A PHP Error was encountered

Severity: Warning

Message: fopen(/var/lib/php/sessions/ci_session55o4b522keekpgiipef6att4lq9soh0g): Failed to open stream: No space left on device

Filename: drivers/Session_files_driver.php

Line Number: 177

Backtrace:

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: session_start(): Failed to read session data: user (path: /var/lib/php/sessions)

Filename: Session/Session.php

Line Number: 137

Backtrace:

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Undefined array key "choices"

Filename: controllers/Detail.php

Line Number: 249

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 249
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Trying to access array offset on value of type null

Filename: controllers/Detail.php

Line Number: 249

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 249
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Trying to access array offset on value of type null

Filename: controllers/Detail.php

Line Number: 249

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 249
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Trying to access array offset on value of type null

Filename: controllers/Detail.php

Line Number: 249

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 249
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: strpos(): Passing null to parameter #1 ($haystack) of type string is deprecated

Filename: models/Detail_model.php

Line Number: 71

Backtrace:

File: /var/www/html/application/models/Detail_model.php
Line: 71
Function: strpos

File: /var/www/html/application/controllers/Detail.php
Line: 252
Function: insertAPISummary

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: str_replace(): Passing null to parameter #3 ($subject) of type array|string is deprecated

Filename: helpers/my_audit_helper.php

Line Number: 8919

Backtrace:

File: /var/www/html/application/helpers/my_audit_helper.php
Line: 8919
Function: str_replace

File: /var/www/html/application/controllers/Detail.php
Line: 255
Function: formatAIDetailSummary

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Undefined array key "choices"

Filename: controllers/Detail.php

Line Number: 256

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 256
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Trying to access array offset on value of type null

Filename: controllers/Detail.php

Line Number: 256

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 256
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Trying to access array offset on value of type null

Filename: controllers/Detail.php

Line Number: 256

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 256
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Undefined array key "usage"

Filename: controllers/Detail.php

Line Number: 257

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 257
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Trying to access array offset on value of type null

Filename: controllers/Detail.php

Line Number: 257

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 257
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Undefined array key "usage"

Filename: controllers/Detail.php

Line Number: 258

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 258
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Trying to access array offset on value of type null

Filename: controllers/Detail.php

Line Number: 258

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 258
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Undefined array key "usage"

Filename: controllers/Detail.php

Line Number: 259

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 259
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Trying to access array offset on value of type null

Filename: controllers/Detail.php

Line Number: 259

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 259
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Undefined array key "usage"

Filename: controllers/Detail.php

Line Number: 260

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 260
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Trying to access array offset on value of type null

Filename: controllers/Detail.php

Line Number: 260

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 260
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Trying to access array offset on value of type null

Filename: controllers/Detail.php

Line Number: 260

Backtrace:

File: /var/www/html/application/controllers/Detail.php
Line: 260
Function: _error_handler

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_get_contents(https://...@gmail.com&api_key=61f08fa0b96a73de8c900d749fcb997acc09): Failed to open stream: HTTP request failed! HTTP/1.1 429 Too Many Requests

Filename: helpers/my_audit_helper.php

Line Number: 143

Backtrace:

File: /var/www/html/application/helpers/my_audit_helper.php
Line: 143
Function: file_get_contents

File: /var/www/html/application/helpers/my_audit_helper.php
Line: 209
Function: simplexml_load_file_from_url

File: /var/www/html/application/helpers/my_audit_helper.php
Line: 3098
Function: getPubMedXML

File: /var/www/html/application/controllers/Detail.php
Line: 574
Function: pubMedSearch_Global

File: /var/www/html/application/controllers/Detail.php
Line: 488
Function: pubMedGetRelatedKeyword

File: /var/www/html/index.php
Line: 316
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: Attempt to read property "Count" on bool

Filename: helpers/my_audit_helper.php

Line Number: 3100

Backtrace:

File: /var/www/html/application/helpers/my_audit_helper.php
Line: 3100
Function: _error_handler

File: /var/www/html/application/controllers/Detail.php
Line: 574
Function: pubMedSearch_Global

File: /var/www/html/application/controllers/Detail.php
Line: 488
Function: pubMedGetRelatedKeyword

File: /var/www/html/index.php
Line: 316
Function: require_once

Numerical estimation of temperature response with step heating of a multi-layer skin under the generalized boundary condition. | LitMetric

Numerical estimation of temperature response with step heating of a multi-layer skin under the generalized boundary condition.

J Therm Biol

Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi - 221005, India. Electronic address:

Published: August 2022

AI Article Synopsis

Article Abstract

In this article, we discussed a one-dimensional bioheat transfer mathematical model that describes the process of temperature distribution in tissue for the multi-layer skin under the step heating generalized boundary condition. The finite difference scheme is used to estimate the temperature profile along with time and distance. We discussed the stability of the numerical scheme and also validated the accuracy of the numerical code by comparing the present results with the previous reference results. To remove heat from the skin is considered by the surface temperature, heat flux, and ambient temperature to be zero with the help of the unit step like function. Then, we observed that the skin temperature in the second kind boundary condition was slowly decreasing over time as compared to the first and third kind boundary conditions. The temperature or heat flux at the skin surface is assumed to be high then there is negligible effect of the blood perfusion rate on the temperature response over a short time period and the effect of blood perfusion rate is visible when the time duration is long. Effect of blood perfusion rate, heating and after removal of heating, water diffusion, and generalized boundary condition for the analysis of the behavior of temperature response in multi-layer skin are discussed in detail and the results obtained are presented graphically.

Download full-text PDF

Source
http://dx.doi.org/10.1016/j.jtherbio.2022.103278DOI Listing

Publication Analysis

Top Keywords

boundary condition
16
temperature response
12
multi-layer skin
12
generalized boundary
12
blood perfusion
12
perfusion rate
12
temperature
9
step heating
8
temperature heat
8
heat flux
8

Similar Publications

Want AI Summaries of new PubMed Abstracts delivered to your In-box?

Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!