Invariant Analysis Research Articles

Invariance analysis and some new exact analytic solutions of the time-fractional coupled Drinfeld-Sokolov-Wilson equations

Invariance analysis and some new exact analytic solutions of the time-fractional coupled Drinfeld-Sokolov-Wilson equations

Examination of the latent structure of the Ruminative Thoughts Style Questionnaire across countries, gender, and over time

The present work aimed to extend the evidence of the structure validity of the Ruminative Thought Style Questionnaire (RTSQ) 15-item version testing: (1) the structure of two competing models (i.e., four-factor correlated model vs a second-order factor model); (2) the measurement invariance of the final model across four countries (U.S., Spain, Argentina, and the Netherlands) and gender groups (male and female); and (3) the invariance across three assessment waves in a subsample of Spanish youths. Participants were college students (mean age = 20.87, SD = 4.47) from the U.S. (n = 1875; 67.1% of females), Spain (T1, n = 732, 63.9% females; T2, n = 370, 71.6% females: T3, n = 307, 60.6% females), Argentina (n = 368, 65.6% females) and the Netherlands (n = 295, 74.8% females). Confirmatory Factor Analyses supported both correlated factors and second-order factor structure in the whole sample. Due to similar fit indices being observed for both models, and considering the theoretical and practical advantages, we kept the second-order model to examine its invariance across groups and time. Measurement invariance analyses showed that the second-order model was invariant across countries, gender, and over time. Comparisons of the total mean score and the subfacet mean scores (i.e., Repetitive Thoughts, Counterfactual Thoughts, Problem-focused Thoughts, and Anticipatory Thoughts) reveled only small differences across country and gender groups. The present work extends the structural validity evidence of the RTSQ, and provides the first evidence concerning its longitudinal stability across time.

A mixed-methods cross-cultural study of teacher care and teacher-student rapport in Iranian and Polish University students’ engagement in pursuing academic goals in an L2 context

A convergent parallel mixed-methods approach was used to explore teacher care, teacher-student rapport, and engagement in pursuing academic goals in a foreign language (L2) context, as perceived by 223 Iranian and 208 Polish L2 students. Quantitative data were obtained through three scales, the cross-cultural validity and factor structure of which were ensured through testing measurement invariance and confirmatory factor analysis, respectively. The structural equation modeling results obtained through running Mplus approved that care and rapport predicted Iranian and Polish students' engagement in pursuing academic goals in an L2 context. For checking the equality of the structural path coefficients, the Omnibus Wald test was employed. Group differences in factor means were tested, showing that Iranian and Polish students differed significantly regarding their levels of engagement. Qualitative data, obtained through running interviews with 30 Iranian and 24 Polish students, selected from the initial sample, approved the predictive links of care and rapport with Iranian and Polish students' engagement in pursuing academic goals in an L2 context. However, the students' qualitative reports revealed how their perceived country's cultural and instructional contexts influenced their engagement, empirically supporting the supposition that engagement is the by-product of the dynamic interaction between the individual factors and the instructional context, necessitating the examination of the role of sociocultural values and home culture in accomplishing this educational objective.

Implicit theories in driving: Scale development, validation, and predictive role on violations and driving self-efficacy

Implicit theories focus on how ability may be perceived by individuals. There are two main beliefs: entity beliefs (i.e., driving ability is a gift) and incremental beliefs (i.e., driving ability is improvable through effort). Implicit theories have been studied in various domains (e.g., education, sport), but never in driving, even though they could improve the knowledge of drivers’ psychological characteristics. The first objective of the present study was to develop and validate a questionnaire measuring implicit theories in driving. The second objective was to assess the predictive role of implicit theories on violations and driving self-efficacy, and the moderating role of gender. In study 1, confirmatory factor analysis, analyses of gender invariance, and concurrent validity were assessed to validate the questionnaire named Implicit Theories in Driving Questionnaire (ITDQ). In study 2, the predictive role of implicit theories on violations and driving self-efficacy was evaluated using multiple regression analyses. Moderation analyses evaluated the moderating role of gender on the relationships between implicit theories and violations, along with driving self-efficacy. The ITDQ showed acceptable psychometric properties. The results highlighted that entity beliefs positively predicted aggressive violations and negatively predicted driving self-efficacy. Conversely, incremental beliefs negatively predicted ordinary violations and positively predicted driving self-efficacy. The ITDQ is a valid scale now available for assessing implicit theories in driving, that have been shown to influence self-reported driving behavior. Future research on implicit theories in driving may help to better understand the psychological characteristics of at-risk drivers and improve driver’s training, to reduce the number of road accidents.

Task and Ego Orientation in Sport Questionnaire (TEOSQ): Psychometric Properties in Its Digital Version.

The Task and Ego Orientation in Sport Questionnaire’s (TEOSQ’s) psychometric properties have been explored in previous studies but never in its digital version, which facilitates data collection. The objective of this study was to analyze the psychometric properties of the online TEOSQ by MenPas 1.0. The sample was composed of 2320 users (58.4% women; 41.6% men), between 18 and 65 years old (M = 25.27, SD = 7.39). The methods used were Confirmatory Factor Analysis (CFA) and invariance analysis from the original 13-item model. The CFA was corrected for all samples (CFI = 0.92–0.94, TLI = 0.93–0.95, RMSEA = 0.07, SRMR = 0.06; df = 64; Bollen-Stine Bootstrap p = 0.02–0.07): general sample (χ2 = 720.72, χ2/df = 11.26), women (χ2 = 496.85, χ2/df = 7.76), men (χ2 = 321.67, χ2/df = 5.03), individual sports (χ2 = 525.26, χ2/df = 8.21), and team sports (χ2 = 306.01, χ2/df = 4.78). The results also indicate optimal adjustments for invariance: convergent, discriminant and composite reliability validity. The study evidence demonstrates the adequate psychometric properties of the digital version. To conclude, considering the results obtained, the model shows a good psychometric fit for the sample in its online format. The principal limitations were computer failures, as well as that the large part of the sample were users between 20 and 25 years old, so the heterogeneity should be improved. The practical implications of this study could improve the efficacy of data collection in sports motivation using the online TEOSQ.

Psychometric Properties of the Interpersonal Needs Questionnaire-15 in Spanish Adolescents

BackgroundThwarted Belongingness (TB) and Perceived Burdensomeness (PB) are considered risk factors of suicide behavior in the Interpersonal Theory of Suicide and constitute the main factors of the Interpersonal Needs Questionnaire—INQ.AimsThe present study analyzes the internal consistency, construct validity, and invariance across sex and age of the INQ-15, which comprises two subscales, in a sample of Spanish community adolescents.MethodsParticipants were 1,536 adolescents from 12 to 19 years old. The INQ-15, the total number of non-suicidal self-injuries (NSSI), the Hopelessness Scale, and the Purpose in Life Test-Adolescents (PIL-A) were used.ResultsThe INQ-15 showed good internal consistency for TB ( = 0.88) and PB ( = 0.78) subscales and construct and concurrent/discriminant validity in the whole sample. Both the PB and TB subscales showed a good fit { = 6.448, p = 0.694, CFI = 1.000, RMSEA = 0.000 [90% CI (0.000, 0.022)] and = 248.973, p = 0.000, CFI = 0.922, RMSEA = 0.073 [90% CI (0.065, 0.082)]}, respectively. Regarding the invariance analyses, we found (1) non-invariance in the PB subscale across sex groups and metric, scalar, and stric invariance across age groups, and (2) that it was not possible to perform the invariance analysis for the TB subscale across both sex and age because the fit was not adequate for both boys and 12–15 years old groups. Positive and significant relationships were found between the INQ-15 subscales and hopelessness and NSSI frequency, and negative and significant correlations with meaning in life.ConclusionsThe INQ-15 is a valid instrument for assessing TB and PB in Spanish adolescents. Future studies should analyze the invariance of this instrument in adolescents across sex and age.

Research on Massive Image Retrieval Method of Mobile Terminal Based on Weighted Aggregation Depth Feature

Image self-coupling and feature interference lead to poor retrieval performance in massive image retrieval of mobile terminals. This paper proposes a massive image retrieval method of mobile terminals based on weighted aggregation depth features. The pixel big data detection model of massive images of mobile terminals is constructed, the collected pixel information of massive images of mobile terminals is restructured, the edge contour feature parameter set of massive images of mobile terminals is extracted, the feature fusion processing of massive images of mobile terminals is carried out in gradient pixel space by means of feature reconstruction and gray moment invariant feature analysis, the depth feature detection of massive images of mobile terminals is realized by using weighted aggregation method, the gradient value of pixels of massive images of each mobile terminal is calculated, and the optimized retrieval of massive images of mobile terminals is realized according to the fusion result of gradient weighted information. Simulation results show that this method has better feature clustering, stronger image detection and recognition, and anti-interference ability and improves the precision and recall of image retrieval.

Measurement invariance of the Perceived Stress Scale-10 across gender in Korean university students

This study examined the factorial structure and gender invariance of the 10-item Perceived Stress Scale (PSS-10) among 582 Korean university students. Data were collected from 582 university students enrolled in a four-year university in the central region of Korea. Confirmatory factor analysis was used to test four distinct factor models identified in previous studies. Analyses of multigroup invariance were also conducted to determine whether the PSS-10 items’ factorial structure exhibited gender invariance. Results indicated that the PSS-10 was the most adequately represented by a bifactor structure, composed of one general factor reflecting overlap across all 10 items and two separate factors of perceived stress and perceived coping. Multigroup invariance tests indicated that PSS-10 items were interpreted similarly between men and women and that responses could be meaningfully compared across gender. The study confirms that the PSS-10 is a theoretically sound instrument that is feasible for both research and university settings.

Non-spherical Harish-Chandra Fourier Transforms on Real Reductive Groups

The Harish-Chandra Fourier transform, $$f\mapsto \mathcal {H}f,$$ is a linear topological algebra isomorphism of the spherical (Schwartz) convolution algebra $$\mathcal {C}^{p}(G//K)$$ (where K is a maximal compact subgroup of any arbitrarily chosen group G in the Harish-Chandra class and $$0<p\le 2$$ ) onto the (Schwartz) multiplication algebra $$\bar{\mathcal {Z}}({\mathfrak {F}}^{\epsilon })$$ (of $$\mathfrak {w}$$ -invariant members of $$\mathcal {Z}({\mathfrak {F}}^{\epsilon }),$$ with $$\epsilon =(2/p)-1$$ ). This is the well-known Trombi–Varadarajan theorem for spherical functions on the real reductive group, G. Even though $$\mathcal {C}^{p}(G//K)$$ is a closed subalgebra of $$\mathcal {C}^{p}(G),$$ a similar theorem has not however been successfully proved for the full Schwartz convolution algebra $$\mathcal {C}^{p}(G)$$ except; for $$\mathcal {C}^{p}(G/K)$$ (whose method is essentially that of Trombi–Varadarajan, as shown by M. Eguchi); for few specific examples of groups (notably $$G=SL(2,\mathbb {R})$$ ) and; for some notable values of p (with restrictions on G and/or on members of $$\;\mathcal {C}^{p}(G)$$ ). In this paper, we construct an appropriate image of the Harish-Chandra Fourier transform for the full Schwartz convolution algebra $$\mathcal {C}^{p}(G),$$ without any restriction on any of G, p and members of $$\;\mathcal {C}^{p}(G).$$ Our proof, that the Harish-Chandra Fourier transform, $$f\mapsto \mathcal {H}f,$$ is a linear topological algebra isomorphism on $$\mathcal {C}^{p}(G),$$ equally shows that its image $$\mathcal {C}^{p}(\widehat{G})$$ can be nicely decomposed, that the full invariant harmonic analysis is available and implies that the definition of the Harish-Chandra Fourier transform may now be extended to include all p-tempered distributions on G and to the zero-Schwartz spaces.

A Validation of the Multidimensional Workaholism Scale

This study aimed to examine the reliability and validity of the Multidimensional Workaholism Scale (MWS) among Korean employees. Evidence in terms of the reliability of internal consistency, measurement invariance tests, discriminant validity, and criterion-related validity support that the MWS is a valid and reliable measure of workaholism for Korean employees. First, the MWS showed good internal consistency coefficients among full-time Korean employees (N = 358). Second, measurement invariance analyses showed that a four-factor model (behavioral, cognitive, motivational, and emotional) also holds in the Korean sample, and factor loadings were equivalent between the Korean and the U.S. (N = 407) samples. Third, correlation analysis and a series of confirmatory factor analysis results provide discriminant validity evidence between the MWS and work engagement. Finally, a portion of the Korean sample (N= 228) provided data for criterion validity. Correlation analysis of the data showed that the MWS revealed the expected relationships with emotional exhaustion, work interfering with family, family interfering with work, and work hours. For the variables of job satisfaction, life satisfaction, and physical symptoms, the expected relationships with the MWS appear when work engagement was controlled for. Overall, this study suggested that the MWS is a valid and reliable measure of workaholism for Korean employees.

Orientation relationship of quasicrystalline approximate phase η-Al5(Mn,Cr) in AA5083 aluminium alloy

ABSTRACT A quasicrystalline approximate monoclinic phase η-Al5(Mn,Cr) with a plate-like or rod-like morphology in AA5083 aluminium alloy was investigated using transmission electron microscopy. Several types of orientation relationships (ORs) between the η-Al5(Mn,Cr) phase and the α-Al matrix were observed and these ORs could be correlated with a rotation operation around the axis with an angle that is an integer times 18.5°. These multiple ORs were interpreted by utilizing an invariant deformation element model – a simplified version of three-dimensional invariant line strain analysis.

Exploratory Study: Measurement Invariance of the Therapeutic Recreation Job Responsibility Scale

The aim of this study was to assess the measurement invariance of the Therapeutic Recreation Job Responsibility Scale (TR-JRS). It measures four dimensions of recreational practitioners’ duties with 27 items: 1) administration, 2) therapy, 3) face-to-face leadership and 4) professional development. Measurement invariance assesses the ability of a single instrument, the TR-JRS, to measure duties among recreational practitioners working in different environments, members of separate professional associations, and to promote different aspects of their work. The sample comprised 417 members of the Canadian Therapeutic Recreation Association and the F´ederation qu´eb´ecoise du loisir en institution. The initial factorial measurement analysis showed metric invariance as the model of choice, though its overall fit was outside the usual acceptable criteria. A factor analysis with a target rotation resulted in a short scale of 14 items with an appropriate Root Mean Square Error of Approximation and Comparative Fit Index. It included the same four dimensions as the 27-item version. A measurement invariance analysis was also run on the short-form scale. The number of factors, position of items within factors, and factor loadings were equal in both groups. The absolute values of the Root Mean Square Error of Approximation and the Comparative Fit Index associated with the short form were over the acceptable cutoff points by a small margin. As expected, items means differed between the two groups and reliability coefficients were high. Such findings reflect this study’s exploratory nature. Hence, further studies on item development could improve fit indices in favor of a stronger invariance status for this scale, which measures an important construct in therapeutic recreation.

Resurgence analysis of quantum invariants of Seifert fibered homology spheres

For a Seifert fibered homology sphere X $X$ , we show that the q $q$ -series invariant Z ̂ 0 ( X ; q ) $\hat{\operatorname{Z}}_0(X;q)$ , introduced by Gukov–Pei–Putrov–Vafa, is a resummation of the Ohtsuki series Z 0 ( X ) $\operatorname{Z}_0(X)$ . We show that for every even k ∈ N $k \in \mathbb {N}$ there exists a full asymptotic expansion of Z ̂ 0 ( X ; q ) $ \hat{\operatorname{Z}}_0(X;q)$ for q $q$ tending to e 2 π i / k $e^{2\pi i/k}$ , and in particular that the limit Z ̂ 0 ( X ; e 2 π i / k ) $\hat{\operatorname{Z}}_0(X;e^{2\pi i/k})$ exists and is equal to the Witten–Reshetikhin–Turaev quantum invariant τ k ( X ) $\tau _k(X)$ . We show that the poles of the Borel transform of Z 0 ( X ) $\operatorname{Z}_0(X)$ coincide with the classical complex Chern–Simons values, which we further show classifies the corresponding components of the moduli space of flat SL ( 2 , C ) $\rm {SL}(2,\mathbb {C})$ -connections.

Psychometric properties of a scale of attitudes toward musical genres linked to social groups in Peru

The present research seeks to develop a scale that can measure attitudes toward different musical expressions representative of different social groups, such as the Andean and Afro-Peruvian groups. The participants were 312 individuals between 18 and 83 years of age ( M = 32.42, SD = 14.97), and the majority had no professional musical knowledge. First, Exploratory Factor Analysis was performed using the Unweighted Least Squares as the extraction method and using Oblimin rotation for the Andean and Afro-Peruvian musical genres. An identical factorial structure with two dimensions was found for both musical genres, obtaining optimal reliability according to Cronbach’s alpha coefficients. This similarity was verified by performing an invariance analysis, obtaining evidence that the proposed scale can be used regardless of the musical genre. Furthermore, correlation analyses were performed between the dimensions of the attitudes scale and variables such as stereotypes (toward the Andean and Afro-Peruvian social groups) and conservative ideology; the results provided evidence of discriminant validity. Finally, comparisons were made between musicians and non-musicians using the same dimensions of the attitude scale as evidence for criterion validity. The results are discussed based on scale’s optimal psychometric functioning, as well as its implications at the level of intergroup dynamics.

(Re-)Designing a measure of student\u2019s attitudes toward science: a longitudinal psychometric approach

BackgroundCapturing measures of students’ attitudes toward science has long been a focus within the field of science education. The resulting interest has led to the development of many instruments over the years. There is considerable disagreement about how attitudes should be measured, and especially whether students’ attitudes toward science can or should be measured unidimensionally, or whether separate attitude dimensions or subscales should be considered. When it is agreed upon that the attitudes toward science construct should be measured along separate subscales, there is no consensus about which subscales should be used.MethodsA streamlined version of the modified Attitudes Towards Science Inventory (mATSI), a widely used science measurement instrument, was validated for a more diverse sample as compared to the original study (Weinburgh and Steele in Journal of Women and Minorities in Science and Engineering 6:87–94, 2000). The analytical approach used factor analyses and longitudinal measurement invariance. The study used a sample of 2016 self-reported responses from 6 and 7th grade students. The factor analysis elucidated the factor structure of students’ attitudes toward science, and some modifications were made in accordance with the results. Measurement invariance analysis was used to confirm the stability of the measure.ResultsOur results support that the subscales, anxiety toward science and value and enjoyment of science, are two factors and stable over time.ConclusionsOur results suggest that our proposed modified factor structure for students’ attitudes toward science is reliable, valid, and appropriate for use in longitudinal studies. This study and its resulting streamlined mATSI survey could be of value to those interested in studying student engagement and measuring middle-school students' attitudes toward science.

Using Multi-Group Invariance Analysis in Exploring Cross-Cultural Differences in Mathematics Anxiety: A Comparison of Australia and Russia

Mathematics anxiety is well known and studied concept. Most of the studies have been focused on the effects of mathematical anxiety on students’ academic achievement, especially from the viewpoint of analysing large national and international data sets. We aim to bring a different perspective to the existing research on mathematics anxiety and resilience by considering the measurement equivalence across cultures, so they can be compared fairly. We used Multi Group Invariance analysis with this purpose. Our findings suggested that full metric and partial scalar model invariance were confirmed which advise that the mathematics anxiety scale can be compared across two countries. We also ran multiple regression using Fisher’s Z to understand the reciprocal relationship among the variables across two samples. Preliminary results revealed that the perceived mathematics anxiety and perceived mathematics ability predict the measured mathematics anxiety equally well for both Australia and Russia.

Measuring Electronic Health Literacy: Development, Validation, and Test of Measurement Invariance of a Revised German Version of the eHealth Literacy Scale.

BackgroundThe World Wide Web has become an essential source of health information. Nevertheless, the amount and quality of information provided may lead to information overload. Therefore, people need certain skills to search for, identify, and evaluate information from the internet. In the context of health information, these competencies are summarized as the construct of eHealth literacy. Previous research has highlighted the relevance of eHealth literacy in terms of health-related outcomes. However, the existing instrument assessing eHealth literacy in the German language reveals methodological limitations regarding test development and validation. The development and validation of a revised scale for this important construct is highly relevant.ObjectiveThe objective of this study was the development and validation of a revised German eHealth literacy scale. In particular, this study aimed to focus on high methodological and psychometric standards to provide a valid and reliable instrument for measuring eHealth literacy in the German language.MethodsTwo internationally validated instruments were merged to cover a wide scope of the construct of eHealth literacy and create a revised eHealth literacy scale. Translation into the German language followed scientific guidelines and recommendations to ensure content validity. Data from German-speaking people (n=470) were collected in a convenience sample from October to November 2020. Validation was performed by factor analyses. Further, correlations were performed to examine convergent, discriminant, and criterion validity. Additionally, analyses of measurement invariance of gender, age, and educational level were conducted.ResultsAnalyses revealed a 2-factorial model of eHealth literacy. By item-reduction, the 2 factors information seeking and information appraisal were measured with 8 items reaching acceptable-to-good model fits (comparative fit index [CFI]: 0.942, Tucker Lewis index [TLI]: 0.915, root mean square error of approximation [RMSEA]: 0.127, and standardized root mean square residual [SRMR]: 0.055). Convergent validity was comprehensively confirmed by significant correlations of information seeking and information appraisal with health literacy, internet confidence, and internet anxiety. Discriminant and criterion validity were examined by correlation analyses with various scales and could partly be confirmed. Scalar level of measurement invariance for gender (CFI: 0.932, TLI: 0.923, RMSEA: 0.122, and SRMR: 0.068) and educational level (CFI: 0.937, TLI: 0.934, RMSEA: 0.112, and SRMR: 0.063) were confirmed. Measurement invariance of age was rejected.ConclusionsFollowing scientific guidelines for translation and test validation, we developed a revised German eHealth Literacy Scale (GR-eHEALS). Our factor analyses confirmed an acceptable-to-good model fit. Construct validation in terms of convergent, discriminant, and criterion validity could mainly be confirmed. Our findings provide evidence for measurement invariance of the instrument regarding gender and educational level. The newly revised GR-eHEALS questionnaire represents a valid instrument to measure the important health-related construct eHealth literacy.

Psychometric Properties of Self-Determination Inventory: Student Report Among Chinese Students With and Without Intellectual and Developmental Disabilities.

This study explores the psychometric properties of Self-Determination Inventory: Student Report (SDI:SR) in students with intellectual and developmental disabilities (IDD) and without disabilities in China. The paper-and-pencil version of SDI:SR Chinese Translation (SDI:SR Chinese) was used to explore self-determination across students with IDD (n = 245) and students without disabilities (n = 315) from 16 schools across six cities in China. We examined the factor structure of the measure, conducted analysis of measurement invariance, and compared the latent means across students with IDD and without disabilities. Findings suggest that the data fit a one-factor model better than a three-factor model. We found greater variability in self-determination among students with IDD than students without disabilities. However, the two groups did not differ in latent means.

Latent transition analysis with random intercepts (RI-LTA).

This article demonstrates that the regular LTA model is unnecessarily restrictive and that an alternative model is readily available that typically fits the data much better, leads to better estimates of the transition probabilities, and extracts new information from the data. By allowing random intercept variation in the model, between-subject variation is separated from the within-subject latent class transitions over time allowing a clearer interpretation of the data. Analysis of two examples from the literature demonstrates the advantages of random intercept LTA. Model variations include Mover-Stayer analysis, measurement invariance analysis, and analysis with covariates. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Turbulent flow and heat transfer characteristics of an impinging jet over a heated wall-mounted cube placed in a cross-flow

The present study aims at a large-eddy simulation of a turbulent flow and heat transfer of an impinging jet over a heated cube placed in a cross-flow. A baseline simulation of turbulent heat transfer over the heated cube without the jet-impingement has also been conducted. Based on previous research as well as the present study of the baseline case, it has been observed that heat transfer at the top and side surfaces of the cube is relatively poor; thus, these surfaces may become the principal targets for the jet-impingement cooling strategy. The Navier–Stokes and energy equations are solved using a finite-volume technique that incorporates a shear enhanced Smagorinsky model to account for the effect of unresolved scales. The cross-flow Reynolds number and Prandtl number are chosen to be 3500 (based on the cube size and the average streamwise velocity) and 0.71, respectively, for both the baseline and jet-impinged configurations. The primary goal of this research is to investigate the variations in turbulent structures caused by jet-impingement and their relationship to heat transfer characteristics on cube surfaces. By conducting an invariant analysis of the Reynolds stress tensor, we discuss the aspect of Reynolds stress anisotropy. Furthermore, the dominant components of Reynolds stresses are determined using the Lumley triangle at the top surface and in the wake region of the cube, which is expected to be mainly influenced by jet-impingement. The preliminary investigation shows that the heat transfer at the top surface of the cube is substantially improved due to the impingement of the jet. In addition, a significant improvement in heat transfer is also found at the side surfaces despite having a marginal loss at the rear surface of the cube.