Correction: Enescu, D. Heat Transfer Mechanisms and Contributions of Wearable Thermoelectrics to Personal Thermal Management. Energies 2024, 17, 285

Text Correction

The temperature t noted in the original publication [1] has been changed to the absolute temperature T, in some equations and the accompanying text, for consistency with other equations in the paper.

1.

$${\dot{q}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}}=k·\left(t_{\mathrm{s}\mathrm{k}\mathrm{i}\mathrm{n}}-t_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{e}}\right)$$

(7)

has been replaced with

$${\dot{q}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}}=k·\left(T_{\mathrm{s}\mathrm{k}\mathrm{i}\mathrm{n}}-T_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{e}}\right)$$

(7)

where k is the thermal conductivity in W/(m$·$K), which is influenced by the thermal properties of both the skin and the solid surface and by the contact solid surface area, $T_{\mathrm{s}\mathrm{k}\mathrm{i}\mathrm{n}}$ is the temperature of the skin body, and $T_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{e}}$ is the temperature of the solid surface.

2.

$${\dot{q}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{v}}=h_{\mathrm{c}}·\left({\overline{t}}_{\mathrm{s}\mathrm{k}\mathrm{i}\mathrm{n}}-t_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{r} \mathrm{a}\mathrm{i}\mathrm{r}}\right)$$

(8)

has been replaced with

$${\dot{q}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{v}}=h_{\mathrm{c}}·\left({\overline{T}}_{\mathrm{s}\mathrm{k}\mathrm{i}\mathrm{n}}-T_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{r} \mathrm{a}\mathrm{i}\mathrm{r}}\right)$$

(8)

where $T_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{r} \mathrm{a}\mathrm{i}\mathrm{r}}$ is the temperature of the surrounding air, and $h_{\mathrm{c}}$ is the convective heat transfer coefficient, which, according to (8), is the ratio of the convective thermal flux density to the temperature difference from the skin to the surrounding air [29].

3. Equations (9)–(12): t has been changed to T for uniform notation, with “characteristic length” in Equation (10) formatted in Cambria Math.

$${\dot{q}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{v}}=f_{\mathrm{c}\mathrm{l}\mathrm{o}}{·h}_{\mathrm{c}}·\left({\overline{t}}_{\mathrm{c}\mathrm{l}\mathrm{o}}-t_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{r} \mathrm{a}\mathrm{i}\mathrm{r}}\right)$$

(9)

has been replaced with

$${\dot{q}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{v}}=f_{\mathrm{c}\mathrm{l}\mathrm{o}}{·h}_{\mathrm{c}}·\left({\overline{T}}_{\mathrm{c}\mathrm{l}\mathrm{o}}-T_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{r} \mathrm{a}\mathrm{i}\mathrm{r}}\right)$$

(9)

The sentence “and ${\overline{t}}_{\mathrm{c}\mathrm{l}\mathrm{o}}$ is the mean surface temperature of the clothed body” has been replaced with “and ${\overline{T}}_{\mathrm{c}\mathrm{l}\mathrm{o}}$ is the mean surface temperature of the clothed body”.

and

$$\mathrm{G}\mathrm{r}={\displaystyle \frac{g·\beta ·\left(t_{\mathrm{s}\mathrm{k}\mathrm{i}\mathrm{n}}-t_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{r} \mathrm{a}\mathrm{i}\mathrm{r}}\right)·l^3}{{\nu }^2}}$$

(10)

has been replaced with

$$\mathrm{G}\mathrm{r}={\displaystyle \frac{g·\beta ·\left(T_{\mathrm{s}\mathrm{k}\mathrm{i}\mathrm{n}}-T_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{r} \mathrm{a}\mathrm{i}\mathrm{r}}\right)·l^3}{{\nu }^2}}$$

(10)

where g = 9.81 m/s² is the gravitational acceleration; $\beta ={\displaystyle \frac{1}{T}}$ is the thermal expansion coefficient of the air; $l$ is a characteristic length, identified with body height; and $\nu$ is the kinematic viscosity of the air.

The paragraph “In the case of a stationary, unclothed individual, with a temperature difference ${∆t=\overline{t}}_{\mathrm{s}\mathrm{k}\mathrm{i}\mathrm{n}}-t_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{r} \mathrm{a}\mathrm{i}\mathrm{r}}\approx 8÷10 \mathrm{℃}$, the flow is laminar up to a height of 1 m and turbulent at 1.5 m [32]” has been replaced with “In the case of a stationary, unclothed individual, with a temperature difference ${∆T=\overline{T}}_{\mathrm{s}\mathrm{k}\mathrm{i}\mathrm{n}}-T_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{r} \mathrm{a}\mathrm{i}\mathrm{r}}\approx 8÷10 \mathrm{℃}$, the flow is laminar up to a height of 1 m and turbulent at 1.5 m [32]”.

Moreover,

$$h_{\mathrm{c}}=a_{\mathrm{n}}·{\left({\overline{t}}_{\mathrm{c}\mathrm{l}\mathrm{o}}-t_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{r} \mathrm{a}\mathrm{i}\mathrm{r}}\right)}^{b_{\mathrm{n}}}$$

(11)

has been replaced with

$$h_{\mathrm{c}}=a_{\mathrm{n}}·{\left({\overline{T}}_{\mathrm{c}\mathrm{l}\mathrm{o}}-T_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{r} \mathrm{a}\mathrm{i}\mathrm{r}}\right)}^{b_{\mathrm{n}}}$$

(11)

and

$$h_{\mathrm{c}}=a_{\mathrm{n}}·{\left({\overline{t}}_{\mathrm{s}\mathrm{k}\mathrm{i}\mathrm{n}}-t_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{r} \mathrm{a}\mathrm{i}\mathrm{r}}\right)}^{b_{\mathrm{n}}}$$

(12)

has been replaced with

$$h_{\mathrm{c}}=a_{\mathrm{n}}·{\left({\overline{T}}_{\mathrm{s}\mathrm{k}\mathrm{i}\mathrm{n}}-T_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{r} \mathrm{a}\mathrm{i}\mathrm{r}}\right)}^{b_{\mathrm{n}}}$$

(12)

4.

$$\mathrm{R}\mathrm{e}={\displaystyle \frac{w·\mathcal{l}}{a}}$$

(13)

where $\mathcal{l}$ is a characteristic length associated with the body and $a$ is the thermal diffusivity

has been replaced with

$$\mathrm{R}\mathrm{e}={\displaystyle \frac{w·l}{\nu }}$$

(13)

where $l$ is a characteristic length associated with the body and $\nu$ is the kinematic viscosity of the air.

Equations (20)–(25): the temperature t has been changed to the absolute temperature T in the equations and accompanying text to ensure uniform notation.

$${\dot{q}}_{\mathrm{r}\mathrm{a}\mathrm{d}}={f_{\mathrm{c}\mathrm{l}\mathrm{o}}·h}_{\mathrm{r}}·\left({\overline{t}}_{\mathrm{c}\mathrm{l}\mathrm{o}}-{\overline{t}}_{\mathrm{r}}\right)$$

(20)

has been replaced with

$${\dot{q}}_{\mathrm{r}\mathrm{a}\mathrm{d}}={f_{\mathrm{c}\mathrm{l}\mathrm{o}}·h}_{\mathrm{r}}·\left({\overline{T}}_{\mathrm{c}\mathrm{l}\mathrm{o}}-{\overline{T}}_{\mathrm{r}}\right)$$

(20)

where $h_{\mathrm{r}}$ is the radiative heat transfer coefficient and ${\overline{T}}_{\mathrm{r}}$ is the mean radiant temperature perceived by the body.

$$h_{\mathrm{r}}=4·\epsilon ·\sigma ·\left({\displaystyle \frac{A_{\mathrm{r}}}{A_{\mathrm{D}}}}\right)·{\left[273.2+{\displaystyle \frac{{\overline{t}}_{\mathrm{c}\mathrm{l}}+{\overline{t}}_{\mathrm{r}}}{2}}\right]}^3$$

(21)

has been replaced with:

$$h_{\mathrm{r}}=4·\epsilon ·\sigma ·\left({\displaystyle \frac{A_{\mathrm{r}}}{A_{\mathrm{D}}}}\right)·{\left[273.2+{\displaystyle \frac{{\overline{T}}_{\mathrm{c}\mathrm{l}}+{\overline{T}}_{\mathrm{r}}}{2}}\right]}^3$$

(21)

where $\epsilon$ is the average body surface emissivity, $\sigma =5.67·{10}^{-8} \mathrm{W}/({\mathrm{m}}^2·\mathrm{K})$ is the Stefan-Boltzmann constant, $A_{\mathrm{r}}$ is the effective radiation area of the human body, $A_{\mathrm{D}}$ is the DuBois body surface area [65], and ${\overline{T}}_{\mathrm{r}}$ is the mean radiant temperature for each segment.

$${\dot{q}}_{\mathrm{s}}=h_{\mathrm{c}}·f_{\mathrm{c}\mathrm{l}\mathrm{o}}·\left({\overline{t}}_{\mathrm{c}\mathrm{l}\mathrm{o}}-t_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{r} \mathrm{a}\mathrm{i}\mathrm{r}}\right)+h_{\mathrm{r}}·f_{\mathrm{c}\mathrm{l}\mathrm{o}}·\left({\overline{t}}_{\mathrm{c}\mathrm{l}\mathrm{o}}-{\overline{t}}_{\mathrm{r}}\right)$$

(22)

has been replaced with:

$${\dot{q}}_{\mathrm{s}}=h_{\mathrm{c}}·f_{\mathrm{c}\mathrm{l}\mathrm{o}}·\left({\overline{T}}_{\mathrm{c}\mathrm{l}\mathrm{o}}-T_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{r} \mathrm{a}\mathrm{i}\mathrm{r}}\right)+h_{\mathrm{r}}·f_{\mathrm{c}\mathrm{l}\mathrm{o}}·\left({\overline{T}}_{\mathrm{c}\mathrm{l}\mathrm{o}}-{\overline{T}}_{\mathrm{r}}\right)$$

(22)

and

$${\dot{q}}_{\mathrm{s}}=h_{\mathrm{c}}·\left({\overline{t}}_{\mathrm{s}\mathrm{k}\mathrm{i}\mathrm{n}}-t_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{r} \mathrm{a}\mathrm{i}\mathrm{r}}\right)+h_{\mathrm{r}}·\left({\overline{t}}_{\mathrm{s}\mathrm{k}\mathrm{i}\mathrm{n}}-{\overline{t}}_{\mathrm{r}}\right)$$

(23)

has been replaced with:

$${\dot{q}}_{\mathrm{s}}=h_{\mathrm{c}}·\left({\overline{T}}_{\mathrm{s}\mathrm{k}\mathrm{i}\mathrm{n}}-T_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{r} \mathrm{a}\mathrm{i}\mathrm{r}}\right)+h_{\mathrm{r}}·\left({\overline{T}}_{\mathrm{s}\mathrm{k}\mathrm{i}\mathrm{n}}-{\overline{T}}_{\mathrm{r}}\right)$$

(23)

and

$$h_{\mathrm{c}}=4.088+6.592·w^{1.715}\mathrm{a}\mathrm{t}0.01{\displaystyle \frac{\mathrm{m}}{\mathrm{s}}}\le w\le 0.73{\displaystyle \frac{\mathrm{m}}{\mathrm{s}}}\mathrm{a}\mathrm{n}\mathrm{d}t=20℃$$

(24)

$$h_{\mathrm{c}}=2.874+7.427·w^{1.345}\mathrm{a}\mathrm{t}0.005{\displaystyle \frac{\mathrm{m}}{\mathrm{s}}}\le w\le 0.71{\displaystyle \frac{\mathrm{m}}{\mathrm{s}}}\mathrm{a}\mathrm{n}\mathrm{d}t=26℃$$

(25)

have been replaced with:

$$h_{\mathrm{c}}=4.088+6.592·w^{1.715}\mathrm{a}\mathrm{t}0.01{\displaystyle \frac{\mathrm{m}}{\mathrm{s}}}\le w\le 0.73{\displaystyle \frac{\mathrm{m}}{s}}\mathrm{a}\mathrm{n}\mathrm{d}T=20℃$$

(24)

$$h_{\mathrm{c}}=2.874+7.427·w^{1.345}\mathrm{a}\mathrm{t}0.005{\displaystyle \frac{\mathrm{m}}{\mathrm{s}}}\le w\le 0.71{\displaystyle \frac{\mathrm{m}}{\mathrm{s}}}\mathrm{a}\mathrm{n}\mathrm{d}T=26℃$$

(25)

5.

The first part of the sentence after Equation (29) has been changed as follows:

“where ${\displaystyle \frac{{\mathrm{d}}^2{T}_{\mathrm{i}}}{\mathrm{d}{x}^2}}$ represents the second spatial derivative of temperature $T_{\mathrm{i}}$ with respect to the spatial coordinate $x$ within the specific layer $\mathrm{i}$ (such as fat, dermis and epidermis)”.

The author states that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.