1,4 x − 1) − 𝛼(e2U1,4 x + e2U1,4 )𝜃w ( ( ))( ))] + Qvo − e2U1,4 − eU1,4 x eU1,4 x − 1 ,
,
The original article can be found online at https://doi.org/10.1007/ s10973-020-09967-3. * Jitendra Singh [email protected]
𝜃(x, Fo ) =
(40)
𝜓10 𝜓11 ⋯ 𝜓1M� −1 𝜓20 𝜓21 ⋯ 𝜓2M� −1 𝜓2k−1 0 𝜓(Fo ) = 𝜓2k−1 1 ⋯ 𝜓2k−1 M� −1
(58)
C2T − Ml C2T X2 − Z2 = 0,
(61)
1 U3,1 (U3,2 + 1)V3 [( ) (( ) U3,2 + U3,3 Qdo 𝜃w + P2f U3,2 − U3,1 (−1 + U3,1 )𝜃b ) ) ( + U3,2 + U3,3 𝜃w (( )( ) ( ) )] + Pmo U3,2 − U3,1 −1 + U3,1 − U3,2 + U3,3 𝛼𝜃w
𝜃(x, Fo ) = −
∞ ∑
) 1 [ Fo V3,n −U3,4 (x+2) (( 2U3,4 x e e + e2U3,4 U V n = 0 3,4 3,n ( ) (( ) 𝜃w Qdo + V3,n + P2f e2U3,4 − eU3,4 x (eU3,4 x − 1)𝜃b ( ) ) + e2U3,4 x + e2U3,4 𝜃w ) (( )( + Pmo e2U3,4 − eU3,4 x eU3,4 x − 1 ( ) ))] − e2U3,4 x + e2U3,4 𝛼𝜃w , +
(62)
13
Vol.:(0123456789)
The word “Temperature” should be omitted in the figure captions 5 to 13. The corrected figure captions are given below: Fig. 5 Epidermis layer: Effect of Foq = 0.00696379 and Fot = 0 on skin temperature with the first kind non-Fourier boundary condition Fig. 6 Dermis layer: Effect of Foq = 0.0140766 and Fot = 0 on skin temperature with the first kind non-Fourier boundary condition Fig. 7 Subcutaneous layer: Effect of Foq = 0.007916
Data Loading...
